%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT026+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:27 AM UTC 2025
% Result : Theorem 0.78s 0.97s
% Output : Proof 0.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT026+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:54:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.78/0.97 % SZS status Theorem
% 0.78/0.97 % SZS output start Proof
% 0.78/0.97 tff(r2_nattra_1_type, type, (
% 0.78/0.97 r2_nattra_1: ( $i * $i * $i * $i ) > $o)).
% 0.78/0.97 tff(k11_isocat_2_type, type, (
% 0.78/0.97 k11_isocat_2: ( $i * $i * $i * $i ) > $i)).
% 0.78/0.97 tff(tptp_fun_E_4_type, type, (
% 0.78/0.97 tptp_fun_E_4: $i)).
% 0.78/0.97 tff(tptp_fun_C_2_type, type, (
% 0.78/0.97 tptp_fun_C_2: $i)).
% 0.78/0.97 tff(tptp_fun_B_1_type, type, (
% 0.78/0.97 tptp_fun_B_1: $i)).
% 0.78/0.97 tff(tptp_fun_A_0_type, type, (
% 0.78/0.97 tptp_fun_A_0: $i)).
% 0.78/0.97 tff(tptp_fun_D_3_type, type, (
% 0.78/0.97 tptp_fun_D_3: $i)).
% 0.78/0.97 tff(k2_isocat_1_type, type, (
% 0.78/0.97 k2_isocat_1: ( $i * $i * $i * $i * $i ) > $i)).
% 0.78/0.97 tff(k16_cat_2_type, type, (
% 0.78/0.97 k16_cat_2: ( $i * $i ) > $i)).
% 0.78/0.97 tff(k11_cat_2_type, type, (
% 0.78/0.97 k11_cat_2: ( $i * $i ) > $i)).
% 0.78/0.97 tff(k8_isocat_2_type, type, (
% 0.78/0.97 k8_isocat_2: ( $i * $i ) > $i)).
% 0.78/0.97 tff(m2_cat_1_type, type, (
% 0.78/0.97 m2_cat_1: ( $i * $i * $i ) > $o)).
% 0.78/0.97 tff(v2_cat_1_type, type, (
% 0.78/0.97 v2_cat_1: $i > $o)).
% 0.78/0.97 tff(l1_cat_1_type, type, (
% 0.78/0.97 l1_cat_1: $i > $o)).
% 0.78/0.97 tff(k12_isocat_2_type, type, (
% 0.78/0.97 k12_isocat_2: ( $i * $i * $i * $i ) > $i)).
% 0.78/0.97 tff(k17_cat_2_type, type, (
% 0.78/0.97 k17_cat_2: ( $i * $i ) > $i)).
% 0.78/0.97 tff(k9_isocat_2_type, type, (
% 0.78/0.97 k9_isocat_2: ( $i * $i ) > $i)).
% 0.78/0.97 tff(1,plain,
% 0.78/0.97 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(2,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[1])).
% 0.78/0.97 tff(3,plain,
% 0.78/0.97 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(4,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[3])).
% 0.78/0.97 tff(5,plain,
% 0.78/0.97 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(6,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[5])).
% 0.78/0.97 tff(7,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(transitivity,[status(thm)],[6, 4])).
% 0.78/0.97 tff(8,plain,
% 0.78/0.97 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(9,plain,
% 0.78/0.97 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[8])).
% 0.78/0.97 tff(10,plain,
% 0.78/0.97 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(11,plain,
% 0.78/0.97 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) <=> ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) <=> ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))))),
% 0.78/0.97 inference(bind,[status(th)],[])).
% 0.78/0.97 tff(12,plain,
% 0.78/0.97 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(quant_intro,[status(thm)],[11])).
% 0.78/0.97 tff(13,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_isocat_2')).
% 0.78/0.97 tff(14,plain,
% 0.78/0.97 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.78/0.97 tff(15,plain,
% 0.78/0.97 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.78/0.97 tff(16,plain,(
% 0.78/0.97 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(skolemize,[status(sab)],[15])).
% 0.78/0.97 tff(17,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.78/0.97 tff(18,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.78/0.97 tff(19,plain,
% 0.78/0.97 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.97 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.78/0.97 tff(20,plain,
% 0.78/0.97 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(21,plain,
% 0.78/0.97 (((v2_cat_1(B!1) & l1_cat_1(B!1)) & (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(22,plain,
% 0.78/0.97 (((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))) <=> (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(23,plain,
% 0.78/0.97 ((~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))) <=> (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))),
% 0.78/0.97 inference(rewrite,[status(thm)],[])).
% 0.78/0.97 tff(24,plain,
% 0.78/0.97 ((m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))) <=> (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[23])).
% 0.78/0.97 tff(25,plain,
% 0.78/0.97 (((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))) <=> ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[24])).
% 0.78/0.97 tff(26,plain,
% 0.78/0.97 (((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))) <=> (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(transitivity,[status(thm)],[25, 22])).
% 0.78/0.97 tff(27,plain,
% 0.78/0.97 (((v2_cat_1(B!1) & l1_cat_1(B!1)) & ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))))) <=> ((v2_cat_1(B!1) & l1_cat_1(B!1)) & (v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))))),
% 0.78/0.97 inference(monotonicity,[status(thm)],[26])).
% 0.78/0.97 tff(28,plain,
% 0.78/0.97 (((v2_cat_1(B!1) & l1_cat_1(B!1)) & ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.97 inference(transitivity,[status(thm)],[27, 21])).
% 0.78/0.98 tff(29,plain,
% 0.78/0.98 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & ((v2_cat_1(B!1) & l1_cat_1(B!1)) & ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))))) <=> ((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[28])).
% 0.78/0.98 tff(30,plain,
% 0.78/0.98 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & ((v2_cat_1(B!1) & l1_cat_1(B!1)) & ((v2_cat_1(C!2) & l1_cat_1(C!2)) & (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))))),
% 0.78/0.98 inference(transitivity,[status(thm)],[29, 20])).
% 0.78/0.98 tff(31,plain,
% 0.78/0.98 ((~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E))))))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(32,plain,
% 0.78/0.98 ((~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => ![E: $i] : (m2_cat_1(E, A, k11_cat_2(B, C)) => (r2_nattra_1(A, k11_cat_2(B, C), D, E) => (r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E)))))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E))))))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(33,axiom,(~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => ![E: $i] : (m2_cat_1(E, A, k11_cat_2(B, C)) => (r2_nattra_1(A, k11_cat_2(B, C), D, E) => (r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_isocat_2')).
% 0.78/0.98 tff(34,plain,
% 0.78/0.98 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)))))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.78/0.98 tff(35,plain,
% 0.78/0.98 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)))))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[34, 31])).
% 0.78/0.98 tff(36,plain,
% 0.78/0.98 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)))))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.78/0.98 tff(37,plain,
% 0.78/0.98 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | ![E: $i] : ((r2_nattra_1(A, B, k11_isocat_2(A, B, C, D), k11_isocat_2(A, B, C, E)) & r2_nattra_1(A, C, k12_isocat_2(A, B, C, D), k12_isocat_2(A, B, C, E))) | (~m2_cat_1(E, A, k11_cat_2(B, C))) | (~r2_nattra_1(A, k11_cat_2(B, C), D, E)))))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[36, 31])).
% 0.78/0.98 tff(38,plain,
% 0.78/0.98 (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & v2_cat_1(C!2) & l1_cat_1(C!2) & m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2)) & (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.78/0.98 tff(39,plain,
% 0.78/0.98 (l1_cat_1(A!0)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(40,plain,
% 0.78/0.98 (v2_cat_1(A!0)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(41,plain,
% 0.78/0.98 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(42,plain,
% 0.78/0.98 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(43,plain,
% 0.78/0.98 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k11_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), B, D, k8_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.78/0.98 tff(44,plain,
% 0.78/0.98 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[43, 40, 39, 19])).
% 0.78/0.98 tff(45,plain,
% 0.78/0.98 (l1_cat_1(B!1)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(46,plain,
% 0.78/0.98 (v2_cat_1(B!1)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(47,plain,
% 0.78/0.98 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(48,plain,
% 0.78/0.98 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C))))))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(49,plain,
% 0.78/0.98 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k11_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), B, D, k8_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.78/0.98 tff(50,plain,
% 0.78/0.98 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[49, 46, 45, 44])).
% 0.78/0.98 tff(51,plain,
% 0.78/0.98 (l1_cat_1(C!2)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(52,plain,
% 0.78/0.98 (v2_cat_1(C!2)),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(53,plain,
% 0.78/0.98 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(54,plain,
% 0.78/0.98 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2)))))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(55,plain,
% 0.78/0.98 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k11_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), B!1, D, k8_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.78/0.98 tff(56,plain,
% 0.78/0.98 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[55, 52, 51, 50])).
% 0.78/0.98 tff(57,plain,
% 0.78/0.98 (~((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)))),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(58,plain,
% 0.78/0.98 (m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))),
% 0.78/0.98 inference(or_elim,[status(thm)],[57])).
% 0.78/0.98 tff(59,plain,
% 0.78/0.98 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(60,plain,
% 0.78/0.98 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(61,plain,
% 0.78/0.98 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.78/0.98 tff(62,plain,
% 0.78/0.98 (k11_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[61, 58, 56])).
% 0.78/0.98 tff(63,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, E!4)),
% 0.78/0.98 inference(symmetry,[status(thm)],[62])).
% 0.78/0.98 tff(64,plain,
% 0.78/0.98 (^[A: $i, B: $i] : refl(((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(65,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[64])).
% 0.78/0.98 tff(66,plain,
% 0.78/0.98 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(67,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[66])).
% 0.78/0.98 tff(68,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(69,plain,
% 0.78/0.98 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(70,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[69])).
% 0.78/0.98 tff(71,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k8_isocat_2(A, B) = k16_cat_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_isocat_2')).
% 0.78/0.98 tff(72,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.78/0.98 tff(73,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.78/0.98 tff(74,plain,(
% 0.78/0.98 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k8_isocat_2(A, B) = k16_cat_2(A, B)))),
% 0.78/0.98 inference(skolemize,[status(sab)],[73])).
% 0.78/0.98 tff(75,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.78/0.98 tff(76,plain,
% 0.78/0.98 (![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.78/0.98 tff(77,plain,
% 0.78/0.98 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(78,plain,
% 0.78/0.98 (((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(79,plain,
% 0.78/0.98 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2))))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[78])).
% 0.78/0.98 tff(80,plain,
% 0.78/0.98 (((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)))),
% 0.78/0.98 inference(transitivity,[status(thm)],[79, 77])).
% 0.78/0.98 tff(81,plain,
% 0.78/0.98 ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(82,plain,
% 0.78/0.98 ((~![A: $i, B: $i] : ((k8_isocat_2(A, B) = k16_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.78/0.98 tff(83,plain,
% 0.78/0.98 (k8_isocat_2(B!1, C!2) = k16_cat_2(B!1, C!2)),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[82, 46, 45, 52, 51, 76])).
% 0.78/0.98 tff(84,plain,
% 0.78/0.98 (k16_cat_2(B!1, C!2) = k8_isocat_2(B!1, C!2)),
% 0.78/0.98 inference(symmetry,[status(thm)],[83])).
% 0.78/0.98 tff(85,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k8_isocat_2(B!1, C!2))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[84])).
% 0.78/0.98 tff(86,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, E!4)),
% 0.78/0.98 inference(transitivity,[status(thm)],[85, 63])).
% 0.78/0.98 tff(87,plain,
% 0.78/0.98 (m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))),
% 0.78/0.98 inference(and_elim,[status(thm)],[38])).
% 0.78/0.98 tff(88,plain,
% 0.78/0.98 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(rewrite,[status(thm)],[])).
% 0.78/0.98 tff(89,plain,
% 0.78/0.98 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))))),
% 0.78/0.98 inference(quant_inst,[status(thm)],[])).
% 0.78/0.98 tff(90,plain,
% 0.78/0.98 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, k8_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2)))),
% 0.78/0.98 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.78/0.98 tff(91,plain,
% 0.78/0.98 (k11_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))),
% 0.78/0.98 inference(unit_resolution,[status(thm)],[90, 87, 56])).
% 0.78/0.98 tff(92,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, D!3)),
% 0.78/0.98 inference(symmetry,[status(thm)],[91])).
% 0.78/0.98 tff(93,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k8_isocat_2(B!1, C!2))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[84])).
% 0.78/0.98 tff(94,plain,
% 0.78/0.98 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)) = k11_isocat_2(A!0, B!1, C!2, D!3)),
% 0.78/0.98 inference(transitivity,[status(thm)],[93, 92])).
% 0.78/0.98 tff(95,plain,
% 0.78/0.98 (r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))) <=> r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))),
% 0.78/0.98 inference(monotonicity,[status(thm)],[94, 86])).
% 0.78/0.98 tff(96,plain,
% 0.78/0.98 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(97,plain,
% 0.78/0.98 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[96])).
% 0.78/0.98 tff(98,plain,
% 0.78/0.98 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))),
% 0.78/0.98 inference(bind,[status(th)],[])).
% 0.78/0.98 tff(99,plain,
% 0.78/0.98 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.98 inference(quant_intro,[status(thm)],[98])).
% 0.78/0.98 tff(100,plain,
% 0.78/0.98 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.98 inference(transitivity,[status(thm)],[99, 97])).
% 0.78/0.98 tff(101,plain,
% 0.78/0.98 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(102,plain,
% 0.78/0.99 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[101])).
% 0.78/0.99 tff(103,plain,
% 0.78/0.99 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(104,plain,
% 0.78/0.99 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(quant_intro(proof_bind(^[G: $i] : trans(monotonicity(rewrite(((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))) <=> ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))), ((m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (m2_cat_1(G, B, C) => ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))), rewrite((m2_cat_1(G, B, C) => ((~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))), ((m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), (![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))) <=> ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))), ((m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> (m2_cat_1(F, B, C) => ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), rewrite((m2_cat_1(F, B, C) => ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))) <=> ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))), ((m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), (![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))) <=> ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), ((m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> (m2_cat_1(E, A, B) => ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), rewrite((m2_cat_1(E, A, B) => ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))) <=> ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))), ((m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))) <=> ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), ((m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> (m2_cat_1(D, A, B) => ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), rewrite((m2_cat_1(D, A, B) => ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))), ((m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))) <=> ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C))))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(105,plain,
% 0.78/0.99 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)))))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[104])).
% 0.78/0.99 tff(106,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, B) => ![E: $i] : (m2_cat_1(E, A, B) => ![F: $i] : (m2_cat_1(F, B, C) => ![G: $i] : (m2_cat_1(G, B, C) => ((r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G)) => r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t27_isocat_1')).
% 0.78/0.99 tff(107,plain,
% 0.78/0.99 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.78/0.99 tff(108,plain,
% 0.78/0.99 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.78/0.99 tff(109,plain,(
% 0.78/0.99 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~(r2_nattra_1(A, B, D, E) & r2_nattra_1(B, C, F, G))) | (~m2_cat_1(G, B, C)))))))))),
% 0.78/0.99 inference(skolemize,[status(sab)],[108])).
% 0.78/0.99 tff(110,plain,
% 0.78/0.99 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.78/0.99 tff(111,plain,
% 0.78/0.99 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.78/0.99 tff(112,plain,
% 0.78/0.99 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(113,plain,
% 0.78/0.99 (((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G))))))))) <=> ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(114,plain,
% 0.78/0.99 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))))),
% 0.78/0.99 inference(monotonicity,[status(thm)],[113])).
% 0.78/0.99 tff(115,plain,
% 0.78/0.99 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E)))))))))),
% 0.78/0.99 inference(transitivity,[status(thm)],[114, 112])).
% 0.78/0.99 tff(116,plain,
% 0.78/0.99 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A!0, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))),
% 0.78/0.99 inference(quant_inst,[status(thm)],[])).
% 0.78/0.99 tff(117,plain,
% 0.78/0.99 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, B)) | ![E: $i] : ((~m2_cat_1(E, A, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : (r2_nattra_1(A, C, k2_isocat_1(A, B, C, D, F), k2_isocat_1(A, B, C, E, G)) | (~m2_cat_1(G, B, C)) | (~r2_nattra_1(A, B, D, E)) | (~r2_nattra_1(B, C, F, G)))))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.78/0.99 tff(118,plain,
% 0.78/0.99 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))),
% 0.78/0.99 inference(unit_resolution,[status(thm)],[117, 40, 39, 111])).
% 0.78/0.99 tff(119,plain,
% 0.78/0.99 (^[A: $i, B: $i] : refl(((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(120,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[119])).
% 0.78/0.99 tff(121,plain,
% 0.78/0.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), rewrite((v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))) <=> (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(122,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[121])).
% 0.78/0.99 tff(123,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.78/0.99 inference(rewrite,[status(thm)],[])).
% 0.78/0.99 tff(124,plain,
% 0.78/0.99 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))))),
% 0.78/0.99 inference(bind,[status(th)],[])).
% 0.78/0.99 tff(125,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.78/0.99 inference(quant_intro,[status(thm)],[124])).
% 0.78/0.99 tff(126,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_cat_2')).
% 0.78/0.99 tff(127,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.78/0.99 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.78/0.99 tff(128,plain,
% 0.78/0.99 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.78/1.00 tff(129,plain,(
% 0.78/1.00 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.78/1.00 inference(skolemize,[status(sab)],[128])).
% 0.78/1.00 tff(130,plain,
% 0.78/1.00 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.78/1.00 tff(131,plain,
% 0.78/1.00 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.78/1.00 tff(132,plain,
% 0.78/1.00 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(133,plain,
% 0.78/1.00 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(134,plain,
% 0.78/1.00 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.78/1.00 tff(135,plain,
% 0.78/1.00 (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[134, 46, 45, 52, 51, 131])).
% 0.78/1.00 tff(136,plain,
% 0.78/1.00 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.78/1.00 inference(tautology,[status(thm)],[])).
% 0.78/1.00 tff(137,plain,
% 0.78/1.00 (l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.78/1.00 tff(138,plain,
% 0.78/1.00 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.78/1.00 inference(tautology,[status(thm)],[])).
% 0.78/1.00 tff(139,plain,
% 0.78/1.00 (v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.78/1.00 tff(140,plain,
% 0.78/1.00 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(141,plain,
% 0.78/1.00 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(142,plain,
% 0.78/1.00 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, B)) | ![E: $i] : ((~m2_cat_1(E, A!0, B)) | ![F: $i] : ((~m2_cat_1(F, B, C)) | ![G: $i] : ((~m2_cat_1(G, B, C)) | (~r2_nattra_1(B, C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, B, C, D, F), k2_isocat_1(A!0, B, C, E, G)) | (~r2_nattra_1(A!0, B, D, E))))))))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.78/1.00 tff(143,plain,
% 0.78/1.00 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[142, 139, 137, 118])).
% 0.78/1.00 tff(144,plain,
% 0.78/1.00 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(145,plain,
% 0.78/1.00 (((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))) <=> ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(146,plain,
% 0.78/1.00 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))))),
% 0.78/1.00 inference(monotonicity,[status(thm)],[145])).
% 0.78/1.00 tff(147,plain,
% 0.78/1.00 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.78/1.00 inference(transitivity,[status(thm)],[146, 144])).
% 0.78/1.00 tff(148,plain,
% 0.78/1.00 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.78/1.00 inference(quant_inst,[status(thm)],[])).
% 0.78/1.00 tff(149,plain,
% 0.78/1.00 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.00 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.78/1.00 tff(150,plain,
% 0.78/1.00 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.00 inference(unit_resolution,[status(thm)],[149, 46, 45, 143])).
% 0.78/1.00 tff(151,plain,
% 0.78/1.00 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(152,plain,
% 0.78/1.00 (((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) <=> ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.00 inference(rewrite,[status(thm)],[])).
% 0.78/1.00 tff(153,plain,
% 0.78/1.00 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[152])).
% 0.78/1.01 tff(154,plain,
% 0.78/1.01 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.01 inference(transitivity,[status(thm)],[153, 151])).
% 0.78/1.01 tff(155,plain,
% 0.78/1.01 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(156,plain,
% 0.78/1.01 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.78/1.01 tff(157,plain,
% 0.78/1.01 (![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[156, 87, 150])).
% 0.78/1.01 tff(158,plain,
% 0.78/1.01 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(159,plain,
% 0.78/1.01 (((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) <=> ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(160,plain,
% 0.78/1.01 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))))),
% 0.78/1.01 inference(monotonicity,[status(thm)],[159])).
% 0.78/1.01 tff(161,plain,
% 0.78/1.01 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.78/1.01 inference(transitivity,[status(thm)],[160, 158])).
% 0.78/1.01 tff(162,plain,
% 0.78/1.01 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))))),
% 0.78/1.01 inference(quant_inst,[status(thm)],[])).
% 0.78/1.01 tff(163,plain,
% 0.78/1.01 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.78/1.01 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.78/1.01 tff(164,plain,
% 0.78/1.01 (![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.78/1.01 inference(unit_resolution,[status(thm)],[163, 58, 157])).
% 0.78/1.01 tff(165,plain,
% 0.78/1.01 (^[A: $i, B: $i] : refl((m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(166,plain,
% 0.78/1.01 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[165])).
% 0.78/1.01 tff(167,plain,
% 0.78/1.01 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.78/1.01 inference(bind,[status(th)],[])).
% 0.78/1.01 tff(168,plain,
% 0.78/1.01 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.78/1.01 inference(quant_intro,[status(thm)],[167])).
% 0.78/1.01 tff(169,plain,
% 0.78/1.01 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.78/1.01 inference(rewrite,[status(thm)],[])).
% 0.78/1.01 tff(170,plain,
% 0.78/1.01 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))))),
% 0.85/1.01 inference(bind,[status(th)],[])).
% 0.85/1.01 tff(171,plain,
% 0.85/1.01 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.01 inference(quant_intro,[status(thm)],[170])).
% 0.85/1.01 tff(172,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k16_cat_2')).
% 0.85/1.01 tff(173,plain,
% 0.85/1.01 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.85/1.01 tff(174,plain,
% 0.85/1.01 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.85/1.01 tff(175,plain,(
% 0.85/1.01 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.01 inference(skolemize,[status(sab)],[174])).
% 0.85/1.01 tff(176,plain,
% 0.85/1.01 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.85/1.01 tff(177,plain,
% 0.85/1.01 (![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.85/1.01 tff(178,plain,
% 0.85/1.01 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(179,plain,
% 0.85/1.01 ((m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(180,plain,
% 0.85/1.01 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.01 inference(monotonicity,[status(thm)],[179])).
% 0.85/1.01 tff(181,plain,
% 0.85/1.01 (((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.01 inference(transitivity,[status(thm)],[180, 178])).
% 0.85/1.01 tff(182,plain,
% 0.85/1.01 ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(183,plain,
% 0.85/1.01 ((~![A: $i, B: $i] : (m2_cat_1(k16_cat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/1.01 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.85/1.01 tff(184,plain,
% 0.85/1.01 (m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/1.01 inference(unit_resolution,[status(thm)],[183, 46, 45, 52, 51, 177])).
% 0.85/1.01 tff(185,plain,
% 0.85/1.01 (((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | ((~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) <=> ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/1.01 inference(rewrite,[status(thm)],[])).
% 0.85/1.01 tff(186,plain,
% 0.85/1.01 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | ((~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))),
% 0.85/1.01 inference(quant_inst,[status(thm)],[])).
% 0.85/1.01 tff(187,plain,
% 0.85/1.01 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, F, G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G))))) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.85/1.02 tff(188,plain,
% 0.85/1.02 (![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[187, 184, 164])).
% 0.85/1.02 tff(189,plain,
% 0.85/1.02 (^[A: $i, B: $i] : refl((m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(190,plain,
% 0.85/1.02 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[189])).
% 0.85/1.02 tff(191,plain,
% 0.85/1.02 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(192,plain,
% 0.85/1.02 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[191])).
% 0.85/1.02 tff(193,plain,
% 0.85/1.02 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(194,plain,
% 0.85/1.02 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(195,plain,
% 0.85/1.02 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[194])).
% 0.85/1.02 tff(196,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_isocat_2')).
% 0.85/1.02 tff(197,plain,
% 0.85/1.02 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.85/1.02 tff(198,plain,
% 0.85/1.02 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[197, 193])).
% 0.85/1.02 tff(199,plain,(
% 0.85/1.02 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A))),
% 0.85/1.02 inference(skolemize,[status(sab)],[198])).
% 0.85/1.02 tff(200,plain,
% 0.85/1.02 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[199, 192])).
% 0.85/1.02 tff(201,plain,
% 0.85/1.02 (![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[200, 190])).
% 0.85/1.02 tff(202,plain,
% 0.85/1.02 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(203,plain,
% 0.85/1.02 ((m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(204,plain,
% 0.85/1.02 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[203])).
% 0.85/1.02 tff(205,plain,
% 0.85/1.02 (((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.02 inference(transitivity,[status(thm)],[204, 202])).
% 0.85/1.02 tff(206,plain,
% 0.85/1.02 ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(207,plain,
% 0.85/1.02 ((~![A: $i, B: $i] : (m2_cat_1(k8_isocat_2(A, B), k11_cat_2(A, B), A) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.85/1.02 tff(208,plain,
% 0.85/1.02 (m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[207, 46, 45, 52, 51, 201])).
% 0.85/1.02 tff(209,plain,
% 0.85/1.02 (^[A: $i, B: $i, C: $i, D: $i] : refl((r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(210,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[209])).
% 0.85/1.02 tff(211,plain,
% 0.85/1.02 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) <=> (~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) <=> (~(~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))))), rewrite((~(~((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))) <=> ((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) <=> ((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> (((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) | r2_nattra_1(A, B, C, C)))), rewrite((((~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B))) | r2_nattra_1(A, B, C, C)) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(212,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[211])).
% 0.85/1.02 tff(213,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(214,plain,
% 0.85/1.02 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & m2_cat_1(C, A, B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(215,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C)) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[214])).
% 0.85/1.02 tff(216,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & m2_cat_1(C, A, B)) & m2_cat_1(D, A, B)) => r2_nattra_1(A, B, C, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r2_nattra_1')).
% 0.85/1.02 tff(217,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.85/1.02 tff(218,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.85/1.02 tff(219,plain,(
% 0.85/1.02 ![A: $i, B: $i, C: $i, D: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C, A, B) & m2_cat_1(D, A, B))) | r2_nattra_1(A, B, C, C))),
% 0.85/1.02 inference(skolemize,[status(sab)],[218])).
% 0.85/1.02 tff(220,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.85/1.02 tff(221,plain,
% 0.85/1.02 (![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[220, 210])).
% 0.85/1.02 tff(222,plain,
% 0.85/1.02 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(223,plain,
% 0.85/1.02 ((r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))) <=> ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(224,plain,
% 0.85/1.02 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))))),
% 0.85/1.02 inference(monotonicity,[status(thm)],[223])).
% 0.85/1.02 tff(225,plain,
% 0.85/1.02 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.02 inference(transitivity,[status(thm)],[224, 222])).
% 0.85/1.02 tff(226,plain,
% 0.85/1.02 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(227,plain,
% 0.85/1.02 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k8_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.85/1.02 tff(228,plain,
% 0.85/1.02 (r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[227, 46, 45, 221, 139, 137, 208, 184])).
% 0.85/1.02 tff(229,plain,
% 0.85/1.02 (r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)),
% 0.85/1.02 inference(or_elim,[status(thm)],[57])).
% 0.85/1.02 tff(230,plain,
% 0.85/1.02 (((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))) <=> ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))),
% 0.85/1.02 inference(rewrite,[status(thm)],[])).
% 0.85/1.02 tff(231,plain,
% 0.85/1.02 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2))))),
% 0.85/1.02 inference(quant_inst,[status(thm)],[])).
% 0.85/1.02 tff(232,plain,
% 0.85/1.02 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k16_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), B!1)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), B!1, k16_cat_2(B!1, C!2), k16_cat_2(B!1, C!2))) | r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.85/1.02 tff(233,plain,
% 0.85/1.02 (r2_nattra_1(A!0, B!1, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, D!3, k16_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), B!1, E!4, k16_cat_2(B!1, C!2)))),
% 0.85/1.02 inference(unit_resolution,[status(thm)],[232, 229, 184, 228, 188])).
% 0.85/1.02 tff(234,plain,
% 0.85/1.02 (r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))),
% 0.85/1.02 inference(modus_ponens,[status(thm)],[233, 95])).
% 0.85/1.02 tff(235,plain,
% 0.85/1.02 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(236,plain,
% 0.85/1.02 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[235])).
% 0.85/1.02 tff(237,plain,
% 0.85/1.02 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(238,plain,
% 0.85/1.02 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[237])).
% 0.85/1.02 tff(239,plain,
% 0.85/1.02 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(240,plain,
% 0.85/1.02 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.02 inference(quant_intro,[status(thm)],[239])).
% 0.85/1.02 tff(241,plain,
% 0.85/1.02 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.02 inference(transitivity,[status(thm)],[240, 238])).
% 0.85/1.02 tff(242,plain,
% 0.85/1.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))), (((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))))),
% 0.85/1.02 inference(bind,[status(th)],[])).
% 0.85/1.02 tff(243,plain,
% 0.85/1.02 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[242])).
% 0.85/1.03 tff(244,plain,
% 0.85/1.03 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(245,plain,
% 0.85/1.03 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) <=> ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) <=> ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), rewrite(((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))), (((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(246,plain,
% 0.85/1.03 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[245])).
% 0.85/1.03 tff(247,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => ![D: $i] : (m2_cat_1(D, A, k11_cat_2(B, C)) => (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_isocat_2')).
% 0.85/1.03 tff(248,plain,
% 0.85/1.03 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.85/1.03 tff(249,plain,
% 0.85/1.03 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.85/1.03 tff(250,plain,(
% 0.85/1.03 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(skolemize,[status(sab)],[249])).
% 0.85/1.03 tff(251,plain,
% 0.85/1.03 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.85/1.03 tff(252,plain,
% 0.85/1.03 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))) | (~v2_cat_1(C)))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[251, 241])).
% 0.85/1.03 tff(253,plain,
% 0.85/1.03 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[252, 236])).
% 0.85/1.03 tff(254,plain,
% 0.85/1.03 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(255,plain,
% 0.85/1.03 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(256,plain,
% 0.85/1.03 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A, k11_cat_2(B, C))) | (k12_isocat_2(A, B, C, D) = k2_isocat_1(A, k11_cat_2(B, C), C, D, k9_isocat_2(B, C)))))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.85/1.03 tff(257,plain,
% 0.85/1.03 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[256, 40, 39, 253])).
% 0.85/1.03 tff(258,plain,
% 0.85/1.03 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(259,plain,
% 0.85/1.03 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C))))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(260,plain,
% 0.85/1.03 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B, C))) | (k12_isocat_2(A!0, B, C, D) = k2_isocat_1(A!0, k11_cat_2(B, C), C, D, k9_isocat_2(B, C))))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.85/1.03 tff(261,plain,
% 0.85/1.03 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[260, 46, 45, 257])).
% 0.85/1.03 tff(262,plain,
% 0.85/1.03 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(263,plain,
% 0.85/1.03 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2)))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(264,plain,
% 0.85/1.03 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C))) | (k12_isocat_2(A!0, B!1, C, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C), C, D, k9_isocat_2(B!1, C)))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.85/1.03 tff(265,plain,
% 0.85/1.03 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[264, 52, 51, 261])).
% 0.85/1.03 tff(266,plain,
% 0.85/1.03 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(267,plain,
% 0.85/1.03 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(268,plain,
% 0.85/1.03 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.85/1.03 tff(269,plain,
% 0.85/1.03 (k12_isocat_2(A!0, B!1, C!2, E!4) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[268, 58, 265])).
% 0.85/1.03 tff(270,plain,
% 0.85/1.03 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, E!4)),
% 0.85/1.03 inference(symmetry,[status(thm)],[269])).
% 0.85/1.03 tff(271,plain,
% 0.85/1.03 (^[A: $i, B: $i] : refl(((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(272,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[271])).
% 0.85/1.03 tff(273,plain,
% 0.85/1.03 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(274,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[273])).
% 0.85/1.03 tff(275,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(276,plain,
% 0.85/1.03 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))))),
% 0.85/1.03 inference(bind,[status(th)],[])).
% 0.85/1.03 tff(277,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.85/1.03 inference(quant_intro,[status(thm)],[276])).
% 0.85/1.03 tff(278,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (k9_isocat_2(A, B) = k17_cat_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k9_isocat_2')).
% 0.85/1.03 tff(279,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.85/1.03 tff(280,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.85/1.03 tff(281,plain,(
% 0.85/1.03 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (k9_isocat_2(A, B) = k17_cat_2(A, B)))),
% 0.85/1.03 inference(skolemize,[status(sab)],[280])).
% 0.85/1.03 tff(282,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.85/1.03 tff(283,plain,
% 0.85/1.03 (![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[282, 272])).
% 0.85/1.03 tff(284,plain,
% 0.85/1.03 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(285,plain,
% 0.85/1.03 (((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(286,plain,
% 0.85/1.03 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2))))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[285])).
% 0.85/1.03 tff(287,plain,
% 0.85/1.03 (((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)))),
% 0.85/1.03 inference(transitivity,[status(thm)],[286, 284])).
% 0.85/1.03 tff(288,plain,
% 0.85/1.03 ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(289,plain,
% 0.85/1.03 ((~![A: $i, B: $i] : ((k9_isocat_2(A, B) = k17_cat_2(A, B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.85/1.03 tff(290,plain,
% 0.85/1.03 (k9_isocat_2(B!1, C!2) = k17_cat_2(B!1, C!2)),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[289, 46, 45, 52, 51, 283])).
% 0.85/1.03 tff(291,plain,
% 0.85/1.03 (k17_cat_2(B!1, C!2) = k9_isocat_2(B!1, C!2)),
% 0.85/1.03 inference(symmetry,[status(thm)],[290])).
% 0.85/1.03 tff(292,plain,
% 0.85/1.03 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k9_isocat_2(B!1, C!2))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[291])).
% 0.85/1.03 tff(293,plain,
% 0.85/1.03 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, E!4)),
% 0.85/1.03 inference(transitivity,[status(thm)],[292, 270])).
% 0.85/1.03 tff(294,plain,
% 0.85/1.03 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(rewrite,[status(thm)],[])).
% 0.85/1.03 tff(295,plain,
% 0.85/1.03 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))))),
% 0.85/1.03 inference(quant_inst,[status(thm)],[])).
% 0.85/1.03 tff(296,plain,
% 0.85/1.03 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, k9_isocat_2(B!1, C!2))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2)))),
% 0.85/1.03 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.85/1.03 tff(297,plain,
% 0.85/1.03 (k12_isocat_2(A!0, B!1, C!2, D!3) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))),
% 0.85/1.03 inference(unit_resolution,[status(thm)],[296, 87, 265])).
% 0.85/1.03 tff(298,plain,
% 0.85/1.03 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, D!3)),
% 0.85/1.03 inference(symmetry,[status(thm)],[297])).
% 0.85/1.03 tff(299,plain,
% 0.85/1.03 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)) = k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k9_isocat_2(B!1, C!2))),
% 0.85/1.03 inference(monotonicity,[status(thm)],[291])).
% 0.85/1.04 tff(300,plain,
% 0.85/1.04 (k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)) = k12_isocat_2(A!0, B!1, C!2, D!3)),
% 0.85/1.04 inference(transitivity,[status(thm)],[299, 298])).
% 0.85/1.04 tff(301,plain,
% 0.85/1.04 (r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))) <=> r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[300, 293])).
% 0.85/1.04 tff(302,plain,
% 0.85/1.04 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(303,plain,
% 0.85/1.04 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E))))))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(304,plain,
% 0.85/1.04 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[303])).
% 0.85/1.04 tff(305,plain,
% 0.85/1.04 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[304, 302])).
% 0.85/1.04 tff(306,plain,
% 0.85/1.04 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(307,plain,
% 0.85/1.04 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C, F, G)) | r2_nattra_1(A!0, C, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C, E, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)))))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | ![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.85/1.04 tff(308,plain,
% 0.85/1.04 (![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[307, 52, 51, 143])).
% 0.85/1.04 tff(309,plain,
% 0.85/1.04 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(310,plain,
% 0.85/1.04 (((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) <=> ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(rewrite,[status(thm)],[])).
% 0.85/1.04 tff(311,plain,
% 0.85/1.04 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))))),
% 0.85/1.04 inference(monotonicity,[status(thm)],[310])).
% 0.85/1.04 tff(312,plain,
% 0.85/1.04 (((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) <=> ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(transitivity,[status(thm)],[311, 309])).
% 0.85/1.04 tff(313,plain,
% 0.85/1.04 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | ((~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))),
% 0.85/1.04 inference(quant_inst,[status(thm)],[])).
% 0.85/1.04 tff(314,plain,
% 0.85/1.04 ((~![D: $i] : ((~m2_cat_1(D, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D, E)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G))))))) | (~m2_cat_1(D!3, A!0, k11_cat_2(B!1, C!2))) | ![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))),
% 0.85/1.04 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.85/1.04 tff(315,plain,
% 0.85/1.04 (![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))),
% 0.85/1.04 inference(unit_resolution,[status(thm)],[314, 87, 308])).
% 0.85/1.04 tff(316,plain,
% 0.85/1.04 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(317,plain,
% 0.85/1.05 (((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) <=> ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(318,plain,
% 0.85/1.05 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[317])).
% 0.85/1.05 tff(319,plain,
% 0.85/1.05 (((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))) <=> ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.85/1.05 inference(transitivity,[status(thm)],[318, 316])).
% 0.85/1.05 tff(320,plain,
% 0.85/1.05 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | ((~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(321,plain,
% 0.85/1.05 ((~![E: $i] : ((~m2_cat_1(E, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E, G)))))) | (~m2_cat_1(E!4, A!0, k11_cat_2(B!1, C!2))) | ![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.85/1.05 tff(322,plain,
% 0.85/1.05 (![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[321, 58, 315])).
% 0.85/1.05 tff(323,plain,
% 0.85/1.05 (^[A: $i, B: $i] : refl((m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(324,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[323])).
% 0.85/1.05 tff(325,plain,
% 0.85/1.05 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(326,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[325])).
% 0.85/1.05 tff(327,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(328,plain,
% 0.85/1.05 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(329,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[328])).
% 0.85/1.05 tff(330,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k17_cat_2')).
% 0.85/1.05 tff(331,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.85/1.05 tff(332,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[331, 327])).
% 0.85/1.05 tff(333,plain,(
% 0.85/1.05 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(skolemize,[status(sab)],[332])).
% 0.85/1.05 tff(334,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[333, 326])).
% 0.85/1.05 tff(335,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[334, 324])).
% 0.85/1.05 tff(336,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(337,plain,
% 0.85/1.05 ((m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(338,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[337])).
% 0.85/1.05 tff(339,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(transitivity,[status(thm)],[338, 336])).
% 0.85/1.05 tff(340,plain,
% 0.85/1.05 ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(341,plain,
% 0.85/1.05 ((~![A: $i, B: $i] : (m2_cat_1(k17_cat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.85/1.05 tff(342,plain,
% 0.85/1.05 (m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[341, 46, 45, 52, 51, 335])).
% 0.85/1.05 tff(343,plain,
% 0.85/1.05 (((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | ((~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) <=> ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(344,plain,
% 0.85/1.05 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | ((~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(345,plain,
% 0.85/1.05 ((~![F: $i] : ((~m2_cat_1(F, k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, F, G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, F), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G))))) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | ![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.85/1.05 tff(346,plain,
% 0.85/1.05 (![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[345, 342, 322])).
% 0.85/1.05 tff(347,plain,
% 0.85/1.05 (^[A: $i, B: $i] : refl((m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(348,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) <=> ![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[347])).
% 0.85/1.05 tff(349,plain,
% 0.85/1.05 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(350,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[349])).
% 0.85/1.05 tff(351,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(352,plain,
% 0.85/1.05 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))))),
% 0.85/1.05 inference(bind,[status(th)],[])).
% 0.85/1.05 tff(353,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B)) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(quant_intro,[status(thm)],[352])).
% 0.85/1.05 tff(354,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k9_isocat_2')).
% 0.85/1.05 tff(355,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.85/1.05 tff(356,plain,
% 0.85/1.05 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[355, 351])).
% 0.85/1.05 tff(357,plain,(
% 0.85/1.05 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B))),
% 0.85/1.05 inference(skolemize,[status(sab)],[356])).
% 0.85/1.05 tff(358,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[357, 350])).
% 0.85/1.05 tff(359,plain,
% 0.85/1.05 (![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[358, 348])).
% 0.85/1.05 tff(360,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(361,plain,
% 0.85/1.05 ((m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(rewrite,[status(thm)],[])).
% 0.85/1.05 tff(362,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.05 inference(monotonicity,[status(thm)],[361])).
% 0.85/1.05 tff(363,plain,
% 0.85/1.05 (((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))) <=> ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.05 inference(transitivity,[status(thm)],[362, 360])).
% 0.85/1.05 tff(364,plain,
% 0.85/1.05 ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)))),
% 0.85/1.05 inference(quant_inst,[status(thm)],[])).
% 0.85/1.05 tff(365,plain,
% 0.85/1.05 ((~![A: $i, B: $i] : (m2_cat_1(k9_isocat_2(A, B), k11_cat_2(A, B), B) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.85/1.05 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.85/1.05 tff(366,plain,
% 0.85/1.05 (m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)),
% 0.85/1.05 inference(unit_resolution,[status(thm)],[365, 46, 45, 52, 51, 359])).
% 0.85/1.05 tff(367,plain,
% 0.85/1.05 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(368,plain,
% 0.85/1.06 ((r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(369,plain,
% 0.85/1.06 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[368])).
% 0.85/1.06 tff(370,plain,
% 0.85/1.06 (((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.06 inference(transitivity,[status(thm)],[369, 367])).
% 0.85/1.06 tff(371,plain,
% 0.85/1.06 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(372,plain,
% 0.85/1.06 ((~![A: $i, B: $i, C: $i, D: $i] : (r2_nattra_1(A, B, C, C) | (~m2_cat_1(D, A, B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~m2_cat_1(C, A, B)))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~m2_cat_1(k9_isocat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.85/1.06 tff(373,plain,
% 0.85/1.06 (r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[372, 52, 51, 221, 139, 137, 366, 342])).
% 0.85/1.06 tff(374,plain,
% 0.85/1.06 (((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))) <=> ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(375,plain,
% 0.85/1.06 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2))))),
% 0.85/1.06 inference(quant_inst,[status(thm)],[])).
% 0.85/1.06 tff(376,plain,
% 0.85/1.06 ((~![G: $i] : ((~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(G, k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), G)) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, G)))) | (~r2_nattra_1(A!0, k11_cat_2(B!1, C!2), D!3, E!4)) | (~m2_cat_1(k17_cat_2(B!1, C!2), k11_cat_2(B!1, C!2), C!2)) | (~r2_nattra_1(k11_cat_2(B!1, C!2), C!2, k17_cat_2(B!1, C!2), k17_cat_2(B!1, C!2))) | r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.85/1.06 tff(377,plain,
% 0.85/1.06 (r2_nattra_1(A!0, C!2, k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, D!3, k17_cat_2(B!1, C!2)), k2_isocat_1(A!0, k11_cat_2(B!1, C!2), C!2, E!4, k17_cat_2(B!1, C!2)))),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[376, 229, 342, 373, 346])).
% 0.85/1.06 tff(378,plain,
% 0.85/1.06 (r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[377, 301])).
% 0.85/1.06 tff(379,plain,
% 0.85/1.06 ((~(~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))))) <=> ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(380,plain,
% 0.85/1.06 ((r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))) <=> (~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))))),
% 0.85/1.06 inference(rewrite,[status(thm)],[])).
% 0.85/1.06 tff(381,plain,
% 0.85/1.06 ((~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))) <=> (~(~((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))))),
% 0.85/1.06 inference(monotonicity,[status(thm)],[380])).
% 0.85/1.06 tff(382,plain,
% 0.85/1.06 ((~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))) <=> ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4))))),
% 0.85/1.06 inference(transitivity,[status(thm)],[381, 379])).
% 0.85/1.06 tff(383,plain,
% 0.85/1.06 (~(r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4)) & r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))),
% 0.85/1.06 inference(or_elim,[status(thm)],[57])).
% 0.85/1.06 tff(384,plain,
% 0.85/1.06 ((~r2_nattra_1(A!0, B!1, k11_isocat_2(A!0, B!1, C!2, D!3), k11_isocat_2(A!0, B!1, C!2, E!4))) | (~r2_nattra_1(A!0, C!2, k12_isocat_2(A!0, B!1, C!2, D!3), k12_isocat_2(A!0, B!1, C!2, E!4)))),
% 0.85/1.06 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.85/1.06 tff(385,plain,
% 0.85/1.06 ($false),
% 0.85/1.06 inference(unit_resolution,[status(thm)],[384, 378, 234])).
% 0.85/1.06 % SZS output end Proof
% 0.85/1.07 % E exiting
%------------------------------------------------------------------------------