%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG226+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 04:58:47 AM UTC 2025
% Result : Theorem 1.13s 1.27s
% Output : Proof 1.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG226+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 10:57:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.13/1.27 % SZS status Theorem
% 1.13/1.27 % SZS output start Proof
% 1.13/1.27 tff(v1_xboole_0_type, type, (
% 1.13/1.27 v1_xboole_0: $i > $o)).
% 1.13/1.27 tff(k1_funct_1_type, type, (
% 1.13/1.27 k1_funct_1: ( $i * $i ) > $i)).
% 1.13/1.27 tff(tptp_fun_D_4_type, type, (
% 1.13/1.27 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 1.13/1.27 tff(k1_closure3_type, type, (
% 1.13/1.27 k1_closure3: ( $i * $i ) > $i)).
% 1.13/1.27 tff(tptp_fun_C_2_type, type, (
% 1.13/1.27 tptp_fun_C_2: $i)).
% 1.13/1.27 tff(tptp_fun_A_0_type, type, (
% 1.13/1.27 tptp_fun_A_0: $i)).
% 1.13/1.27 tff(k1_xboole_0_type, type, (
% 1.13/1.27 k1_xboole_0: $i)).
% 1.13/1.27 tff(m1_subset_1_type, type, (
% 1.13/1.27 m1_subset_1: ( $i * $i ) > $o)).
% 1.13/1.27 tff(r2_hidden_type, type, (
% 1.13/1.27 r2_hidden: ( $i * $i ) > $o)).
% 1.13/1.27 tff(a_2_0_closure3_type, type, (
% 1.13/1.27 a_2_0_closure3: ( $i * $i ) > $i)).
% 1.13/1.27 tff(m1_pboole_type, type, (
% 1.13/1.27 m1_pboole: ( $i * $i ) > $o)).
% 1.13/1.27 tff(v2_relat_1_type, type, (
% 1.13/1.27 v2_relat_1: $i > $o)).
% 1.13/1.27 tff(k7_relat_1_type, type, (
% 1.13/1.27 k7_relat_1: ( $i * $i ) > $i)).
% 1.13/1.27 tff(tptp_fun_B_1_type, type, (
% 1.13/1.27 tptp_fun_B_1: $i)).
% 1.13/1.27 tff(r6_pboole_type, type, (
% 1.13/1.27 r6_pboole: ( $i * $i * $i ) > $o)).
% 1.13/1.27 tff(k3_xboole_0_type, type, (
% 1.13/1.27 k3_xboole_0: ( $i * $i ) > $i)).
% 1.13/1.27 tff(tptp_fun_C_19_type, type, (
% 1.13/1.27 tptp_fun_C_19: ( $i * $i ) > $i)).
% 1.13/1.27 tff(k1_relat_1_type, type, (
% 1.13/1.27 k1_relat_1: $i > $i)).
% 1.13/1.27 tff(v1_relat_1_type, type, (
% 1.13/1.27 v1_relat_1: $i > $o)).
% 1.13/1.27 tff(v1_funct_1_type, type, (
% 1.13/1.27 v1_funct_1: $i > $o)).
% 1.13/1.27 tff(tptp_fun_C_3_type, type, (
% 1.13/1.27 tptp_fun_C_3: ( $i * $i ) > $i)).
% 1.13/1.27 tff(1,plain,
% 1.13/1.27 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))) <=> (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))))),
% 1.13/1.27 inference(bind,[status(th)],[])).
% 1.13/1.27 tff(2,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))),
% 1.13/1.27 inference(quant_intro,[status(thm)],[1])).
% 1.13/1.27 tff(3,plain,
% 1.13/1.27 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_pboole(C, B)) <=> (~(v1_xboole_0(B) | (~m1_pboole(C, B))))), ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) <=> (~(~(v1_xboole_0(B) | (~m1_pboole(C, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_pboole(C, B))))) <=> (v1_xboole_0(B) | (~m1_pboole(C, B)))), ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) <=> (v1_xboole_0(B) | (~m1_pboole(C, B))))), trans(trans(monotonicity(rewrite(((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)) <=> (~((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))))), ((r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))) <=> (r2_hidden(A, a_2_0_closure3(B, C)) <=> (~((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))))))), rewrite((r2_hidden(A, a_2_0_closure3(B, C)) <=> (~((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))))) <=> (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))), ((r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))) <=> (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))), rewrite((~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))) <=> (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))), ((r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))) <=> (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))), (((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))) <=> ((v1_xboole_0(B) | (~m1_pboole(C, B))) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))))), rewrite(((v1_xboole_0(B) | (~m1_pboole(C, B))) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C))))) <=> (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))), (((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))) <=> (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))))),
% 1.13/1.27 inference(bind,[status(th)],[])).
% 1.13/1.27 tff(4,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))),
% 1.13/1.27 inference(quant_intro,[status(thm)],[3])).
% 1.13/1.27 tff(5,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))),
% 1.13/1.27 inference(rewrite,[status(thm)],[])).
% 1.13/1.27 tff(6,plain,
% 1.13/1.27 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r2_hidden(A, a_2_0_closure3(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = D)) & (~(k1_funct_1(C, D) = k1_xboole_0)))) <=> (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))), ((((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = D)) & (~(k1_funct_1(C, D) = k1_xboole_0))))) <=> (((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))), ((((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = D)) & (~(k1_funct_1(C, D) = k1_xboole_0))))) <=> ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))))),
% 1.13/1.27 inference(bind,[status(th)],[])).
% 1.13/1.27 tff(7,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = D)) & (~(k1_funct_1(C, D) = k1_xboole_0))))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))),
% 1.13/1.27 inference(quant_intro,[status(thm)],[6])).
% 1.13/1.27 tff(8,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_pboole(C, B)) => (r2_hidden(A, a_2_0_closure3(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, B) & (A = D)) & (~(k1_funct_1(C, D) = k1_xboole_0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fraenkel_a_2_0_closure3')).
% 1.13/1.27 tff(9,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))),
% 1.13/1.27 inference(modus_ponens,[status(thm)],[8, 7])).
% 1.13/1.27 tff(10,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))),
% 1.13/1.27 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.13/1.27 tff(11,plain,(
% 1.13/1.27 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_pboole(C, B))) | (r2_hidden(A, a_2_0_closure3(B, C)) <=> ((~(k1_funct_1(C, A) = k1_xboole_0)) & m1_subset_1(A, B))))),
% 1.13/1.27 inference(skolemize,[status(sab)],[10])).
% 1.13/1.27 tff(12,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))),
% 1.13/1.27 inference(modus_ponens,[status(thm)],[11, 4])).
% 1.13/1.27 tff(13,plain,
% 1.13/1.27 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))),
% 1.13/1.27 inference(modus_ponens,[status(thm)],[12, 2])).
% 1.13/1.27 tff(14,plain,
% 1.13/1.27 (((~v1_xboole_0(A!0)) & (v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))) <=> ((~v1_xboole_0(A!0)) & v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))),
% 1.13/1.27 inference(rewrite,[status(thm)],[])).
% 1.13/1.27 tff(15,plain,
% 1.13/1.27 (((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))) <=> (v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))),
% 1.13/1.27 inference(rewrite,[status(thm)],[])).
% 1.13/1.27 tff(16,plain,
% 1.13/1.27 ((~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))) <=> (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))),
% 1.13/1.27 inference(rewrite,[status(thm)],[])).
% 1.13/1.27 tff(17,plain,
% 1.13/1.27 (((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))) <=> ((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))),
% 1.13/1.27 inference(monotonicity,[status(thm)],[16])).
% 1.13/1.27 tff(18,plain,
% 1.13/1.27 (((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))) <=> (v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))),
% 1.13/1.27 inference(transitivity,[status(thm)],[17, 15])).
% 1.13/1.27 tff(19,plain,
% 1.13/1.27 (((~v1_xboole_0(A!0)) & ((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))) <=> ((~v1_xboole_0(A!0)) & (v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))))),
% 1.13/1.27 inference(monotonicity,[status(thm)],[18])).
% 1.13/1.27 tff(20,plain,
% 1.13/1.27 (((~v1_xboole_0(A!0)) & ((v2_relat_1(B!1) & m1_pboole(B!1, A!0)) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))) <=> ((~v1_xboole_0(A!0)) & v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))))),
% 1.13/1.28 inference(transitivity,[status(thm)],[19, 14])).
% 1.13/1.28 tff(21,plain,
% 1.13/1.28 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A)))))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(22,plain,
% 1.13/1.28 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_relat_1(B) & m1_pboole(B, A)) => ![C: $i] : ((v2_relat_1(C) & m1_pboole(C, A)) => (((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C)))) => r6_pboole(A, B, C)))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A)))))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(23,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_relat_1(B) & m1_pboole(B, A)) => ![C: $i] : ((v2_relat_1(C) & m1_pboole(C, A)) => (((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C)))) => r6_pboole(A, B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_closure3')).
% 1.13/1.28 tff(24,plain,
% 1.13/1.28 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A))))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.13/1.28 tff(25,plain,
% 1.13/1.28 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A))))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[24, 21])).
% 1.13/1.28 tff(26,plain,
% 1.13/1.28 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A))))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.13/1.28 tff(27,plain,
% 1.13/1.28 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_relat_1(B) & m1_pboole(B, A))) | ![C: $i] : (r6_pboole(A, B, C) | (~((k1_closure3(A, B) = k1_closure3(A, C)) & (k7_relat_1(B, k1_closure3(A, B)) = k7_relat_1(C, k1_closure3(A, C))))) | (~(v2_relat_1(C) & m1_pboole(C, A))))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[26, 21])).
% 1.13/1.28 tff(28,plain,
% 1.13/1.28 ((~v1_xboole_0(A!0)) & v2_relat_1(B!1) & m1_pboole(B!1, A!0) & (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.13/1.28 tff(29,plain,
% 1.13/1.28 (~(r6_pboole(A!0, B!1, C!2) | (~((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~(v2_relat_1(C!2) & m1_pboole(C!2, A!0))))),
% 1.13/1.28 inference(and_elim,[status(thm)],[28])).
% 1.13/1.28 tff(30,plain,
% 1.13/1.28 (v2_relat_1(C!2) & m1_pboole(C!2, A!0)),
% 1.13/1.28 inference(or_elim,[status(thm)],[29])).
% 1.13/1.28 tff(31,plain,
% 1.13/1.28 (m1_pboole(C!2, A!0)),
% 1.13/1.28 inference(and_elim,[status(thm)],[30])).
% 1.13/1.28 tff(32,plain,
% 1.13/1.28 (~v1_xboole_0(A!0)),
% 1.13/1.28 inference(and_elim,[status(thm)],[28])).
% 1.13/1.28 tff(33,plain,
% 1.13/1.28 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(34,plain,
% 1.13/1.28 ((v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0) | (~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))))) <=> (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(35,plain,
% 1.13/1.28 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0) | (~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))))))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[34])).
% 1.13/1.28 tff(36,plain,
% 1.13/1.28 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0) | (~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))),
% 1.13/1.28 inference(transitivity,[status(thm)],[35, 33])).
% 1.13/1.28 tff(37,plain,
% 1.13/1.28 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | (v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0) | (~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(38,plain,
% 1.13/1.28 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_pboole(C, B)) | (~(((k1_funct_1(C, A) = k1_xboole_0) | (~m1_subset_1(A, B))) <=> r2_hidden(A, a_2_0_closure3(B, C)))))) | v1_xboole_0(A!0) | (~m1_pboole(C!2, A!0)) | (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.13/1.28 tff(39,plain,
% 1.13/1.28 (~(((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[38, 32, 31, 13])).
% 1.13/1.28 tff(40,plain,
% 1.13/1.28 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(41,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[40])).
% 1.13/1.28 tff(42,plain,
% 1.13/1.28 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(43,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[42])).
% 1.13/1.28 tff(44,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(transitivity,[status(thm)],[43, 41])).
% 1.13/1.28 tff(45,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(46,plain,
% 1.13/1.28 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))) <=> ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))), (![B: $i] : (m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))) <=> ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(47,plain,
% 1.13/1.28 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[46])).
% 1.13/1.28 tff(48,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_pboole(B, A) => ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_closure3')).
% 1.13/1.28 tff(49,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.13/1.28 tff(50,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.13/1.28 tff(51,plain,(
% 1.13/1.28 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(skolemize,[status(sab)],[50])).
% 1.13/1.28 tff(52,plain,
% 1.13/1.28 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[51, 44])).
% 1.13/1.28 tff(53,plain,
% 1.13/1.28 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))) | (v1_xboole_0(A!0) | ![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B)))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))) | v1_xboole_0(A!0) | ![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B)))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(54,plain,
% 1.13/1.28 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))) | (v1_xboole_0(A!0) | ![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B)))))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(55,plain,
% 1.13/1.28 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_pboole(B, A)) | ![C: $i] : ((C = k1_closure3(A, B)) <=> (C = a_2_0_closure3(A, B)))))) | v1_xboole_0(A!0) | ![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.13/1.28 tff(56,plain,
% 1.13/1.28 (![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[55, 32, 52])).
% 1.13/1.28 tff(57,plain,
% 1.13/1.28 (((~![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))) | ((~m1_pboole(C!2, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2))))) <=> ((~![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))) | (~m1_pboole(C!2, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(58,plain,
% 1.13/1.28 ((~![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))) | ((~m1_pboole(C!2, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2))))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(59,plain,
% 1.13/1.28 ((~![B: $i] : ((~m1_pboole(B, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, B)) <=> (C = a_2_0_closure3(A!0, B))))) | (~m1_pboole(C!2, A!0)) | ![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.13/1.28 tff(60,plain,
% 1.13/1.28 (![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[59, 31, 56])).
% 1.13/1.28 tff(61,plain,
% 1.13/1.28 (((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))) <=> ((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(62,plain,
% 1.13/1.28 (($true <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(63,plain,
% 1.13/1.28 ((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> $true),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(64,plain,
% 1.13/1.28 (((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))) <=> ($true <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[63])).
% 1.13/1.28 tff(65,plain,
% 1.13/1.28 (((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))),
% 1.13/1.28 inference(transitivity,[status(thm)],[64, 62])).
% 1.13/1.28 tff(66,plain,
% 1.13/1.28 (((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | ((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))) <=> ((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[65])).
% 1.13/1.28 tff(67,plain,
% 1.13/1.28 (((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | ((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))) <=> ((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(transitivity,[status(thm)],[66, 61])).
% 1.13/1.28 tff(68,plain,
% 1.13/1.28 ((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | ((k1_closure3(A!0, C!2) = k1_closure3(A!0, C!2)) <=> (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(69,plain,
% 1.13/1.28 ((~![C: $i] : ((C = k1_closure3(A!0, C!2)) <=> (C = a_2_0_closure3(A!0, C!2)))) | (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.13/1.28 tff(70,plain,
% 1.13/1.28 (k1_closure3(A!0, C!2) = a_2_0_closure3(A!0, C!2)),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[69, 60])).
% 1.13/1.28 tff(71,plain,
% 1.13/1.28 (a_2_0_closure3(A!0, C!2) = k1_closure3(A!0, C!2)),
% 1.13/1.28 inference(symmetry,[status(thm)],[70])).
% 1.13/1.28 tff(72,plain,
% 1.13/1.28 (r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[71])).
% 1.13/1.28 tff(73,plain,
% 1.13/1.28 (r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))),
% 1.13/1.28 inference(symmetry,[status(thm)],[72])).
% 1.13/1.28 tff(74,plain,
% 1.13/1.28 ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) <=> (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2)))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[73])).
% 1.13/1.28 tff(75,plain,
% 1.13/1.28 ((k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)) & (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2)))),
% 1.13/1.28 inference(or_elim,[status(thm)],[29])).
% 1.13/1.28 tff(76,plain,
% 1.13/1.28 (k7_relat_1(B!1, k1_closure3(A!0, B!1)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))),
% 1.13/1.28 inference(and_elim,[status(thm)],[75])).
% 1.13/1.28 tff(77,plain,
% 1.13/1.28 (k1_closure3(A!0, B!1) = k1_closure3(A!0, C!2)),
% 1.13/1.28 inference(and_elim,[status(thm)],[75])).
% 1.13/1.28 tff(78,plain,
% 1.13/1.28 (k1_closure3(A!0, C!2) = k1_closure3(A!0, B!1)),
% 1.13/1.28 inference(symmetry,[status(thm)],[77])).
% 1.13/1.28 tff(79,plain,
% 1.13/1.28 (k7_relat_1(B!1, k1_closure3(A!0, C!2)) = k7_relat_1(B!1, k1_closure3(A!0, B!1))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[78])).
% 1.13/1.28 tff(80,plain,
% 1.13/1.28 (k7_relat_1(B!1, k1_closure3(A!0, C!2)) = k7_relat_1(C!2, k1_closure3(A!0, C!2))),
% 1.13/1.28 inference(transitivity,[status(thm)],[79, 76])).
% 1.13/1.28 tff(81,plain,
% 1.13/1.28 (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[80])).
% 1.13/1.28 tff(82,plain,
% 1.13/1.28 (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2))),
% 1.13/1.28 inference(symmetry,[status(thm)],[81])).
% 1.13/1.28 tff(83,plain,
% 1.13/1.28 (^[A: $i, B: $i] : refl(((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(84,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[83])).
% 1.13/1.28 tff(85,plain,
% 1.13/1.28 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B))) <=> ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B))))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(86,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[85])).
% 1.13/1.28 tff(87,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(88,plain,
% 1.13/1.28 (^[A: $i, B: $i] : rewrite((m1_pboole(B, A) => (v1_relat_1(B) & v1_funct_1(B))) <=> ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(89,plain,
% 1.13/1.28 (![A: $i, B: $i] : (m1_pboole(B, A) => (v1_relat_1(B) & v1_funct_1(B))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[88])).
% 1.13/1.28 tff(90,axiom,(![A: $i, B: $i] : (m1_pboole(B, A) => (v1_relat_1(B) & v1_funct_1(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_pboole')).
% 1.13/1.28 tff(91,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.13/1.28 tff(92,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[91, 87])).
% 1.13/1.28 tff(93,plain,(
% 1.13/1.28 ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v1_relat_1(B) & v1_funct_1(B)))),
% 1.13/1.28 inference(skolemize,[status(sab)],[92])).
% 1.13/1.28 tff(94,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[93, 86])).
% 1.13/1.28 tff(95,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[94, 84])).
% 1.13/1.28 tff(96,plain,
% 1.13/1.28 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_pboole(C!2, A!0)) | (~((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_pboole(C!2, A!0)) | (~((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(97,plain,
% 1.13/1.28 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_pboole(C!2, A!0)) | (~((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(98,plain,
% 1.13/1.28 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_pboole(C!2, A!0)) | (~((~v1_relat_1(C!2)) | (~v1_funct_1(C!2))))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[97, 96])).
% 1.13/1.28 tff(99,plain,
% 1.13/1.28 (~((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[98, 31, 95])).
% 1.13/1.28 tff(100,plain,
% 1.13/1.28 (((~v1_relat_1(C!2)) | (~v1_funct_1(C!2))) | v1_relat_1(C!2)),
% 1.13/1.28 inference(tautology,[status(thm)],[])).
% 1.13/1.28 tff(101,plain,
% 1.13/1.28 (v1_relat_1(C!2)),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[100, 99])).
% 1.13/1.28 tff(102,plain,
% 1.13/1.28 (((~v1_relat_1(C!2)) | (~v1_funct_1(C!2))) | v1_funct_1(C!2)),
% 1.13/1.28 inference(tautology,[status(thm)],[])).
% 1.13/1.28 tff(103,plain,
% 1.13/1.28 (v1_funct_1(C!2)),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[102, 99])).
% 1.13/1.28 tff(104,plain,
% 1.13/1.28 (^[A: $i, B: $i] : refl(((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(105,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B))) <=> ![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[104])).
% 1.13/1.28 tff(106,plain,
% 1.13/1.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> (((~v1_relat_1(B)) | (~v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))))), rewrite((((~v1_relat_1(B)) | (~v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))), (((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(107,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[106])).
% 1.13/1.28 tff(108,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(109,plain,
% 1.13/1.28 (^[A: $i, B: $i] : rewrite(((v1_relat_1(B) & v1_funct_1(B)) => (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A))))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(110,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (m1_pboole(B, A) <=> (k1_relat_1(B) = A))) <=> ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[109])).
% 1.13/1.28 tff(111,axiom,(![A: $i, B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_pboole')).
% 1.13/1.28 tff(112,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.13/1.28 tff(113,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.13/1.28 tff(114,plain,(
% 1.13/1.28 ![A: $i, B: $i] : ((~(v1_relat_1(B) & v1_funct_1(B))) | (m1_pboole(B, A) <=> (k1_relat_1(B) = A)))),
% 1.13/1.28 inference(skolemize,[status(sab)],[113])).
% 1.13/1.28 tff(115,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[114, 107])).
% 1.13/1.28 tff(116,plain,
% 1.13/1.28 (![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[115, 105])).
% 1.13/1.28 tff(117,plain,
% 1.13/1.28 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(118,plain,
% 1.13/1.28 (((m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2))) <=> ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(119,plain,
% 1.13/1.28 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0))))),
% 1.13/1.28 inference(monotonicity,[status(thm)],[118])).
% 1.13/1.28 tff(120,plain,
% 1.13/1.28 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)))),
% 1.13/1.28 inference(transitivity,[status(thm)],[119, 117])).
% 1.13/1.28 tff(121,plain,
% 1.13/1.28 ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))),
% 1.13/1.28 inference(quant_inst,[status(thm)],[])).
% 1.13/1.28 tff(122,plain,
% 1.13/1.28 ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0))),
% 1.13/1.28 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.13/1.28 tff(123,plain,
% 1.13/1.28 ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0))),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[122, 116])).
% 1.13/1.28 tff(124,plain,
% 1.13/1.28 (m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0)),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[123, 103, 101])).
% 1.13/1.28 tff(125,plain,
% 1.13/1.28 ((~(m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0))) | (~m1_pboole(C!2, A!0)) | (k1_relat_1(C!2) = A!0)),
% 1.13/1.28 inference(tautology,[status(thm)],[])).
% 1.13/1.28 tff(126,plain,
% 1.13/1.28 ((~(m1_pboole(C!2, A!0) <=> (k1_relat_1(C!2) = A!0))) | (k1_relat_1(C!2) = A!0)),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[125, 31])).
% 1.13/1.28 tff(127,plain,
% 1.13/1.28 (k1_relat_1(C!2) = A!0),
% 1.13/1.28 inference(unit_resolution,[status(thm)],[126, 124])).
% 1.13/1.28 tff(128,plain,
% 1.13/1.28 (A!0 = k1_relat_1(C!2)),
% 1.13/1.28 inference(symmetry,[status(thm)],[127])).
% 1.13/1.28 tff(129,assumption,(A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)), introduced(assumption)).
% 1.13/1.28 tff(130,plain,
% 1.13/1.28 (k3_xboole_0(k1_closure3(A!0, C!2), A!0) = A!0),
% 1.13/1.28 inference(symmetry,[status(thm)],[129])).
% 1.13/1.28 tff(131,plain,
% 1.13/1.28 (^[A: $i, B: $i] : refl((k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> (k3_xboole_0(A, B) = k3_xboole_0(B, A)))),
% 1.13/1.28 inference(bind,[status(th)],[])).
% 1.13/1.28 tff(132,plain,
% 1.13/1.28 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.13/1.28 inference(quant_intro,[status(thm)],[131])).
% 1.13/1.28 tff(133,plain,
% 1.13/1.28 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A)) <=> ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.13/1.28 inference(rewrite,[status(thm)],[])).
% 1.13/1.28 tff(134,axiom,(![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 1.13/1.29 tff(135,plain,
% 1.13/1.29 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.13/1.29 tff(136,plain,(
% 1.13/1.29 ![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.13/1.29 inference(skolemize,[status(sab)],[135])).
% 1.13/1.29 tff(137,plain,
% 1.13/1.29 (![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[136, 132])).
% 1.13/1.29 tff(138,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : (k3_xboole_0(A, B) = k3_xboole_0(B, A))) | (k3_xboole_0(A!0, k1_closure3(A!0, C!2)) = k3_xboole_0(k1_closure3(A!0, C!2), A!0))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(139,plain,
% 1.13/1.29 (k3_xboole_0(A!0, k1_closure3(A!0, C!2)) = k3_xboole_0(k1_closure3(A!0, C!2), A!0)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[138, 137])).
% 1.13/1.29 tff(140,plain,
% 1.13/1.29 (m1_pboole(B!1, A!0)),
% 1.13/1.29 inference(and_elim,[status(thm)],[28])).
% 1.13/1.29 tff(141,plain,
% 1.13/1.29 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_pboole(B!1, A!0)) | (~((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_pboole(B!1, A!0)) | (~((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(142,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | ((~m1_pboole(B!1, A!0)) | (~((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(143,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~v1_relat_1(B)) | (~v1_funct_1(B)))))) | (~m1_pboole(B!1, A!0)) | (~((~v1_relat_1(B!1)) | (~v1_funct_1(B!1))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.13/1.29 tff(144,plain,
% 1.13/1.29 (~((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[143, 140, 95])).
% 1.13/1.29 tff(145,plain,
% 1.13/1.29 (((~v1_relat_1(B!1)) | (~v1_funct_1(B!1))) | v1_relat_1(B!1)),
% 1.13/1.29 inference(tautology,[status(thm)],[])).
% 1.13/1.29 tff(146,plain,
% 1.13/1.29 (v1_relat_1(B!1)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.13/1.29 tff(147,plain,
% 1.13/1.29 (((~v1_relat_1(B!1)) | (~v1_funct_1(B!1))) | v1_funct_1(B!1)),
% 1.13/1.29 inference(tautology,[status(thm)],[])).
% 1.13/1.29 tff(148,plain,
% 1.13/1.29 (v1_funct_1(B!1)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[147, 144])).
% 1.13/1.29 tff(149,plain,
% 1.13/1.29 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(150,plain,
% 1.13/1.29 (((m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1))) <=> ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(151,plain,
% 1.13/1.29 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0))))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[150])).
% 1.13/1.29 tff(152,plain,
% 1.13/1.29 (((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))) <=> ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)))),
% 1.13/1.29 inference(transitivity,[status(thm)],[151, 149])).
% 1.13/1.29 tff(153,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | ((m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(154,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((m1_pboole(B, A) <=> (k1_relat_1(B) = A)) | (~v1_relat_1(B)) | (~v1_funct_1(B)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.13/1.29 tff(155,plain,
% 1.13/1.29 ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[154, 116])).
% 1.13/1.29 tff(156,plain,
% 1.13/1.29 (m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[155, 148, 146])).
% 1.13/1.29 tff(157,plain,
% 1.13/1.29 ((~(m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0))) | (~m1_pboole(B!1, A!0)) | (k1_relat_1(B!1) = A!0)),
% 1.13/1.29 inference(tautology,[status(thm)],[])).
% 1.13/1.29 tff(158,plain,
% 1.13/1.29 ((~(m1_pboole(B!1, A!0) <=> (k1_relat_1(B!1) = A!0))) | (k1_relat_1(B!1) = A!0)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[157, 140])).
% 1.13/1.29 tff(159,plain,
% 1.13/1.29 (k1_relat_1(B!1) = A!0),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[158, 156])).
% 1.13/1.29 tff(160,plain,
% 1.13/1.29 (A!0 = k1_relat_1(B!1)),
% 1.13/1.29 inference(symmetry,[status(thm)],[159])).
% 1.13/1.29 tff(161,plain,
% 1.13/1.29 (k3_xboole_0(A!0, k1_closure3(A!0, C!2)) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[160])).
% 1.13/1.29 tff(162,plain,
% 1.13/1.29 (k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2)) = k3_xboole_0(A!0, k1_closure3(A!0, C!2))),
% 1.13/1.29 inference(symmetry,[status(thm)],[161])).
% 1.13/1.29 tff(163,plain,
% 1.13/1.29 (k1_relat_1(C!2) = k1_relat_1(B!1)),
% 1.13/1.29 inference(transitivity,[status(thm)],[127, 160])).
% 1.13/1.29 tff(164,plain,
% 1.13/1.29 (k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2)) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[163])).
% 1.13/1.29 tff(165,plain,
% 1.13/1.29 (^[A: $i, B: $i] : refl(((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))) <=> ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(166,plain,
% 1.13/1.29 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[165])).
% 1.13/1.29 tff(167,plain,
% 1.13/1.29 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(168,plain,
% 1.13/1.29 (^[A: $i, B: $i] : rewrite((v1_relat_1(B) => (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))) <=> ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(169,plain,
% 1.13/1.29 (![A: $i, B: $i] : (v1_relat_1(B) => (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A))) <=> ![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[168])).
% 1.13/1.29 tff(170,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t90_relat_1')).
% 1.13/1.29 tff(171,plain,
% 1.13/1.29 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[170, 169])).
% 1.13/1.29 tff(172,plain,
% 1.13/1.29 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[171, 167])).
% 1.13/1.29 tff(173,plain,(
% 1.13/1.29 ![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(skolemize,[status(sab)],[172])).
% 1.13/1.29 tff(174,plain,
% 1.13/1.29 (![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[173, 166])).
% 1.13/1.29 tff(175,plain,
% 1.13/1.29 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | ((~v1_relat_1(C!2)) | (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | (~v1_relat_1(C!2)) | (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(176,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | ((~v1_relat_1(C!2)) | (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2))))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(177,plain,
% 1.13/1.29 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | (~v1_relat_1(C!2)) | (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.13/1.29 tff(178,plain,
% 1.13/1.29 ((~v1_relat_1(C!2)) | (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2)))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[177, 174])).
% 1.13/1.29 tff(179,plain,
% 1.13/1.29 (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(C!2), k1_closure3(A!0, C!2))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[178, 101])).
% 1.13/1.29 tff(180,plain,
% 1.13/1.29 (k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))) = k1_relat_1(C!2)),
% 1.13/1.29 inference(transitivity,[status(thm)],[179, 164, 162, 139, 130, 128])).
% 1.13/1.29 tff(181,plain,
% 1.13/1.29 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)))) <=> r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[180])).
% 1.13/1.29 tff(182,plain,
% 1.13/1.29 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2)) <=> r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))),
% 1.13/1.29 inference(symmetry,[status(thm)],[181])).
% 1.13/1.29 tff(183,plain,
% 1.13/1.29 ((C!2 = B!1) <=> (B!1 = C!2)),
% 1.13/1.29 inference(commutativity,[status(thm)],[])).
% 1.13/1.29 tff(184,plain,
% 1.13/1.29 ((B!1 = C!2) <=> (C!2 = B!1)),
% 1.13/1.29 inference(symmetry,[status(thm)],[183])).
% 1.13/1.29 tff(185,plain,
% 1.13/1.29 ((~(B!1 = C!2)) <=> (~(C!2 = B!1))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[184])).
% 1.13/1.29 tff(186,plain,
% 1.13/1.29 (^[A: $i, B: $i, C: $i] : refl(((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A))) <=> ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(187,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A))) <=> ![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[186])).
% 1.13/1.29 tff(188,plain,
% 1.13/1.29 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_pboole(B, A) & m1_pboole(C, A)) <=> (~((~m1_pboole(B, A)) | (~m1_pboole(C, A))))), ((~(m1_pboole(B, A) & m1_pboole(C, A))) <=> (~(~((~m1_pboole(B, A)) | (~m1_pboole(C, A))))))), rewrite((~(~((~m1_pboole(B, A)) | (~m1_pboole(C, A))))) <=> ((~m1_pboole(B, A)) | (~m1_pboole(C, A)))), ((~(m1_pboole(B, A) & m1_pboole(C, A))) <=> ((~m1_pboole(B, A)) | (~m1_pboole(C, A))))), (((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))) <=> (((~m1_pboole(B, A)) | (~m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))))), rewrite((((~m1_pboole(B, A)) | (~m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))) <=> ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))), (((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))) <=> ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(189,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[188])).
% 1.13/1.29 tff(190,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(191,plain,
% 1.13/1.29 (^[A: $i, B: $i, C: $i] : rewrite(((m1_pboole(B, A) & m1_pboole(C, A)) => (r6_pboole(A, B, C) <=> (B = C))) <=> ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(192,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((m1_pboole(B, A) & m1_pboole(C, A)) => (r6_pboole(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C)))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[191])).
% 1.13/1.29 tff(193,axiom,(![A: $i, B: $i, C: $i] : ((m1_pboole(B, A) & m1_pboole(C, A)) => (r6_pboole(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r6_pboole')).
% 1.13/1.29 tff(194,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.13/1.29 tff(195,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.13/1.29 tff(196,plain,(
% 1.13/1.29 ![A: $i, B: $i, C: $i] : ((~(m1_pboole(B, A) & m1_pboole(C, A))) | (r6_pboole(A, B, C) <=> (B = C)))),
% 1.13/1.29 inference(skolemize,[status(sab)],[195])).
% 1.13/1.29 tff(197,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.13/1.29 tff(198,plain,
% 1.13/1.29 (![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[197, 187])).
% 1.13/1.29 tff(199,plain,
% 1.13/1.29 (((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | ((~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(200,plain,
% 1.13/1.29 (((r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0))) <=> ((~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(201,plain,
% 1.13/1.29 (((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | ((r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | ((~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2))))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[200])).
% 1.13/1.29 tff(202,plain,
% 1.13/1.29 (((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | ((r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)))),
% 1.13/1.29 inference(transitivity,[status(thm)],[201, 199])).
% 1.13/1.29 tff(203,plain,
% 1.13/1.29 ((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | ((r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(204,plain,
% 1.13/1.29 ((~![A: $i, B: $i, C: $i] : ((r6_pboole(A, B, C) <=> (B = C)) | (~m1_pboole(B, A)) | (~m1_pboole(C, A)))) | (~m1_pboole(B!1, A!0)) | (~m1_pboole(C!2, A!0)) | (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.13/1.29 tff(205,plain,
% 1.13/1.29 (r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[204, 140, 31, 198])).
% 1.13/1.29 tff(206,plain,
% 1.13/1.29 (~r6_pboole(A!0, B!1, C!2)),
% 1.13/1.29 inference(or_elim,[status(thm)],[29])).
% 1.13/1.29 tff(207,plain,
% 1.13/1.29 ((~(r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2))) | r6_pboole(A!0, B!1, C!2) | (~(B!1 = C!2))),
% 1.13/1.29 inference(tautology,[status(thm)],[])).
% 1.13/1.29 tff(208,plain,
% 1.13/1.29 ((~(r6_pboole(A!0, B!1, C!2) <=> (B!1 = C!2))) | (~(B!1 = C!2))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[207, 206])).
% 1.13/1.29 tff(209,plain,
% 1.13/1.29 (~(B!1 = C!2)),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[208, 205])).
% 1.13/1.29 tff(210,plain,
% 1.13/1.29 (~(C!2 = B!1)),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[209, 185])).
% 1.13/1.29 tff(211,plain,
% 1.13/1.29 (^[A: $i] : refl(((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(212,plain,
% 1.13/1.29 (![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[211])).
% 1.13/1.29 tff(213,plain,
% 1.13/1.29 (^[A: $i] : rewrite(((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(214,plain,
% 1.13/1.29 (![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[213])).
% 1.13/1.29 tff(215,plain,
% 1.13/1.29 (![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(transitivity,[status(thm)],[214, 212])).
% 1.13/1.29 tff(216,plain,
% 1.13/1.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(A) & v1_funct_1(A)) <=> (~((~v1_relat_1(A)) | (~v1_funct_1(A))))), ((~(v1_relat_1(A) & v1_funct_1(A))) <=> (~(~((~v1_relat_1(A)) | (~v1_funct_1(A))))))), rewrite((~(~((~v1_relat_1(A)) | (~v1_funct_1(A))))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A)))), ((~(v1_relat_1(A) & v1_funct_1(A))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(B) & v1_funct_1(B)) <=> (~((~v1_relat_1(B)) | (~v1_funct_1(B))))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> (~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))))), rewrite((~(~((~v1_relat_1(B)) | (~v1_funct_1(B))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)))), ((~(v1_relat_1(B) & v1_funct_1(B))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B))))), (((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))) <=> ((A = B) | ((~v1_relat_1(B)) | (~v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))), rewrite(((A = B) | ((~v1_relat_1(B)) | (~v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))) <=> ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))), (((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))) <=> ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))), (![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))) <=> ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))), (((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> (((~v1_relat_1(A)) | (~v1_funct_1(A))) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))), rewrite((((~v1_relat_1(A)) | (~v1_funct_1(A))) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))), (((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(217,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))) <=> ![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[216])).
% 1.13/1.29 tff(218,plain,
% 1.13/1.29 (^[A: $i] : rewrite(((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | ((~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) <=> ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(219,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | ((~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) <=> ![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[218])).
% 1.13/1.29 tff(220,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))))) <=> ![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(221,plain,
% 1.13/1.29 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) <=> ((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))), ((((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)) <=> (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)))), rewrite((((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)) <=> ((~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))) | (A = B))), ((((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)) <=> ((~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))) | (A = B)))), (((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B))) <=> ((v1_relat_1(B) & v1_funct_1(B)) => ((~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))) | (A = B))))), rewrite(((v1_relat_1(B) & v1_funct_1(B)) => ((~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))) | (A = B))) <=> ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))))), (((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B))) <=> ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))))))), (![B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B))) <=> ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))), (((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)))) <=> ((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))))))), rewrite(((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C))))))) <=> ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))), (((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)))) <=> ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(222,plain,
% 1.13/1.29 (![A: $i] : ((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B)))) <=> ![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[221])).
% 1.13/1.29 tff(223,axiom,(![A: $i] : ((v1_relat_1(A) & v1_funct_1(A)) => ![B: $i] : ((v1_relat_1(B) & v1_funct_1(B)) => (((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : (r2_hidden(C, k1_relat_1(A)) => (k1_funct_1(A, C) = k1_funct_1(B, C)))) => (A = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_funct_1')).
% 1.13/1.29 tff(224,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.13/1.29 tff(225,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~((k1_relat_1(A) = k1_relat_1(B)) & ![C: $i] : ((~r2_hidden(C, k1_relat_1(A))) | (k1_funct_1(A, C) = k1_funct_1(B, C)))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[224, 220])).
% 1.13/1.29 tff(226,plain,(
% 1.13/1.29 ![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | ((~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A))))))))),
% 1.13/1.29 inference(skolemize,[status(sab)],[225])).
% 1.13/1.29 tff(227,plain,
% 1.13/1.29 (![A: $i] : ((~(v1_relat_1(A) & v1_funct_1(A))) | ![B: $i] : ((A = B) | (~(v1_relat_1(B) & v1_funct_1(B))) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[226, 219])).
% 1.13/1.29 tff(228,plain,
% 1.13/1.29 (![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[227, 217])).
% 1.13/1.29 tff(229,plain,
% 1.13/1.29 (![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[228, 215])).
% 1.13/1.29 tff(230,plain,
% 1.13/1.29 (((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(231,plain,
% 1.13/1.29 (((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) <=> ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(232,plain,
% 1.13/1.29 (^[B: $i] : rewrite(((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))) <=> ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(bind,[status(th)],[])).
% 1.13/1.29 tff(233,plain,
% 1.13/1.29 (![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))) <=> ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))),
% 1.13/1.29 inference(quant_intro,[status(thm)],[232])).
% 1.13/1.29 tff(234,plain,
% 1.13/1.29 (((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) <=> ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[233])).
% 1.13/1.29 tff(235,plain,
% 1.13/1.29 (((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) <=> ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(transitivity,[status(thm)],[234, 231])).
% 1.13/1.29 tff(236,plain,
% 1.13/1.29 (((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))))),
% 1.13/1.29 inference(monotonicity,[status(thm)],[235])).
% 1.13/1.29 tff(237,plain,
% 1.13/1.29 (((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(transitivity,[status(thm)],[236, 230])).
% 1.13/1.29 tff(238,plain,
% 1.13/1.29 ((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((C!2 = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2)))))))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(239,plain,
% 1.13/1.29 ((~![A: $i] : ((~v1_relat_1(A)) | (~v1_funct_1(A)) | ![B: $i] : ((A = B) | (~v1_relat_1(B)) | (~v1_funct_1(B)) | (~(k1_relat_1(A) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, A), k1_relat_1(A))) | (k1_funct_1(A, tptp_fun_C_19(B, A)) = k1_funct_1(B, tptp_fun_C_19(B, A)))))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | ![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[238, 237])).
% 1.13/1.29 tff(240,plain,
% 1.13/1.29 (![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[239, 229, 101, 103])).
% 1.13/1.29 tff(241,plain,
% 1.13/1.29 (((~![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (C!2 = B!1) | (~(k1_relat_1(C!2) = k1_relat_1(B!1))) | (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))))))) <=> ((~![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (C!2 = B!1) | (~(k1_relat_1(C!2) = k1_relat_1(B!1))) | (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))))))),
% 1.13/1.29 inference(rewrite,[status(thm)],[])).
% 1.13/1.29 tff(242,plain,
% 1.13/1.29 ((~![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (C!2 = B!1) | (~(k1_relat_1(C!2) = k1_relat_1(B!1))) | (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))))))),
% 1.13/1.29 inference(quant_inst,[status(thm)],[])).
% 1.13/1.29 tff(243,plain,
% 1.13/1.29 ((~![B: $i] : ((~v1_relat_1(B)) | (~v1_funct_1(B)) | (C!2 = B) | (~(k1_relat_1(C!2) = k1_relat_1(B))) | (~((~r2_hidden(tptp_fun_C_19(B, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B, C!2)) = k1_funct_1(B, tptp_fun_C_19(B, C!2))))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (C!2 = B!1) | (~(k1_relat_1(C!2) = k1_relat_1(B!1))) | (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))))),
% 1.13/1.29 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.13/1.29 tff(244,plain,
% 1.13/1.29 ((C!2 = B!1) | (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))))),
% 1.13/1.29 inference(unit_resolution,[status(thm)],[243, 146, 148, 240, 163])).
% 1.13/1.29 tff(245,plain,
% 1.13/1.29 (~((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[244, 210])).
% 1.13/1.30 tff(246,plain,
% 1.13/1.30 (((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))) | r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))),
% 1.13/1.30 inference(tautology,[status(thm)],[])).
% 1.13/1.30 tff(247,plain,
% 1.13/1.30 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[246, 245])).
% 1.13/1.30 tff(248,plain,
% 1.13/1.30 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[247, 182])).
% 1.13/1.30 tff(249,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : refl(((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(250,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C))) <=> ![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[249])).
% 1.13/1.30 tff(251,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_relat_1(C) & v1_funct_1(C)) <=> (~((~v1_relat_1(C)) | (~v1_funct_1(C))))), ((~(v1_relat_1(C) & v1_funct_1(C))) <=> (~(~((~v1_relat_1(C)) | (~v1_funct_1(C))))))), rewrite((~(~((~v1_relat_1(C)) | (~v1_funct_1(C))))) <=> ((~v1_relat_1(C)) | (~v1_funct_1(C)))), ((~(v1_relat_1(C) & v1_funct_1(C))) <=> ((~v1_relat_1(C)) | (~v1_funct_1(C))))), (((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | ((~v1_relat_1(C)) | (~v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))))), rewrite(((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | ((~v1_relat_1(C)) | (~v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))), (((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(252,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))) <=> ![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[251])).
% 1.13/1.30 tff(253,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A))))) <=> ![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(254,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r2_hidden(B, k1_relat_1(k7_relat_1(C, A))) => (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B))) <=> ((~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))), (((v1_relat_1(C) & v1_funct_1(C)) => (r2_hidden(B, k1_relat_1(k7_relat_1(C, A))) => (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))) <=> ((v1_relat_1(C) & v1_funct_1(C)) => ((~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))))), rewrite(((v1_relat_1(C) & v1_funct_1(C)) => ((~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))), (((v1_relat_1(C) & v1_funct_1(C)) => (r2_hidden(B, k1_relat_1(k7_relat_1(C, A))) => (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))) <=> ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(255,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => (r2_hidden(B, k1_relat_1(k7_relat_1(C, A))) => (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[254])).
% 1.13/1.30 tff(256,axiom,(![A: $i, B: $i, C: $i] : ((v1_relat_1(C) & v1_funct_1(C)) => (r2_hidden(B, k1_relat_1(k7_relat_1(C, A))) => (k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t70_funct_1')).
% 1.13/1.30 tff(257,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.13/1.30 tff(258,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[257, 253])).
% 1.13/1.30 tff(259,plain,(
% 1.13/1.30 ![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~(v1_relat_1(C) & v1_funct_1(C))) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))))),
% 1.13/1.30 inference(skolemize,[status(sab)],[258])).
% 1.13/1.30 tff(260,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[259, 252])).
% 1.13/1.30 tff(261,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[260, 250])).
% 1.13/1.30 tff(262,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(263,plain,
% 1.13/1.30 (((k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2))) <=> ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(264,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[263])).
% 1.13/1.30 tff(265,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[264, 262])).
% 1.13/1.30 tff(266,plain,
% 1.13/1.30 ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2))))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(267,plain,
% 1.13/1.30 ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(C!2)) | (~v1_funct_1(C!2)) | (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.13/1.30 tff(268,plain,
% 1.13/1.30 ((k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[267, 261, 101, 103])).
% 1.13/1.30 tff(269,plain,
% 1.13/1.30 (k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[268, 248])).
% 1.13/1.30 tff(270,plain,
% 1.13/1.30 (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(k7_relat_1(C!2, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2))),
% 1.13/1.30 inference(symmetry,[status(thm)],[269])).
% 1.13/1.30 tff(271,plain,
% 1.13/1.30 (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2))),
% 1.13/1.30 inference(transitivity,[status(thm)],[270, 82])).
% 1.13/1.30 tff(272,plain,
% 1.13/1.30 ((k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) <=> (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[271])).
% 1.13/1.30 tff(273,plain,
% 1.13/1.30 ((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) <=> (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))),
% 1.13/1.30 inference(symmetry,[status(thm)],[272])).
% 1.13/1.30 tff(274,plain,
% 1.13/1.30 (((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | ((~v1_relat_1(B!1)) | (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))))) <=> ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | (~v1_relat_1(B!1)) | (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(275,plain,
% 1.13/1.30 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | ((~v1_relat_1(B!1)) | (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(276,plain,
% 1.13/1.30 ((~![A: $i, B: $i] : ((~v1_relat_1(B)) | (k1_relat_1(k7_relat_1(B, A)) = k3_xboole_0(k1_relat_1(B), A)))) | (~v1_relat_1(B!1)) | (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2)))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[275, 274])).
% 1.13/1.30 tff(277,plain,
% 1.13/1.30 ((~v1_relat_1(B!1)) | (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[276, 174])).
% 1.13/1.30 tff(278,plain,
% 1.13/1.30 (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k3_xboole_0(k1_relat_1(B!1), k1_closure3(A!0, C!2))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[277, 146])).
% 1.13/1.30 tff(279,plain,
% 1.13/1.30 (k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))) = k1_relat_1(C!2)),
% 1.13/1.30 inference(transitivity,[status(thm)],[278, 162, 139, 130, 128])).
% 1.13/1.30 tff(280,plain,
% 1.13/1.30 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)))) <=> r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[279])).
% 1.13/1.30 tff(281,plain,
% 1.13/1.30 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2)) <=> r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))),
% 1.13/1.30 inference(symmetry,[status(thm)],[280])).
% 1.13/1.30 tff(282,plain,
% 1.13/1.30 (r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[247, 281])).
% 1.13/1.30 tff(283,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(284,plain,
% 1.13/1.30 (((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1))) <=> ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(285,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)))))))),
% 1.13/1.30 inference(monotonicity,[status(thm)],[284])).
% 1.13/1.30 tff(286,plain,
% 1.13/1.30 (((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[285, 283])).
% 1.13/1.30 tff(287,plain,
% 1.13/1.30 ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | ((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2))))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(288,plain,
% 1.13/1.30 ((~![A: $i, B: $i, C: $i] : ((k1_funct_1(k7_relat_1(C, A), B) = k1_funct_1(C, B)) | (~r2_hidden(B, k1_relat_1(k7_relat_1(C, A)))) | (~v1_relat_1(C)) | (~v1_funct_1(C)))) | (~v1_relat_1(B!1)) | (~v1_funct_1(B!1)) | (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.13/1.30 tff(289,plain,
% 1.13/1.30 ((k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))) | (~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)))))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[288, 261, 146, 148])).
% 1.13/1.30 tff(290,plain,
% 1.13/1.30 (k1_funct_1(k7_relat_1(B!1, k1_closure3(A!0, C!2)), tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[289, 282])).
% 1.13/1.30 tff(291,plain,
% 1.13/1.30 (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[290, 273])).
% 1.13/1.30 tff(292,plain,
% 1.13/1.30 (((~r2_hidden(tptp_fun_C_19(B!1, C!2), k1_relat_1(C!2))) | (k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))) | (~(k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2))))),
% 1.13/1.30 inference(tautology,[status(thm)],[])).
% 1.13/1.30 tff(293,plain,
% 1.13/1.30 (~(k1_funct_1(C!2, tptp_fun_C_19(B!1, C!2)) = k1_funct_1(B!1, tptp_fun_C_19(B!1, C!2)))),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[292, 245])).
% 1.13/1.30 tff(294,plain,
% 1.13/1.30 ($false),
% 1.13/1.30 inference(unit_resolution,[status(thm)],[293, 291])).
% 1.13/1.30 tff(295,plain,(~(A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.30 tff(296,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(297,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[296])).
% 1.13/1.30 tff(298,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(pull_quant,[status(thm)],[])).
% 1.13/1.30 tff(299,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C)))) <=> ![D: $i] : ((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) <=> (~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))))), pull_quant((~![D: $i] : ((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C)))))), ((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) <=> ?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))), (((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(300,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[299])).
% 1.13/1.30 tff(301,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[300, 298])).
% 1.13/1.30 tff(302,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[301, 297])).
% 1.13/1.30 tff(303,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(304,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[303])).
% 1.13/1.30 tff(305,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(transitivity,[status(thm)],[304, 302])).
% 1.13/1.30 tff(306,plain,
% 1.13/1.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) <=> ((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))), rewrite(((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), A) & r2_hidden(tptp_fun_D_4(C, B, A), B))))) <=> ((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), A) & r2_hidden(tptp_fun_D_4(C, B, A), B)))))) <=> (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C)))) & ((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))))), rewrite((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C)))) & ((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C)))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))), ((((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), A) & r2_hidden(tptp_fun_D_4(C, B, A), B)))))) <=> (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))))),
% 1.13/1.30 inference(bind,[status(th)],[])).
% 1.13/1.30 tff(307,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), A) & r2_hidden(tptp_fun_D_4(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(quant_intro,[status(thm)],[306])).
% 1.13/1.30 tff(308,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 1.13/1.30 inference(rewrite,[status(thm)],[])).
% 1.13/1.30 tff(309,axiom,(![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_xboole_0')).
% 1.13/1.30 tff(310,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : ((C = k3_xboole_0(A, B)) <=> ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.13/1.30 tff(311,plain,(
% 1.13/1.30 ![A: $i, B: $i, C: $i] : (((~(C = k3_xboole_0(A, B))) | ![D: $i] : (r2_hidden(D, C) <=> (r2_hidden(D, A) & r2_hidden(D, B)))) & ((C = k3_xboole_0(A, B)) | (~(r2_hidden(tptp_fun_D_4(C, B, A), C) <=> (r2_hidden(tptp_fun_D_4(C, B, A), A) & r2_hidden(tptp_fun_D_4(C, B, A), B))))))),
% 1.13/1.30 inference(skolemize,[status(sab)],[310])).
% 1.13/1.30 tff(312,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = k3_xboole_0(A, B))) | ![D: $i] : (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[311, 307])).
% 1.13/1.30 tff(313,plain,
% 1.13/1.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))),
% 1.13/1.30 inference(modus_ponens,[status(thm)],[312, 305])).
% 1.13/1.30 tff(314,plain,
% 1.13/1.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = k3_xboole_0(A, B))) | (~(((~r2_hidden(D, B)) | (~r2_hidden(D, A))) <=> r2_hidden(D, C))))) | (~((C = k3_xboole_0(A, B)) | (((~r2_hidden(tptp_fun_D_4(C, B, A), A)) | (~r2_hidden(tptp_fun_D_4(C, B, A), B))) <=> r2_hidden(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0))) | (~(((~r2_hidden(tptp_fun_C_19(C!2, B!1), A!0)) | (~r2_hidden(tptp_fun_C_19(C!2, B!1), k1_closure3(A!0, C!2)))) <=> r2_hidden(tptp_fun_C_19(C!2, B!1), A!0))))) | (~((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))))))),
% 1.13/1.30 inference(quant_inst,[status(thm)],[])).
% 1.13/1.30 tff(315,plain,
% 1.13/1.30 (~((~((~(A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0))) | (~(((~r2_hidden(tptp_fun_C_19(C!2, B!1), A!0)) | (~r2_hidden(tptp_fun_C_19(C!2, B!1), k1_closure3(A!0, C!2)))) <=> r2_hidden(tptp_fun_C_19(C!2, B!1), A!0))))) | (~((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[314, 313])).
% 1.13/1.31 tff(316,plain,
% 1.13/1.31 (((~((~(A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0))) | (~(((~r2_hidden(tptp_fun_C_19(C!2, B!1), A!0)) | (~r2_hidden(tptp_fun_C_19(C!2, B!1), k1_closure3(A!0, C!2)))) <=> r2_hidden(tptp_fun_C_19(C!2, B!1), A!0))))) | (~((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))))) | ((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(317,plain,
% 1.13/1.31 ((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[316, 315])).
% 1.13/1.31 tff(318,plain,
% 1.13/1.31 ((~((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))) | (A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(319,plain,
% 1.13/1.31 ((A!0 = k3_xboole_0(k1_closure3(A!0, C!2), A!0)) | (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[318, 317])).
% 1.13/1.31 tff(320,plain,
% 1.13/1.31 (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[319, 295])).
% 1.13/1.31 tff(321,assumption,(((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)), introduced(assumption)).
% 1.13/1.31 tff(322,assumption,(~((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))), introduced(assumption)).
% 1.13/1.31 tff(323,plain,
% 1.13/1.31 (((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) | r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(324,plain,
% 1.13/1.31 (r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[323, 322])).
% 1.13/1.31 tff(325,plain,
% 1.13/1.31 ((~(((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) | ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(326,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[325, 324, 322, 321])).
% 1.13/1.31 tff(327,plain,(((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) | (~(((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))), inference(lemma,lemma(discharge,[]))).
% 1.13/1.31 tff(328,plain,
% 1.13/1.31 ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[327, 320])).
% 1.13/1.31 tff(329,plain,
% 1.13/1.31 ((~(((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) | (~((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))) | r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(330,plain,
% 1.13/1.31 (r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[329, 328, 320])).
% 1.13/1.31 tff(331,plain,
% 1.13/1.31 ((~((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(332,plain,
% 1.13/1.31 (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), k1_closure3(A!0, C!2))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[331, 330, 328])).
% 1.13/1.31 tff(333,plain,
% 1.13/1.31 (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[332, 74])).
% 1.13/1.31 tff(334,plain,
% 1.13/1.31 ((((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) <=> r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))) | ((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)) | r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), a_2_0_closure3(A!0, C!2))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(335,plain,
% 1.13/1.31 ((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[334, 333, 39])).
% 1.13/1.31 tff(336,plain,
% 1.13/1.31 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(337,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[336])).
% 1.13/1.31 tff(338,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(339,plain,
% 1.13/1.31 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(340,plain,
% 1.13/1.31 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[339])).
% 1.13/1.31 tff(341,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 1.13/1.31 tff(342,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[341, 340])).
% 1.13/1.31 tff(343,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[342, 338])).
% 1.13/1.31 tff(344,plain,(
% 1.13/1.31 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(skolemize,[status(sab)],[343])).
% 1.13/1.31 tff(345,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[344, 337])).
% 1.13/1.31 tff(346,plain,
% 1.13/1.31 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(347,plain,
% 1.13/1.31 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(348,plain,
% 1.13/1.31 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[347, 346])).
% 1.13/1.31 tff(349,plain,
% 1.13/1.31 (m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[348, 345, 330])).
% 1.13/1.31 tff(350,plain,
% 1.13/1.31 ((~((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0))) | (~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(351,plain,
% 1.13/1.31 ((~((~m1_subset_1(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0))) | (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0)),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[350, 349])).
% 1.13/1.31 tff(352,plain,
% 1.13/1.31 (k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))) = k1_xboole_0),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[351, 335])).
% 1.13/1.31 tff(353,plain,
% 1.13/1.31 (v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)))) <=> v1_xboole_0(k1_xboole_0)),
% 1.13/1.31 inference(monotonicity,[status(thm)],[352])).
% 1.13/1.31 tff(354,plain,
% 1.13/1.31 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))),
% 1.13/1.31 inference(symmetry,[status(thm)],[353])).
% 1.13/1.31 tff(355,plain,
% 1.13/1.31 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(356,axiom,(v1_xboole_0(k1_xboole_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 1.13/1.31 tff(357,plain,
% 1.13/1.31 (v1_xboole_0(k1_xboole_0)),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.13/1.31 tff(358,plain,
% 1.13/1.31 (v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[357, 354])).
% 1.13/1.31 tff(359,plain,
% 1.13/1.31 (^[A: $i, B: $i] : refl(((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))) <=> ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(360,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[359])).
% 1.13/1.31 tff(361,plain,
% 1.13/1.31 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))) <=> ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(362,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[361])).
% 1.13/1.31 tff(363,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(transitivity,[status(thm)],[362, 360])).
% 1.13/1.31 tff(364,plain,
% 1.13/1.31 (^[A: $i, B: $i] : rewrite(((~m1_pboole(B, A)) | (((~v2_relat_1(B)) | ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))) & (v2_relat_1(B) | (r2_hidden(tptp_fun_C_3(B, A), A) & v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))) <=> ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))))))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(365,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (((~v2_relat_1(B)) | ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))) & (v2_relat_1(B) | (r2_hidden(tptp_fun_C_3(B, A), A) & v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A))))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[364])).
% 1.13/1.31 tff(366,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(367,plain,
% 1.13/1.31 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))) <=> (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))), ((m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))) <=> (m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))))), rewrite((m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))) <=> ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))), ((m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))) <=> ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))))),
% 1.13/1.31 inference(bind,[status(th)],[])).
% 1.13/1.31 tff(368,plain,
% 1.13/1.31 (![A: $i, B: $i] : (m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C)))))) <=> ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))),
% 1.13/1.31 inference(quant_intro,[status(thm)],[367])).
% 1.13/1.31 tff(369,axiom,(![A: $i, B: $i] : (m1_pboole(B, A) => (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d16_pboole')).
% 1.13/1.31 tff(370,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[369, 368])).
% 1.13/1.31 tff(371,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (v2_relat_1(B) <=> ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[370, 366])).
% 1.13/1.31 tff(372,plain,(
% 1.13/1.31 ![A: $i, B: $i] : ((~m1_pboole(B, A)) | (((~v2_relat_1(B)) | ![C: $i] : (~(r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))))) & (v2_relat_1(B) | (r2_hidden(tptp_fun_C_3(B, A), A) & v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))),
% 1.13/1.31 inference(skolemize,[status(sab)],[371])).
% 1.13/1.31 tff(373,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[372, 365])).
% 1.13/1.31 tff(374,plain,
% 1.13/1.31 (![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[373, 363])).
% 1.13/1.31 tff(375,plain,
% 1.13/1.31 (((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))) | ((~m1_pboole(C!2, A!0)) | (~((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0)))))))))))) <=> ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))) | (~m1_pboole(C!2, A!0)) | (~((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0)))))))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(376,plain,
% 1.13/1.31 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))) | ((~m1_pboole(C!2, A!0)) | (~((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0)))))))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(377,plain,
% 1.13/1.31 ((~![A: $i, B: $i] : ((~m1_pboole(B, A)) | (~((~((~v2_relat_1(B)) | ![C: $i] : ((~r2_hidden(C, A)) | (~v1_xboole_0(k1_funct_1(B, C)))))) | (~(v2_relat_1(B) | (~((~r2_hidden(tptp_fun_C_3(B, A), A)) | (~v1_xboole_0(k1_funct_1(B, tptp_fun_C_3(B, A)))))))))))) | (~m1_pboole(C!2, A!0)) | (~((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0))))))))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.13/1.31 tff(378,plain,
% 1.13/1.31 (~((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0)))))))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[377, 31, 374])).
% 1.13/1.31 tff(379,plain,
% 1.13/1.31 (((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~(v2_relat_1(C!2) | (~((~r2_hidden(tptp_fun_C_3(C!2, A!0), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_C_3(C!2, A!0))))))))) | ((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(380,plain,
% 1.13/1.31 ((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[379, 378])).
% 1.13/1.31 tff(381,plain,
% 1.13/1.31 (v2_relat_1(C!2)),
% 1.13/1.31 inference(and_elim,[status(thm)],[30])).
% 1.13/1.31 tff(382,plain,
% 1.13/1.31 ((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | (~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))),
% 1.13/1.31 inference(tautology,[status(thm)],[])).
% 1.13/1.31 tff(383,plain,
% 1.13/1.31 ((~((~v2_relat_1(C!2)) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C)))))) | ![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[382, 381])).
% 1.13/1.31 tff(384,plain,
% 1.13/1.31 (![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[383, 380])).
% 1.13/1.31 tff(385,plain,
% 1.13/1.31 (((~![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))) | ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))))) <=> ((~![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))))),
% 1.13/1.31 inference(rewrite,[status(thm)],[])).
% 1.13/1.31 tff(386,plain,
% 1.13/1.31 ((~![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))) | ((~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))))),
% 1.13/1.31 inference(quant_inst,[status(thm)],[])).
% 1.13/1.31 tff(387,plain,
% 1.13/1.31 ((~![C: $i] : ((~r2_hidden(C, A!0)) | (~v1_xboole_0(k1_funct_1(C!2, C))))) | (~r2_hidden(tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)), A!0)) | (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2)))))),
% 1.13/1.31 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.13/1.31 tff(388,plain,
% 1.13/1.31 (~v1_xboole_0(k1_funct_1(C!2, tptp_fun_D_4(A!0, A!0, k1_closure3(A!0, C!2))))),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[387, 384, 330])).
% 1.13/1.31 tff(389,plain,
% 1.13/1.31 ($false),
% 1.13/1.31 inference(unit_resolution,[status(thm)],[388, 358])).
% 1.13/1.31 % SZS output end Proof
% 1.13/1.32 % E exiting
%------------------------------------------------------------------------------