%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT033+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:29 AM UTC 2025
% Result : Theorem 4.03s 4.27s
% Output : Proof 4.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT033+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 11:58:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.03/4.27 % SZS status Theorem
% 4.03/4.27 % SZS output start Proof
% 4.03/4.27 tff(r1_tarski_type, type, (
% 4.03/4.27 r1_tarski: ( $i * $i ) > $o)).
% 4.03/4.27 tff(k17_ens_1_type, type, (
% 4.03/4.27 k17_ens_1: $i > $i)).
% 4.03/4.27 tff(tptp_fun_A_0_type, type, (
% 4.03/4.27 tptp_fun_A_0: $i)).
% 4.03/4.27 tff(m2_cat_1_type, type, (
% 4.03/4.27 m2_cat_1: ( $i * $i * $i ) > $o)).
% 4.03/4.27 tff(k12_ens_1_type, type, (
% 4.03/4.27 k12_ens_1: $i > $i)).
% 4.03/4.27 tff(k20_ens_1_type, type, (
% 4.03/4.27 k20_ens_1: ( $i * $i ) > $i)).
% 4.03/4.27 tff(tptp_fun_B_1_type, type, (
% 4.03/4.27 tptp_fun_B_1: $i)).
% 4.03/4.27 tff(k1_yoneda_1_type, type, (
% 4.03/4.27 k1_yoneda_1: $i > $i)).
% 4.03/4.27 tff(v2_cat_1_type, type, (
% 4.03/4.27 v2_cat_1: $i > $o)).
% 4.03/4.27 tff(l1_cat_1_type, type, (
% 4.03/4.27 l1_cat_1: $i > $o)).
% 4.03/4.27 tff(m1_subset_1_type, type, (
% 4.03/4.27 m1_subset_1: ( $i * $i ) > $o)).
% 4.03/4.27 tff(u1_cat_1_type, type, (
% 4.03/4.27 u1_cat_1: $i > $i)).
% 4.03/4.27 tff(v1_xboole_0_type, type, (
% 4.03/4.27 v1_xboole_0: $i > $o)).
% 4.03/4.27 tff(1,plain,
% 4.03/4.27 (^[A: $i] : refl(((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(2,plain,
% 4.03/4.27 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[1])).
% 4.03/4.27 tff(3,plain,
% 4.03/4.27 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))), (((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(4,plain,
% 4.03/4.27 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[3])).
% 4.03/4.27 tff(5,plain,
% 4.03/4.27 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(6,plain,
% 4.03/4.27 (^[A: $i] : rewrite(((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(7,plain,
% 4.03/4.27 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A)))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[6])).
% 4.03/4.27 tff(8,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_yoneda_1')).
% 4.03/4.27 tff(9,plain,
% 4.03/4.27 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.03/4.27 tff(10,plain,
% 4.03/4.27 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[9, 5])).
% 4.03/4.27 tff(11,plain,(
% 4.03/4.27 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | (k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))))),
% 4.03/4.27 inference(skolemize,[status(sab)],[10])).
% 4.03/4.27 tff(12,plain,
% 4.03/4.27 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[11, 4])).
% 4.03/4.27 tff(13,plain,
% 4.03/4.27 (![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[12, 2])).
% 4.03/4.27 tff(14,plain,
% 4.03/4.27 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(15,plain,
% 4.03/4.27 ((~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A)))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(16,plain,
% 4.03/4.27 ((~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : (m1_subset_1(B, u1_cat_1(A)) => m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A)))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(17,axiom,(~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : (m1_subset_1(B, u1_cat_1(A)) => m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_yoneda_1')).
% 4.03/4.27 tff(18,plain,
% 4.03/4.27 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[17, 16])).
% 4.03/4.27 tff(19,plain,
% 4.03/4.27 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[18, 15])).
% 4.03/4.27 tff(20,plain,
% 4.03/4.27 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[19, 15])).
% 4.03/4.27 tff(21,plain,
% 4.03/4.27 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~m1_subset_1(B, u1_cat_1(A))) | m2_cat_1(k20_ens_1(A, B), A, k1_yoneda_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[20, 15])).
% 4.03/4.27 tff(22,plain,
% 4.03/4.27 (v2_cat_1(A!0) & l1_cat_1(A!0) & (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[21, 14])).
% 4.03/4.27 tff(23,plain,
% 4.03/4.27 (l1_cat_1(A!0)),
% 4.03/4.27 inference(and_elim,[status(thm)],[22])).
% 4.03/4.27 tff(24,plain,
% 4.03/4.27 (v2_cat_1(A!0)),
% 4.03/4.27 inference(and_elim,[status(thm)],[22])).
% 4.03/4.27 tff(25,plain,
% 4.03/4.27 (((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(26,plain,
% 4.03/4.27 ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 4.03/4.27 inference(quant_inst,[status(thm)],[])).
% 4.03/4.27 tff(27,plain,
% 4.03/4.27 ((~![A: $i] : ((k1_yoneda_1(A) = k12_ens_1(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[26, 25])).
% 4.03/4.27 tff(28,plain,
% 4.03/4.27 (k1_yoneda_1(A!0) = k12_ens_1(k17_ens_1(A!0))),
% 4.03/4.27 inference(unit_resolution,[status(thm)],[27, 24, 23, 13])).
% 4.03/4.27 tff(29,plain,
% 4.03/4.27 (k12_ens_1(k17_ens_1(A!0)) = k1_yoneda_1(A!0)),
% 4.03/4.27 inference(symmetry,[status(thm)],[28])).
% 4.03/4.27 tff(30,plain,
% 4.03/4.27 (m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) <=> m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))),
% 4.03/4.27 inference(monotonicity,[status(thm)],[29])).
% 4.03/4.27 tff(31,plain,
% 4.03/4.27 (m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)) <=> m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 4.03/4.27 inference(symmetry,[status(thm)],[30])).
% 4.03/4.27 tff(32,plain,
% 4.03/4.27 ((~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))) <=> (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 4.03/4.27 inference(monotonicity,[status(thm)],[31])).
% 4.03/4.27 tff(33,plain,
% 4.03/4.27 (~((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0)))),
% 4.03/4.27 inference(and_elim,[status(thm)],[22])).
% 4.03/4.27 tff(34,plain,
% 4.03/4.27 (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k1_yoneda_1(A!0))),
% 4.03/4.27 inference(or_elim,[status(thm)],[33])).
% 4.03/4.27 tff(35,plain,
% 4.03/4.27 (~m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[34, 32])).
% 4.03/4.27 tff(36,plain,
% 4.03/4.27 (^[A: $i] : refl(((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(37,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[36])).
% 4.03/4.27 tff(38,plain,
% 4.03/4.27 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), (((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | ((~l1_cat_1(A)) | (~v2_cat_1(A)))))), rewrite(((~v1_xboole_0(k17_ens_1(A))) | ((~l1_cat_1(A)) | (~v2_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))), (((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(39,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[38])).
% 4.03/4.27 tff(40,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(41,plain,
% 4.03/4.27 (^[A: $i] : rewrite(((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A)))) <=> ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(42,plain,
% 4.03/4.27 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A)))) <=> ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[41])).
% 4.03/4.27 tff(43,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => (~v1_xboole_0(k17_ens_1(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_ens_1')).
% 4.03/4.27 tff(44,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.03/4.27 tff(45,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[44, 40])).
% 4.03/4.27 tff(46,plain,(
% 4.03/4.27 ![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~(v2_cat_1(A) & l1_cat_1(A))))),
% 4.03/4.27 inference(skolemize,[status(sab)],[45])).
% 4.03/4.27 tff(47,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[46, 39])).
% 4.03/4.27 tff(48,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[47, 37])).
% 4.03/4.27 tff(49,plain,
% 4.03/4.27 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(50,plain,
% 4.03/4.27 (((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0))) <=> ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(51,plain,
% 4.03/4.27 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0)))))),
% 4.03/4.27 inference(monotonicity,[status(thm)],[50])).
% 4.03/4.27 tff(52,plain,
% 4.03/4.27 (((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))) <=> ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0))))),
% 4.03/4.27 inference(transitivity,[status(thm)],[51, 49])).
% 4.03/4.27 tff(53,plain,
% 4.03/4.27 ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | ((~v1_xboole_0(k17_ens_1(A!0))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)))),
% 4.03/4.27 inference(quant_inst,[status(thm)],[])).
% 4.03/4.27 tff(54,plain,
% 4.03/4.27 ((~![A: $i] : ((~v1_xboole_0(k17_ens_1(A))) | (~l1_cat_1(A)) | (~v2_cat_1(A)))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | (~v1_xboole_0(k17_ens_1(A!0)))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[53, 52])).
% 4.03/4.27 tff(55,plain,
% 4.03/4.27 (~v1_xboole_0(k17_ens_1(A!0))),
% 4.03/4.27 inference(unit_resolution,[status(thm)],[54, 24, 23, 48])).
% 4.03/4.27 tff(56,plain,
% 4.03/4.27 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(57,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[56])).
% 4.03/4.27 tff(58,plain,
% 4.03/4.27 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(59,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[58])).
% 4.03/4.27 tff(60,plain,
% 4.03/4.27 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(61,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[60])).
% 4.03/4.27 tff(62,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(transitivity,[status(thm)],[61, 59])).
% 4.03/4.27 tff(63,plain,
% 4.03/4.27 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B)))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(64,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[63])).
% 4.03/4.27 tff(65,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(66,plain,
% 4.03/4.27 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))) <=> ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))), ((m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m1_subset_1(C, u1_cat_1(B)) => ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))), rewrite((m1_subset_1(C, u1_cat_1(B)) => ((~r1_tarski(k17_ens_1(B), A)) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))), ((m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))) <=> ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))), (((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))))),
% 4.03/4.27 inference(bind,[status(th)],[])).
% 4.03/4.27 tff(67,plain,
% 4.03/4.27 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(quant_intro,[status(thm)],[66])).
% 4.03/4.27 tff(68,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : (m1_subset_1(C, u1_cat_1(B)) => (r1_tarski(k17_ens_1(B), A) => m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t49_ens_1')).
% 4.03/4.27 tff(69,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[68, 67])).
% 4.03/4.27 tff(70,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[69, 65])).
% 4.03/4.27 tff(71,plain,(
% 4.03/4.27 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(skolemize,[status(sab)],[70])).
% 4.03/4.27 tff(72,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[71, 64])).
% 4.03/4.27 tff(73,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A))) | (~v2_cat_1(B))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[72, 62])).
% 4.03/4.27 tff(74,plain,
% 4.03/4.27 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[73, 57])).
% 4.03/4.27 tff(75,plain,
% 4.03/4.27 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(76,plain,
% 4.03/4.27 ((v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) <=> (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(77,plain,
% 4.03/4.27 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))))),
% 4.03/4.27 inference(monotonicity,[status(thm)],[76])).
% 4.03/4.27 tff(78,plain,
% 4.03/4.27 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 4.03/4.27 inference(transitivity,[status(thm)],[77, 75])).
% 4.03/4.27 tff(79,plain,
% 4.03/4.27 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | (v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0))))))),
% 4.03/4.27 inference(quant_inst,[status(thm)],[])).
% 4.03/4.27 tff(80,plain,
% 4.03/4.27 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(A)) | (~m1_subset_1(C, u1_cat_1(B))) | (~r1_tarski(k17_ens_1(B), A)))))) | v1_xboole_0(k17_ens_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[79, 78])).
% 4.03/4.27 tff(81,plain,
% 4.03/4.27 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))),
% 4.03/4.27 inference(unit_resolution,[status(thm)],[80, 74, 55])).
% 4.03/4.27 tff(82,plain,
% 4.03/4.27 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(83,plain,
% 4.03/4.27 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))))),
% 4.03/4.27 inference(quant_inst,[status(thm)],[])).
% 4.03/4.27 tff(84,plain,
% 4.03/4.27 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(B))) | m2_cat_1(k20_ens_1(B, C), B, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(B), k17_ens_1(A!0)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 4.03/4.27 inference(modus_ponens,[status(thm)],[83, 82])).
% 4.03/4.27 tff(85,plain,
% 4.03/4.27 (![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 4.03/4.27 inference(unit_resolution,[status(thm)],[84, 24, 23, 81])).
% 4.03/4.27 tff(86,plain,
% 4.03/4.27 (m1_subset_1(B!1, u1_cat_1(A!0))),
% 4.03/4.27 inference(or_elim,[status(thm)],[33])).
% 4.03/4.27 tff(87,plain,
% 4.03/4.27 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(88,plain,
% 4.03/4.27 (((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0)))) <=> ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 4.03/4.27 inference(rewrite,[status(thm)],[])).
% 4.03/4.27 tff(89,plain,
% 4.03/4.27 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))))),
% 4.13/4.30 inference(monotonicity,[status(thm)],[88])).
% 4.13/4.30 tff(90,plain,
% 4.13/4.30 (((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))))),
% 4.13/4.30 inference(transitivity,[status(thm)],[89, 87])).
% 4.13/4.30 tff(91,plain,
% 4.13/4.30 ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | ((~m1_subset_1(B!1, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))),
% 4.13/4.30 inference(quant_inst,[status(thm)],[])).
% 4.13/4.30 tff(92,plain,
% 4.13/4.30 ((~![C: $i] : ((~m1_subset_1(C, u1_cat_1(A!0))) | m2_cat_1(k20_ens_1(A!0, C), A!0, k12_ens_1(k17_ens_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))))) | (~m1_subset_1(B!1, u1_cat_1(A!0))) | (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 4.13/4.30 inference(modus_ponens,[status(thm)],[91, 90])).
% 4.13/4.30 tff(93,plain,
% 4.13/4.30 ((~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))) | m2_cat_1(k20_ens_1(A!0, B!1), A!0, k12_ens_1(k17_ens_1(A!0)))),
% 4.13/4.30 inference(unit_resolution,[status(thm)],[92, 86, 85])).
% 4.13/4.30 tff(94,plain,
% 4.13/4.30 (~r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))),
% 4.13/4.30 inference(unit_resolution,[status(thm)],[93, 35])).
% 4.13/4.30 tff(95,plain,
% 4.13/4.30 (^[A: $i] : refl(r1_tarski(A, A) <=> r1_tarski(A, A))),
% 4.13/4.30 inference(bind,[status(th)],[])).
% 4.13/4.30 tff(96,plain,
% 4.13/4.30 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(quant_intro,[status(thm)],[95])).
% 4.13/4.30 tff(97,plain,
% 4.13/4.30 (![A: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(rewrite,[status(thm)],[])).
% 4.13/4.30 tff(98,plain,
% 4.13/4.30 (![A: $i, B: $i] : r1_tarski(A, A) <=> ![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(elim_unused_vars,[status(thm)],[])).
% 4.13/4.30 tff(99,axiom,(![A: $i, B: $i] : r1_tarski(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 4.13/4.30 tff(100,plain,
% 4.13/4.30 (![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(modus_ponens,[status(thm)],[99, 98])).
% 4.13/4.30 tff(101,plain,
% 4.13/4.30 (![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(modus_ponens,[status(thm)],[100, 97])).
% 4.13/4.30 tff(102,plain,(
% 4.13/4.30 ![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(skolemize,[status(sab)],[101])).
% 4.13/4.30 tff(103,plain,
% 4.13/4.30 (![A: $i] : r1_tarski(A, A)),
% 4.13/4.30 inference(modus_ponens,[status(thm)],[102, 96])).
% 4.13/4.30 tff(104,plain,
% 4.13/4.30 ((~![A: $i] : r1_tarski(A, A)) | r1_tarski(k17_ens_1(A!0), k17_ens_1(A!0))),
% 4.13/4.30 inference(quant_inst,[status(thm)],[])).
% 4.13/4.30 tff(105,plain,
% 4.13/4.30 ($false),
% 4.13/4.30 inference(unit_resolution,[status(thm)],[104, 103, 94])).
% 4.13/4.30 % SZS output end Proof
% 4.13/4.31 % E exiting
%------------------------------------------------------------------------------