%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP622+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:08:11 AM UTC 2025
% Result : Theorem 0.41s 0.57s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP622+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 16:28:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.41/0.57 % SZS status Theorem
% 0.41/0.57 % SZS output start Proof
% 0.41/0.57 tff(m2_relset_1_type, type, (
% 0.41/0.57 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(u1_struct_0_type, type, (
% 0.41/0.57 u1_struct_0: $i > $i)).
% 0.41/0.57 tff(tptp_fun_A_0_type, type, (
% 0.41/0.57 tptp_fun_A_0: $i)).
% 0.41/0.57 tff(tptp_fun_C_1_type, type, (
% 0.41/0.57 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.41/0.57 tff(k4_autgroup_type, type, (
% 0.41/0.57 k4_autgroup: $i > $i)).
% 0.41/0.57 tff(k1_fraenkel_type, type, (
% 0.41/0.57 k1_fraenkel: ( $i * $i ) > $i)).
% 0.41/0.57 tff(v1_funct_2_type, type, (
% 0.41/0.57 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(v1_funct_1_type, type, (
% 0.41/0.57 v1_funct_1: $i > $o)).
% 0.41/0.57 tff(m2_fraenkel_type, type, (
% 0.41/0.57 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.41/0.57 tff(m1_subset_1_type, type, (
% 0.41/0.57 m1_subset_1: ( $i * $i ) > $o)).
% 0.41/0.57 tff(m1_fraenkel_type, type, (
% 0.41/0.57 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(v4_group_1_type, type, (
% 0.41/0.57 v4_group_1: $i > $o)).
% 0.41/0.57 tff(v3_group_1_type, type, (
% 0.41/0.57 v3_group_1: $i > $o)).
% 0.41/0.57 tff(l1_group_1_type, type, (
% 0.41/0.57 l1_group_1: $i > $o)).
% 0.41/0.57 tff(v1_group_1_type, type, (
% 0.41/0.57 v1_group_1: $i > $o)).
% 0.41/0.57 tff(v3_struct_0_type, type, (
% 0.41/0.57 v3_struct_0: $i > $o)).
% 0.41/0.57 tff(r1_tarski_type, type, (
% 0.41/0.57 r1_tarski: ( $i * $i ) > $o)).
% 0.41/0.57 tff(v1_xboole_0_type, type, (
% 0.41/0.57 v1_xboole_0: $i > $o)).
% 0.41/0.57 tff(l1_struct_0_type, type, (
% 0.41/0.57 l1_struct_0: $i > $o)).
% 0.41/0.57 tff(r2_hidden_type, type, (
% 0.41/0.57 r2_hidden: ( $i * $i ) > $o)).
% 0.41/0.57 tff(k1_funct_2_type, type, (
% 0.41/0.57 k1_funct_2: ( $i * $i ) > $i)).
% 0.41/0.57 tff(1,plain,
% 0.41/0.57 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(2,plain,
% 0.41/0.57 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.41/0.57 tff(3,plain,
% 0.41/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(4,plain,
% 0.41/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.41/0.57 tff(5,plain,
% 0.41/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(6,plain,
% 0.41/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(7,plain,
% 0.41/0.57 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[6])).
% 0.41/0.57 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 0.41/0.57 tff(9,plain,
% 0.41/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.41/0.57 tff(10,plain,
% 0.41/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.41/0.57 tff(11,plain,(
% 0.41/0.57 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.41/0.57 inference(skolemize,[status(sab)],[10])).
% 0.41/0.57 tff(12,plain,
% 0.41/0.57 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.41/0.57 tff(13,plain,
% 0.41/0.57 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.41/0.57 tff(14,plain,
% 0.41/0.57 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(15,plain,
% 0.41/0.57 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(16,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_autgroup')).
% 0.41/0.57 tff(17,plain,
% 0.41/0.57 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.41/0.57 tff(18,plain,
% 0.41/0.57 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.41/0.57 tff(19,plain,
% 0.41/0.57 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.41/0.57 tff(20,plain,
% 0.41/0.57 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.41/0.57 tff(21,plain,(
% 0.41/0.57 ~((~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))) | r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.57 inference(skolemize,[status(sab)],[20])).
% 0.41/0.57 tff(22,plain,
% 0.41/0.57 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)),
% 0.41/0.57 inference(or_elim,[status(thm)],[21])).
% 0.41/0.57 tff(23,plain,
% 0.41/0.57 (l1_group_1(A!0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[22])).
% 0.41/0.57 tff(24,plain,
% 0.41/0.57 (v4_group_1(A!0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[22])).
% 0.41/0.57 tff(25,plain,
% 0.41/0.57 (v3_group_1(A!0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[22])).
% 0.41/0.57 tff(26,plain,
% 0.41/0.57 (v1_group_1(A!0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[22])).
% 0.41/0.57 tff(27,plain,
% 0.41/0.57 (~v3_struct_0(A!0)),
% 0.41/0.57 inference(and_elim,[status(thm)],[22])).
% 0.41/0.57 tff(28,plain,
% 0.41/0.57 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(29,plain,
% 0.41/0.57 ((v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(30,plain,
% 0.41/0.57 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.41/0.58 tff(31,plain,
% 0.41/0.58 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.41/0.58 inference(transitivity,[status(thm)],[30, 28])).
% 0.41/0.58 tff(32,plain,
% 0.41/0.58 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(33,plain,
% 0.41/0.58 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.41/0.58 tff(34,plain,
% 0.41/0.58 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 0.41/0.58 tff(35,plain,
% 0.41/0.58 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(36,plain,
% 0.41/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[35])).
% 0.41/0.58 tff(37,plain,
% 0.41/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(38,plain,
% 0.41/0.58 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(39,plain,
% 0.41/0.58 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[38])).
% 0.41/0.58 tff(40,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.41/0.58 tff(41,plain,
% 0.41/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.41/0.58 tff(42,plain,
% 0.41/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.41/0.58 tff(43,plain,(
% 0.41/0.58 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[42])).
% 0.41/0.58 tff(44,plain,
% 0.41/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.41/0.58 tff(45,plain,
% 0.41/0.58 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(46,plain,
% 0.41/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(47,plain,
% 0.41/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.41/0.58 tff(48,plain,
% 0.41/0.58 (l1_struct_0(A!0)),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[47, 23, 44])).
% 0.41/0.58 tff(49,plain,
% 0.41/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(50,plain,
% 0.41/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[49])).
% 0.41/0.58 tff(51,plain,
% 0.41/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(52,plain,
% 0.41/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[51])).
% 0.41/0.58 tff(53,plain,
% 0.41/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(54,plain,
% 0.41/0.58 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(55,plain,
% 0.41/0.58 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[54])).
% 0.41/0.58 tff(56,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.41/0.58 tff(57,plain,
% 0.41/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.41/0.58 tff(58,plain,
% 0.41/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.41/0.58 tff(59,plain,(
% 0.41/0.58 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.41/0.58 inference(skolemize,[status(sab)],[58])).
% 0.41/0.58 tff(60,plain,
% 0.41/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.41/0.58 tff(61,plain,
% 0.41/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.41/0.58 tff(62,plain,
% 0.41/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(63,plain,
% 0.41/0.58 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(64,plain,
% 0.41/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[63])).
% 0.41/0.58 tff(65,plain,
% 0.41/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[64, 62])).
% 0.41/0.58 tff(66,plain,
% 0.41/0.58 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(67,plain,
% 0.41/0.58 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.41/0.58 tff(68,plain,
% 0.41/0.58 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[67, 27, 61])).
% 0.41/0.58 tff(69,plain,
% 0.41/0.58 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[68, 48])).
% 0.41/0.58 tff(70,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(71,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[70])).
% 0.41/0.58 tff(72,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(73,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[72])).
% 0.41/0.58 tff(74,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(75,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[74])).
% 0.41/0.58 tff(76,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(transitivity,[status(thm)],[75, 73])).
% 0.41/0.58 tff(77,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(78,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[77])).
% 0.41/0.58 tff(79,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(80,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(81,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[80])).
% 0.41/0.58 tff(82,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 0.41/0.58 tff(83,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.41/0.58 tff(84,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.41/0.58 tff(85,plain,(
% 0.41/0.58 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[84])).
% 0.41/0.58 tff(86,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.41/0.58 tff(87,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.41/0.58 tff(88,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[87, 71])).
% 0.41/0.58 tff(89,plain,
% 0.41/0.58 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(90,plain,
% 0.41/0.58 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(91,plain,
% 0.41/0.58 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.41/0.58 tff(92,plain,
% 0.41/0.58 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[91, 88, 69, 34])).
% 0.41/0.58 tff(93,plain,
% 0.41/0.58 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))) | (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(94,plain,
% 0.41/0.58 (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.41/0.58 tff(95,plain,
% 0.41/0.58 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(96,plain,
% 0.41/0.58 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[95])).
% 0.41/0.58 tff(97,plain,
% 0.41/0.58 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(98,plain,
% 0.41/0.58 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[97])).
% 0.41/0.58 tff(99,plain,
% 0.41/0.58 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[98, 96])).
% 0.41/0.58 tff(100,plain,
% 0.41/0.58 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(101,plain,
% 0.41/0.58 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[100])).
% 0.41/0.58 tff(102,plain,
% 0.41/0.58 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(103,plain,
% 0.41/0.58 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(104,plain,
% 0.41/0.58 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[103])).
% 0.41/0.58 tff(105,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.41/0.58 tff(106,plain,
% 0.41/0.58 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.41/0.58 tff(107,plain,
% 0.41/0.58 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.41/0.58 tff(108,plain,(
% 0.41/0.58 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))),
% 0.41/0.58 inference(skolemize,[status(sab)],[107])).
% 0.41/0.58 tff(109,plain,
% 0.41/0.58 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.41/0.58 tff(110,plain,
% 0.41/0.58 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.41/0.58 tff(111,plain,
% 0.41/0.58 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))) | (~((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(112,plain,
% 0.41/0.58 (~((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.41/0.58 tff(113,plain,
% 0.41/0.58 (((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))))) | (r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(114,plain,
% 0.41/0.58 (r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.41/0.58 tff(115,plain,
% 0.41/0.58 (~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.58 inference(or_elim,[status(thm)],[21])).
% 0.41/0.58 tff(116,plain,
% 0.41/0.58 ((~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))) | r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(117,plain,
% 0.41/0.58 ((~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.41/0.58 tff(118,plain,
% 0.41/0.58 (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[117, 114])).
% 0.41/0.58 tff(119,plain,
% 0.41/0.58 (((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(120,plain,
% 0.41/0.58 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.41/0.58 tff(121,plain,
% 0.41/0.58 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(122,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[121])).
% 0.41/0.58 tff(123,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(124,plain,
% 0.41/0.58 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(125,plain,
% 0.41/0.58 (![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))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[124])).
% 0.41/0.58 tff(126,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 0.41/0.58 tff(127,plain,
% 0.41/0.58 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.41/0.58 tff(128,plain,
% 0.41/0.58 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.41/0.58 tff(129,plain,(
% 0.41/0.58 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.41/0.58 inference(skolemize,[status(sab)],[128])).
% 0.41/0.58 tff(130,plain,
% 0.41/0.58 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.41/0.58 tff(131,plain,
% 0.41/0.58 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(132,plain,
% 0.41/0.58 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(133,plain,
% 0.41/0.58 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.41/0.58 tff(134,plain,
% 0.41/0.58 (m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[133, 130, 120])).
% 0.41/0.58 tff(135,plain,
% 0.41/0.58 ((~(m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.41/0.58 inference(tautology,[status(thm)],[])).
% 0.41/0.58 tff(136,plain,
% 0.41/0.58 ((~(m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.41/0.58 tff(137,plain,
% 0.41/0.58 (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[136, 94])).
% 0.41/0.58 tff(138,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(139,plain,
% 0.41/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[138])).
% 0.41/0.58 tff(140,plain,
% 0.41/0.58 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(141,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[140])).
% 0.41/0.59 tff(142,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[141, 139])).
% 0.41/0.59 tff(143,plain,
% 0.41/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(144,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[143])).
% 0.41/0.59 tff(145,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(146,plain,
% 0.41/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> (m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), rewrite((m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), (![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(147,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[146])).
% 0.41/0.59 tff(148,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_fraenkel')).
% 0.41/0.59 tff(149,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.41/0.59 tff(150,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.41/0.59 tff(151,plain,(
% 0.41/0.59 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.41/0.59 inference(skolemize,[status(sab)],[150])).
% 0.41/0.59 tff(152,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.41/0.59 tff(153,plain,
% 0.41/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.41/0.59 tff(154,plain,
% 0.41/0.59 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(155,plain,
% 0.41/0.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(156,plain,
% 0.41/0.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.41/0.59 tff(157,plain,
% 0.41/0.59 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[156, 153, 69, 34])).
% 0.41/0.59 tff(158,plain,
% 0.41/0.59 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(159,plain,
% 0.41/0.59 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(160,plain,
% 0.41/0.59 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.41/0.59 tff(161,plain,
% 0.41/0.59 (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[160, 157, 137])).
% 0.41/0.59 tff(162,plain,
% 0.41/0.59 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(tautology,[status(thm)],[])).
% 0.41/0.59 tff(163,plain,
% 0.41/0.59 (m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.41/0.59 tff(164,plain,
% 0.41/0.59 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(165,plain,
% 0.41/0.59 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[164])).
% 0.41/0.59 tff(166,plain,
% 0.41/0.59 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(167,plain,
% 0.41/0.59 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(168,plain,
% 0.41/0.59 (![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[167])).
% 0.41/0.59 tff(169,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_fraenkel')).
% 0.41/0.59 tff(170,plain,
% 0.41/0.59 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.41/0.59 tff(171,plain,
% 0.41/0.59 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.41/0.59 tff(172,plain,(
% 0.41/0.59 ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[171])).
% 0.41/0.59 tff(173,plain,
% 0.41/0.59 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[172, 165])).
% 0.41/0.59 tff(174,plain,
% 0.41/0.59 (((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(175,plain,
% 0.41/0.59 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(176,plain,
% 0.41/0.59 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.41/0.59 tff(177,plain,
% 0.41/0.59 (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[176, 173])).
% 0.41/0.59 tff(178,plain,
% 0.41/0.59 (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[177, 69])).
% 0.41/0.59 tff(179,plain,
% 0.41/0.59 (k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(symmetry,[status(thm)],[178])).
% 0.41/0.59 tff(180,plain,
% 0.41/0.59 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[179])).
% 0.41/0.59 tff(181,plain,
% 0.41/0.59 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) <=> r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(symmetry,[status(thm)],[180])).
% 0.41/0.59 tff(182,plain,
% 0.41/0.59 ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[181])).
% 0.41/0.59 tff(183,plain,
% 0.41/0.59 (((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(tautology,[status(thm)],[])).
% 0.41/0.59 tff(184,plain,
% 0.41/0.59 (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[183, 118])).
% 0.41/0.59 tff(185,plain,
% 0.41/0.59 (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[184, 182])).
% 0.41/0.59 tff(186,plain,
% 0.41/0.59 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 0.41/0.59 inference(tautology,[status(thm)],[])).
% 0.41/0.59 tff(187,plain,
% 0.41/0.59 (v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[186, 161])).
% 0.41/0.59 tff(188,plain,
% 0.41/0.59 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(tautology,[status(thm)],[])).
% 0.41/0.59 tff(189,plain,
% 0.41/0.59 (v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[188, 161])).
% 0.41/0.59 tff(190,plain,
% 0.41/0.59 (^[A: $i, B: $i] : refl((r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(191,plain,
% 0.41/0.59 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) <=> ![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[190])).
% 0.41/0.59 tff(192,plain,
% 0.41/0.59 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))), ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))), ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))), (((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))), (((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(193,plain,
% 0.41/0.59 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[192])).
% 0.41/0.59 tff(194,plain,
% 0.41/0.59 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(195,plain,
% 0.41/0.59 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) <=> (v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))), ((((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))), ((((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(196,plain,
% 0.41/0.59 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[195])).
% 0.41/0.59 tff(197,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_funct_2')).
% 0.41/0.59 tff(198,plain,
% 0.41/0.59 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.41/0.59 tff(199,plain,
% 0.41/0.59 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.41/0.59 tff(200,plain,(
% 0.41/0.59 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[199])).
% 0.41/0.59 tff(201,plain,
% 0.41/0.59 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[200, 193])).
% 0.41/0.59 tff(202,plain,
% 0.41/0.59 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[201, 191])).
% 0.41/0.59 tff(203,plain,
% 0.41/0.59 (((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(204,plain,
% 0.41/0.59 ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.41/0.60 inference(quant_inst,[status(thm)],[])).
% 0.41/0.60 tff(205,plain,
% 0.41/0.60 ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.60 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.41/0.60 tff(206,plain,
% 0.41/0.60 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[205, 202])).
% 0.41/0.60 tff(207,plain,
% 0.41/0.60 ($false),
% 0.41/0.60 inference(unit_resolution,[status(thm)],[206, 189, 187, 185, 163])).
% 0.41/0.60 % SZS output end Proof
% 0.41/0.60 % E exiting
%------------------------------------------------------------------------------