%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP623+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.39s 0.62s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP623+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 16:27:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.39/0.62 % SZS status Theorem
% 0.39/0.62 % SZS output start Proof
% 0.39/0.62 tff(m2_fraenkel_type, type, (
% 0.39/0.62 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.39/0.62 tff(k1_autgroup_type, type, (
% 0.39/0.62 k1_autgroup: $i > $i)).
% 0.39/0.62 tff(tptp_fun_A_0_type, type, (
% 0.39/0.62 tptp_fun_A_0: $i)).
% 0.39/0.62 tff(u1_struct_0_type, type, (
% 0.39/0.62 u1_struct_0: $i > $i)).
% 0.39/0.62 tff(tptp_fun_C_1_type, type, (
% 0.39/0.62 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.39/0.62 tff(k4_autgroup_type, type, (
% 0.39/0.62 k4_autgroup: $i > $i)).
% 0.39/0.62 tff(m1_subset_1_type, type, (
% 0.39/0.62 m1_subset_1: ( $i * $i ) > $o)).
% 0.39/0.62 tff(v1_xboole_0_type, type, (
% 0.39/0.62 v1_xboole_0: $i > $o)).
% 0.39/0.62 tff(l1_struct_0_type, type, (
% 0.39/0.62 l1_struct_0: $i > $o)).
% 0.39/0.62 tff(l1_group_1_type, type, (
% 0.39/0.62 l1_group_1: $i > $o)).
% 0.39/0.62 tff(v4_group_1_type, type, (
% 0.39/0.62 v4_group_1: $i > $o)).
% 0.39/0.62 tff(v3_group_1_type, type, (
% 0.39/0.62 v3_group_1: $i > $o)).
% 0.39/0.62 tff(v1_group_1_type, type, (
% 0.39/0.62 v1_group_1: $i > $o)).
% 0.39/0.62 tff(v3_struct_0_type, type, (
% 0.39/0.62 v3_struct_0: $i > $o)).
% 0.39/0.62 tff(r1_tarski_type, type, (
% 0.39/0.62 r1_tarski: ( $i * $i ) > $o)).
% 0.39/0.62 tff(m1_fraenkel_type, type, (
% 0.39/0.62 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.39/0.62 tff(v1_fraenkel_type, type, (
% 0.39/0.62 v1_fraenkel: $i > $o)).
% 0.39/0.62 tff(r2_hidden_type, type, (
% 0.39/0.62 r2_hidden: ( $i * $i ) > $o)).
% 0.39/0.62 tff(1,plain,
% 0.39/0.62 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(2,plain,
% 0.39/0.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.62 tff(3,plain,
% 0.39/0.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(4,plain,
% 0.39/0.62 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(5,plain,
% 0.39/0.62 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[4])).
% 0.39/0.62 tff(6,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.39/0.62 tff(7,plain,
% 0.39/0.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.39/0.62 tff(8,plain,
% 0.39/0.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.39/0.62 tff(9,plain,(
% 0.39/0.62 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[8])).
% 0.39/0.62 tff(10,plain,
% 0.39/0.62 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.39/0.62 tff(11,plain,
% 0.39/0.62 ((~![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_autgroup(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_autgroup(A))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(12,plain,
% 0.39/0.62 ((~![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_autgroup(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_autgroup(A))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(13,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_autgroup(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14_autgroup')).
% 0.39/0.62 tff(14,plain,
% 0.39/0.62 (~![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_autgroup(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.39/0.62 tff(15,plain,
% 0.39/0.62 (~![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_autgroup(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.39/0.62 tff(16,plain,
% 0.39/0.62 (~![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_autgroup(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.39/0.62 tff(17,plain,
% 0.39/0.62 (~![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_autgroup(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.39/0.62 tff(18,plain,(
% 0.39/0.62 ~((~((~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_autgroup(A!0)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[17])).
% 0.39/0.62 tff(19,plain,
% 0.39/0.62 ((~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)),
% 0.39/0.62 inference(or_elim,[status(thm)],[18])).
% 0.39/0.62 tff(20,plain,
% 0.39/0.62 (l1_group_1(A!0)),
% 0.39/0.62 inference(and_elim,[status(thm)],[19])).
% 0.39/0.62 tff(21,plain,
% 0.39/0.62 (((~![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)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(22,plain,
% 0.39/0.62 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(23,plain,
% 0.39/0.62 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.39/0.62 tff(24,plain,
% 0.39/0.62 (l1_struct_0(A!0)),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.39/0.62 tff(25,plain,
% 0.39/0.62 (^[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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(26,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[25])).
% 0.39/0.62 tff(27,plain,
% 0.39/0.62 (^[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)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(28,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[27])).
% 0.39/0.62 tff(29,plain,
% 0.39/0.62 (![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))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(30,plain,
% 0.39/0.62 (^[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)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(31,plain,
% 0.39/0.62 (![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))))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[30])).
% 0.39/0.62 tff(32,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.39/0.62 tff(33,plain,
% 0.39/0.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.39/0.62 tff(34,plain,
% 0.39/0.62 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.39/0.62 tff(35,plain,(
% 0.39/0.62 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.39/0.62 inference(skolemize,[status(sab)],[34])).
% 0.39/0.62 tff(36,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.39/0.62 tff(37,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.39/0.62 tff(38,plain,
% 0.39/0.62 (~v3_struct_0(A!0)),
% 0.39/0.62 inference(and_elim,[status(thm)],[19])).
% 0.39/0.62 tff(39,plain,
% 0.39/0.62 (((~![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))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(40,plain,
% 0.39/0.62 ((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))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(41,plain,
% 0.39/0.62 (((~![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)))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[40])).
% 0.39/0.62 tff(42,plain,
% 0.39/0.62 (((~![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))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[41, 39])).
% 0.39/0.62 tff(43,plain,
% 0.39/0.62 ((~![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)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(44,plain,
% 0.39/0.62 ((~![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.39/0.62 tff(45,plain,
% 0.39/0.62 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[44, 38, 37, 24])).
% 0.39/0.62 tff(46,plain,
% 0.39/0.62 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_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(k1_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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(47,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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(k1_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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[46])).
% 0.39/0.62 tff(48,plain,
% 0.39/0.62 (^[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(k1_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(k1_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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_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)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(49,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[48])).
% 0.39/0.62 tff(50,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(51,plain,
% 0.39/0.62 (^[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(k1_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(k1_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(k1_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(k1_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(k1_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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(52,plain,
% 0.39/0.62 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[51])).
% 0.39/0.62 tff(53,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(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 0.39/0.62 tff(54,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.39/0.62 tff(55,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.39/0.62 tff(56,plain,(
% 0.39/0.62 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[55])).
% 0.39/0.62 tff(57,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.39/0.62 tff(58,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.39/0.62 tff(59,plain,
% 0.39/0.62 (v4_group_1(A!0)),
% 0.39/0.62 inference(and_elim,[status(thm)],[19])).
% 0.39/0.62 tff(60,plain,
% 0.39/0.62 (v3_group_1(A!0)),
% 0.39/0.62 inference(and_elim,[status(thm)],[19])).
% 0.39/0.62 tff(61,plain,
% 0.39/0.62 (v1_group_1(A!0)),
% 0.39/0.62 inference(and_elim,[status(thm)],[19])).
% 0.39/0.62 tff(62,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(63,plain,
% 0.39/0.62 ((v3_struct_0(A!0) | m1_fraenkel(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(64,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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(k1_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(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[63])).
% 0.39/0.62 tff(65,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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(k1_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(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.39/0.62 inference(transitivity,[status(thm)],[64, 62])).
% 0.39/0.62 tff(66,plain,
% 0.39/0.62 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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(k1_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)))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(67,plain,
% 0.39/0.62 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_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) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.39/0.62 tff(68,plain,
% 0.39/0.62 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[67, 38, 61, 60, 59, 20, 58])).
% 0.39/0.62 tff(69,plain,
% 0.39/0.62 (^[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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(70,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[69])).
% 0.39/0.62 tff(71,plain,
% 0.39/0.62 (^[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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(72,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[71])).
% 0.39/0.62 tff(73,plain,
% 0.39/0.62 (^[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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(74,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[73])).
% 0.39/0.62 tff(75,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(transitivity,[status(thm)],[74, 72])).
% 0.39/0.62 tff(76,plain,
% 0.39/0.62 (^[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)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(77,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[76])).
% 0.39/0.62 tff(78,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(79,plain,
% 0.39/0.62 (^[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))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(80,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[79])).
% 0.39/0.62 tff(81,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/sandbox/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 0.39/0.62 tff(82,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.39/0.62 tff(83,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.39/0.62 tff(84,plain,(
% 0.39/0.62 ![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)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[83])).
% 0.39/0.62 tff(85,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.39/0.62 tff(86,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.39/0.62 tff(87,plain,
% 0.39/0.62 (![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)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[86, 70])).
% 0.39/0.62 tff(88,plain,
% 0.39/0.62 (((~![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(k1_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), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_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(k1_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), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(89,plain,
% 0.39/0.63 ((~![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(k1_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), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(90,plain,
% 0.39/0.63 ((~![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(k1_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), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.39/0.63 tff(91,plain,
% 0.39/0.63 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[90, 87, 68, 45])).
% 0.39/0.63 tff(92,plain,
% 0.39/0.63 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(93,plain,
% 0.39/0.63 (m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.39/0.63 tff(94,plain,
% 0.39/0.63 (^[A: $i, B: $i, C: $i] : refl(((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(95,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[94])).
% 0.39/0.63 tff(96,plain,
% 0.39/0.63 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(97,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[96])).
% 0.39/0.63 tff(98,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(99,plain,
% 0.39/0.63 (^[A: $i, B: $i, C: $i] : rewrite((m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(100,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[99])).
% 0.39/0.63 tff(101,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 0.39/0.63 tff(102,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.39/0.63 tff(103,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.39/0.63 tff(104,plain,(
% 0.39/0.63 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.39/0.63 inference(skolemize,[status(sab)],[103])).
% 0.39/0.63 tff(105,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.39/0.63 tff(106,plain,
% 0.39/0.63 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.39/0.63 tff(107,plain,
% 0.39/0.63 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(108,plain,
% 0.39/0.63 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(109,plain,
% 0.39/0.63 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.39/0.63 tff(110,plain,
% 0.39/0.63 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[109, 106, 68])).
% 0.39/0.63 tff(111,plain,
% 0.39/0.63 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 0.39/0.63 inference(tautology,[status(thm)],[])).
% 0.39/0.63 tff(112,plain,
% 0.39/0.63 (~v1_xboole_0(k1_autgroup(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.39/0.63 tff(113,plain,
% 0.39/0.63 (^[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))))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(114,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[113])).
% 0.39/0.63 tff(115,plain,
% 0.39/0.63 (^[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))))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(116,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[115])).
% 0.39/0.63 tff(117,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[116, 114])).
% 0.39/0.63 tff(118,plain,
% 0.39/0.63 (^[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)))))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(119,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[118])).
% 0.39/0.63 tff(120,plain,
% 0.39/0.63 (![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)))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(121,plain,
% 0.39/0.63 (^[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))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(122,plain,
% 0.39/0.63 (![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)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[121])).
% 0.39/0.63 tff(123,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.39/0.63 tff(124,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.39/0.63 tff(125,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.39/0.63 tff(126,plain,(
% 0.39/0.63 ![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)))))),
% 0.39/0.63 inference(skolemize,[status(sab)],[125])).
% 0.39/0.63 tff(127,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.39/0.63 tff(128,plain,
% 0.39/0.63 (![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)))))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.39/0.63 tff(129,plain,
% 0.39/0.63 ((~![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_autgroup(A!0))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_autgroup(A!0))))) | (~(r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(130,plain,
% 0.39/0.63 (~((~((~r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_autgroup(A!0))))) | (~(r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.39/0.63 tff(131,plain,
% 0.39/0.63 (((~((~r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_autgroup(A!0))))) | (~(r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))))) | (r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))))),
% 0.39/0.63 inference(tautology,[status(thm)],[])).
% 0.39/0.63 tff(132,plain,
% 0.39/0.63 (r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.39/0.63 tff(133,plain,
% 0.39/0.63 (~r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0))),
% 0.39/0.63 inference(or_elim,[status(thm)],[18])).
% 0.39/0.63 tff(134,plain,
% 0.39/0.63 ((~(r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))))) | r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))),
% 0.39/0.63 inference(tautology,[status(thm)],[])).
% 0.39/0.63 tff(135,plain,
% 0.39/0.63 ((~(r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0)) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))))) | (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.39/0.63 tff(136,plain,
% 0.39/0.63 (~((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.39/0.63 tff(137,plain,
% 0.39/0.63 (((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))) | (~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))),
% 0.39/0.63 inference(tautology,[status(thm)],[])).
% 0.39/0.63 tff(138,plain,
% 0.39/0.63 (~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.39/0.63 tff(139,plain,
% 0.39/0.63 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(140,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[139])).
% 0.39/0.63 tff(141,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(142,plain,
% 0.39/0.63 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(143,plain,
% 0.39/0.63 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[142])).
% 0.39/0.63 tff(144,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.39/0.63 tff(145,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.39/0.63 tff(146,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.39/0.63 tff(147,plain,(
% 0.39/0.63 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(skolemize,[status(sab)],[146])).
% 0.39/0.63 tff(148,plain,
% 0.39/0.63 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.39/0.63 tff(149,plain,
% 0.39/0.63 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(150,plain,
% 0.39/0.63 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(151,plain,
% 0.39/0.63 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.39/0.63 tff(152,plain,
% 0.39/0.63 (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[151, 148, 138])).
% 0.39/0.63 tff(153,plain,
% 0.39/0.63 (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[152, 112])).
% 0.39/0.63 tff(154,plain,
% 0.39/0.63 ((~(m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))) | (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(155,plain,
% 0.48/0.63 ((~(m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0)))) | (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.48/0.63 tff(156,plain,
% 0.48/0.63 (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[155, 93])).
% 0.48/0.63 tff(157,plain,
% 0.48/0.63 (^[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))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(158,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[157])).
% 0.48/0.63 tff(159,plain,
% 0.48/0.63 (^[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)))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(160,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[159])).
% 0.48/0.63 tff(161,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(162,plain,
% 0.48/0.63 (^[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)))))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(163,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[162])).
% 0.48/0.63 tff(164,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/sandbox/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 0.48/0.63 tff(165,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.48/0.63 tff(166,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[165, 161])).
% 0.48/0.63 tff(167,plain,(
% 0.48/0.63 ![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)))),
% 0.48/0.63 inference(skolemize,[status(sab)],[166])).
% 0.48/0.63 tff(168,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[167, 160])).
% 0.48/0.63 tff(169,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[168, 158])).
% 0.48/0.63 tff(170,plain,
% 0.48/0.63 (((~![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) | (~v4_group_1(A!0)) | (~v3_group_1(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)))) <=> ((~![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) | (~v4_group_1(A!0)) | (~v3_group_1(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)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(171,plain,
% 0.48/0.63 ((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) | (~v4_group_1(A!0)) | (~v3_group_1(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)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(172,plain,
% 0.48/0.63 (((~![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) | (~v4_group_1(A!0)) | (~v3_group_1(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))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[171])).
% 0.48/0.63 tff(173,plain,
% 0.48/0.63 (((~![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) | (~v4_group_1(A!0)) | (~v3_group_1(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)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[172, 170])).
% 0.48/0.63 tff(174,plain,
% 0.48/0.63 ((~![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)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(175,plain,
% 0.48/0.63 ((~![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) | (~v4_group_1(A!0)) | (~v3_group_1(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))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.48/0.63 tff(176,plain,
% 0.48/0.63 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[175, 38, 61, 60, 59, 20, 169])).
% 0.48/0.63 tff(177,plain,
% 0.48/0.63 (((~![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))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(178,plain,
% 0.48/0.63 ((~![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))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(179,plain,
% 0.48/0.63 ((~![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)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.48/0.63 tff(180,plain,
% 0.48/0.63 (![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)))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[179, 87, 176, 45])).
% 0.48/0.63 tff(181,plain,
% 0.48/0.63 ((~![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_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(182,plain,
% 0.48/0.63 (m2_fraenkel(tptp_fun_C_1(k1_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.48/0.63 tff(183,plain,
% 0.48/0.63 (((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.48/0.63 inference(tautology,[status(thm)],[])).
% 0.48/0.63 tff(184,plain,
% 0.48/0.63 (r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[183, 136])).
% 0.48/0.63 tff(185,plain,
% 0.48/0.63 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(186,plain,
% 0.48/0.63 (![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))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[185])).
% 0.48/0.63 tff(187,plain,
% 0.48/0.63 (![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))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(188,plain,
% 0.48/0.63 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.48/0.63 inference(bind,[status(th)],[])).
% 0.48/0.63 tff(189,plain,
% 0.48/0.63 (![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))),
% 0.48/0.63 inference(quant_intro,[status(thm)],[188])).
% 0.48/0.63 tff(190,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.48/0.63 tff(191,plain,
% 0.48/0.63 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.48/0.63 tff(192,plain,
% 0.48/0.63 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.48/0.64 tff(193,plain,(
% 0.48/0.64 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.48/0.64 inference(skolemize,[status(sab)],[192])).
% 0.48/0.64 tff(194,plain,
% 0.48/0.64 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.48/0.64 tff(195,plain,
% 0.48/0.64 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(196,plain,
% 0.48/0.64 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(197,plain,
% 0.48/0.64 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.48/0.64 tff(198,plain,
% 0.48/0.64 (m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[197, 194, 184])).
% 0.48/0.64 tff(199,plain,
% 0.48/0.64 ((~(m2_fraenkel(tptp_fun_C_1(k1_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(200,plain,
% 0.48/0.64 ((~(m2_fraenkel(tptp_fun_C_1(k1_autgroup(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_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.48/0.64 tff(201,plain,
% 0.48/0.64 (m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[200, 182])).
% 0.48/0.64 tff(202,plain,
% 0.48/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(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)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(203,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[202])).
% 0.48/0.64 tff(204,plain,
% 0.48/0.64 (^[A: $i] : refl((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(205,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[204])).
% 0.48/0.64 tff(206,plain,
% 0.48/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(207,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[206])).
% 0.48/0.64 tff(208,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[207, 205])).
% 0.48/0.64 tff(209,plain,
% 0.48/0.64 (^[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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite(((v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(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))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(210,plain,
% 0.48/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[209])).
% 0.48/0.64 tff(211,plain,
% 0.48/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(212,plain,
% 0.48/0.64 (^[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)))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) <=> ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(213,plain,
% 0.48/0.64 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[212])).
% 0.48/0.64 tff(214,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A)) => m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13_autgroup')).
% 0.48/0.64 tff(215,plain,
% 0.48/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.48/0.64 tff(216,plain,
% 0.48/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.48/0.64 tff(217,plain,(
% 0.48/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(skolemize,[status(sab)],[216])).
% 0.48/0.64 tff(218,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.48/0.64 tff(219,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[218, 208])).
% 0.48/0.64 tff(220,plain,
% 0.48/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[219, 203])).
% 0.48/0.64 tff(221,plain,
% 0.48/0.64 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(222,plain,
% 0.48/0.64 ((v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(223,plain,
% 0.48/0.64 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[222])).
% 0.48/0.64 tff(224,plain,
% 0.48/0.64 (((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[223, 221])).
% 0.48/0.64 tff(225,plain,
% 0.48/0.64 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | (v3_struct_0(A!0) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(226,plain,
% 0.48/0.64 ((~![A: $i] : (v3_struct_0(A) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k4_autgroup(A))) | m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))) | v3_struct_0(A!0) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.48/0.64 tff(227,plain,
% 0.48/0.64 (![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[226, 38, 61, 60, 59, 20, 220])).
% 0.48/0.64 tff(228,plain,
% 0.48/0.64 (((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) <=> ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(229,plain,
% 0.48/0.64 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | ((~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(230,plain,
% 0.48/0.64 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.48/0.64 tff(231,plain,
% 0.48/0.64 ($false),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[230, 227, 201, 156])).
% 0.48/0.64 % SZS output end Proof
% 0.48/0.65 % E exiting
%------------------------------------------------------------------------------