TSTP Solution File: GRP623+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP623+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Fri Sep 16 22:28:53 EDT 2022
% Result : Theorem 0.66s 0.69s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP623+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 18:12:48 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.66/0.69 % SZS status Theorem
% 0.66/0.69 % SZS output start Proof
% 0.66/0.69 tff(m2_fraenkel_type, type, (
% 0.66/0.69 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.66/0.69 tff(k1_autgroup_type, type, (
% 0.66/0.69 k1_autgroup: $i > $i)).
% 0.66/0.69 tff(tptp_fun_A_0_type, type, (
% 0.66/0.69 tptp_fun_A_0: $i)).
% 0.66/0.69 tff(u1_struct_0_type, type, (
% 0.66/0.69 u1_struct_0: $i > $i)).
% 0.66/0.69 tff(tptp_fun_C_1_type, type, (
% 0.66/0.69 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.66/0.69 tff(k4_autgroup_type, type, (
% 0.66/0.69 k4_autgroup: $i > $i)).
% 0.66/0.69 tff(m1_subset_1_type, type, (
% 0.66/0.69 m1_subset_1: ( $i * $i ) > $o)).
% 0.66/0.69 tff(v1_xboole_0_type, type, (
% 0.66/0.69 v1_xboole_0: $i > $o)).
% 0.66/0.69 tff(l1_struct_0_type, type, (
% 0.66/0.69 l1_struct_0: $i > $o)).
% 0.66/0.69 tff(l1_group_1_type, type, (
% 0.66/0.69 l1_group_1: $i > $o)).
% 0.66/0.69 tff(v4_group_1_type, type, (
% 0.66/0.69 v4_group_1: $i > $o)).
% 0.66/0.69 tff(v3_group_1_type, type, (
% 0.66/0.69 v3_group_1: $i > $o)).
% 0.66/0.69 tff(v1_group_1_type, type, (
% 0.66/0.69 v1_group_1: $i > $o)).
% 0.66/0.69 tff(v3_struct_0_type, type, (
% 0.66/0.69 v3_struct_0: $i > $o)).
% 0.66/0.69 tff(r1_tarski_type, type, (
% 0.66/0.69 r1_tarski: ( $i * $i ) > $o)).
% 0.66/0.69 tff(m1_fraenkel_type, type, (
% 0.66/0.69 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.66/0.69 tff(v1_fraenkel_type, type, (
% 0.66/0.69 v1_fraenkel: $i > $o)).
% 0.66/0.69 tff(r2_hidden_type, type, (
% 0.66/0.69 r2_hidden: ( $i * $i ) > $o)).
% 0.66/0.69 tff(1,plain,
% 0.66/0.69 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(2,plain,
% 0.66/0.69 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.66/0.69 tff(3,plain,
% 0.66/0.69 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(4,plain,
% 0.66/0.69 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(5,plain,
% 0.66/0.69 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[4])).
% 0.66/0.69 tff(6,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.66/0.69 tff(7,plain,
% 0.66/0.69 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.66/0.69 tff(8,plain,
% 0.66/0.69 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.66/0.69 tff(9,plain,(
% 0.66/0.69 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(skolemize,[status(sab)],[8])).
% 0.66/0.69 tff(10,plain,
% 0.66/0.69 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.66/0.69 tff(11,plain,
% 0.66/0.69 ((~![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))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(12,plain,
% 0.66/0.69 ((~![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))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 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')).
% 0.66/0.69 tff(14,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.66/0.69 tff(15,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.66/0.69 tff(16,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.66/0.69 tff(17,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.66/0.69 tff(18,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.66/0.69 tff(19,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.66/0.69 tff(20,plain,
% 0.66/0.69 (~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.66/0.69 tff(21,plain,(
% 0.66/0.69 ~((~((~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)))),
% 0.66/0.69 inference(skolemize,[status(sab)],[20])).
% 0.66/0.69 tff(22,plain,
% 0.66/0.69 ((~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)),
% 0.66/0.69 inference(or_elim,[status(thm)],[21])).
% 0.66/0.69 tff(23,plain,
% 0.66/0.69 (l1_group_1(A!0)),
% 0.66/0.69 inference(and_elim,[status(thm)],[22])).
% 0.66/0.69 tff(24,plain,
% 0.66/0.69 (((~![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)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(25,plain,
% 0.66/0.69 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(26,plain,
% 0.66/0.69 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.66/0.69 tff(27,plain,
% 0.66/0.69 (l1_struct_0(A!0)),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.66/0.69 tff(28,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(29,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[28])).
% 0.66/0.69 tff(30,plain,
% 0.66/0.69 (^[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)))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(31,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[30])).
% 0.66/0.69 tff(32,plain,
% 0.66/0.69 (![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))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(33,plain,
% 0.66/0.69 (^[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)))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(34,plain,
% 0.66/0.69 (![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))))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[33])).
% 0.66/0.69 tff(35,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')).
% 0.66/0.69 tff(36,plain,
% 0.66/0.69 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.66/0.69 tff(37,plain,
% 0.66/0.69 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.66/0.69 tff(38,plain,(
% 0.66/0.69 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.66/0.69 inference(skolemize,[status(sab)],[37])).
% 0.66/0.69 tff(39,plain,
% 0.66/0.69 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.66/0.69 tff(40,plain,
% 0.66/0.69 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.66/0.69 tff(41,plain,
% 0.66/0.69 (~v3_struct_0(A!0)),
% 0.66/0.69 inference(and_elim,[status(thm)],[22])).
% 0.66/0.69 tff(42,plain,
% 0.66/0.69 (((~![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))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(43,plain,
% 0.66/0.69 ((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))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(44,plain,
% 0.66/0.69 (((~![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)))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[43])).
% 0.66/0.69 tff(45,plain,
% 0.66/0.69 (((~![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))))),
% 0.66/0.69 inference(transitivity,[status(thm)],[44, 42])).
% 0.66/0.69 tff(46,plain,
% 0.66/0.69 ((~![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)))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(47,plain,
% 0.66/0.69 ((~![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.66/0.69 tff(48,plain,
% 0.66/0.69 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[47, 41, 40, 27])).
% 0.66/0.69 tff(49,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(50,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[49])).
% 0.66/0.69 tff(51,plain,
% 0.66/0.69 (^[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)))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(52,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[51])).
% 0.66/0.69 tff(53,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(54,plain,
% 0.66/0.69 (^[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)))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(55,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[54])).
% 0.66/0.69 tff(56,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')).
% 0.66/0.69 tff(57,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.66/0.69 tff(58,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.66/0.69 tff(59,plain,(
% 0.66/0.69 ![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)))),
% 0.66/0.69 inference(skolemize,[status(sab)],[58])).
% 0.66/0.69 tff(60,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.66/0.69 tff(61,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.66/0.69 tff(62,plain,
% 0.66/0.69 (v4_group_1(A!0)),
% 0.66/0.69 inference(and_elim,[status(thm)],[22])).
% 0.66/0.69 tff(63,plain,
% 0.66/0.69 (v3_group_1(A!0)),
% 0.66/0.69 inference(and_elim,[status(thm)],[22])).
% 0.66/0.69 tff(64,plain,
% 0.66/0.69 (v1_group_1(A!0)),
% 0.66/0.69 inference(and_elim,[status(thm)],[22])).
% 0.66/0.69 tff(65,plain,
% 0.66/0.69 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(66,plain,
% 0.66/0.69 ((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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(67,plain,
% 0.66/0.69 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[66])).
% 0.66/0.69 tff(68,plain,
% 0.66/0.69 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.69 inference(transitivity,[status(thm)],[67, 65])).
% 0.66/0.69 tff(69,plain,
% 0.66/0.69 ((~![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)))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(70,plain,
% 0.66/0.69 ((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.66/0.69 tff(71,plain,
% 0.66/0.69 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[70, 41, 64, 63, 62, 23, 61])).
% 0.66/0.69 tff(72,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(73,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[72])).
% 0.66/0.69 tff(74,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(75,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[74])).
% 0.66/0.69 tff(76,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(77,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[76])).
% 0.66/0.69 tff(78,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(transitivity,[status(thm)],[77, 75])).
% 0.66/0.69 tff(79,plain,
% 0.66/0.69 (^[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)))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(80,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[79])).
% 0.66/0.69 tff(81,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(82,plain,
% 0.66/0.69 (^[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))))),
% 0.66/0.69 inference(bind,[status(th)],[])).
% 0.66/0.69 tff(83,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(quant_intro,[status(thm)],[82])).
% 0.66/0.69 tff(84,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')).
% 0.66/0.69 tff(85,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.66/0.69 tff(86,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.66/0.69 tff(87,plain,(
% 0.66/0.69 ![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)))),
% 0.66/0.69 inference(skolemize,[status(sab)],[86])).
% 0.66/0.69 tff(88,plain,
% 0.66/0.69 (![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)))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.66/0.70 tff(89,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.66/0.70 tff(90,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[89, 73])).
% 0.66/0.70 tff(91,plain,
% 0.66/0.70 (((~![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))))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(92,plain,
% 0.66/0.70 ((~![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))))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(93,plain,
% 0.66/0.70 ((~![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)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.66/0.70 tff(94,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[93, 90, 71, 48])).
% 0.66/0.70 tff(95,plain,
% 0.66/0.70 ((~![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)))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(96,plain,
% 0.66/0.70 (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))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.66/0.70 tff(97,plain,
% 0.66/0.70 (^[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))))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(98,plain,
% 0.66/0.70 (![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)))))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[97])).
% 0.66/0.70 tff(99,plain,
% 0.66/0.70 (^[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))))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(100,plain,
% 0.66/0.70 (![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)))))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[99])).
% 0.66/0.70 tff(101,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(102,plain,
% 0.66/0.70 (^[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))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(103,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[102])).
% 0.66/0.70 tff(104,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')).
% 0.66/0.70 tff(105,plain,
% 0.66/0.70 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.66/0.70 tff(106,plain,
% 0.66/0.70 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.66/0.70 tff(107,plain,(
% 0.66/0.70 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 0.66/0.70 inference(skolemize,[status(sab)],[106])).
% 0.66/0.70 tff(108,plain,
% 0.66/0.70 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.66/0.70 tff(109,plain,
% 0.66/0.70 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[108, 98])).
% 0.66/0.70 tff(110,plain,
% 0.66/0.70 (((~![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))))))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(111,plain,
% 0.66/0.70 ((~![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))))))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(112,plain,
% 0.66/0.70 ((~![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)))))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.66/0.70 tff(113,plain,
% 0.66/0.70 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[112, 109, 71])).
% 0.66/0.70 tff(114,plain,
% 0.66/0.70 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(115,plain,
% 0.66/0.70 (~v1_xboole_0(k1_autgroup(A!0))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.66/0.70 tff(116,plain,
% 0.66/0.70 (^[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))))))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(117,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[116])).
% 0.66/0.70 tff(118,plain,
% 0.66/0.70 (^[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))))))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(119,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[118])).
% 0.66/0.70 tff(120,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(transitivity,[status(thm)],[119, 117])).
% 0.66/0.70 tff(121,plain,
% 0.66/0.70 (^[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)))))))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(122,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[121])).
% 0.66/0.70 tff(123,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(124,plain,
% 0.66/0.70 (^[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))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(125,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[124])).
% 0.66/0.70 tff(126,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')).
% 0.66/0.70 tff(127,plain,
% 0.66/0.70 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.66/0.70 tff(128,plain,
% 0.66/0.70 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.66/0.70 tff(129,plain,(
% 0.66/0.70 ![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)))))),
% 0.66/0.70 inference(skolemize,[status(sab)],[128])).
% 0.66/0.70 tff(130,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.66/0.70 tff(131,plain,
% 0.66/0.70 (![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)))))))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.66/0.70 tff(132,plain,
% 0.66/0.70 ((~![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))))))))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(133,plain,
% 0.66/0.70 (~((~((~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)))))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.66/0.70 tff(134,plain,
% 0.66/0.70 (((~((~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)))))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(135,plain,
% 0.66/0.70 (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))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.66/0.70 tff(136,plain,
% 0.66/0.70 (~r1_tarski(k4_autgroup(A!0), k1_autgroup(A!0))),
% 0.66/0.70 inference(or_elim,[status(thm)],[21])).
% 0.66/0.70 tff(137,plain,
% 0.66/0.70 ((~(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))))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(138,plain,
% 0.66/0.70 ((~(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))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.66/0.70 tff(139,plain,
% 0.66/0.70 (~((~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)))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.66/0.70 tff(140,plain,
% 0.66/0.70 (((~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)))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(141,plain,
% 0.66/0.70 (~r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.66/0.70 tff(142,plain,
% 0.66/0.70 (^[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))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(143,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[142])).
% 0.66/0.70 tff(144,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(145,plain,
% 0.66/0.70 (^[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))))),
% 0.66/0.70 inference(bind,[status(th)],[])).
% 0.66/0.70 tff(146,plain,
% 0.66/0.70 (![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)))),
% 0.66/0.70 inference(quant_intro,[status(thm)],[145])).
% 0.66/0.70 tff(147,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')).
% 0.66/0.70 tff(148,plain,
% 0.66/0.70 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.66/0.70 tff(149,plain,
% 0.66/0.70 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.66/0.70 tff(150,plain,(
% 0.66/0.70 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.66/0.70 inference(skolemize,[status(sab)],[149])).
% 0.66/0.70 tff(151,plain,
% 0.66/0.70 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.66/0.70 tff(152,plain,
% 0.66/0.70 (((~![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))))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(153,plain,
% 0.66/0.70 ((~![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))))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(154,plain,
% 0.66/0.70 ((~![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.66/0.71 tff(155,plain,
% 0.66/0.71 (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)))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[154, 151, 141])).
% 0.66/0.71 tff(156,plain,
% 0.66/0.71 (~m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k1_autgroup(A!0))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[155, 115])).
% 0.66/0.71 tff(157,plain,
% 0.66/0.71 ((~(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))),
% 0.66/0.71 inference(tautology,[status(thm)],[])).
% 0.66/0.71 tff(158,plain,
% 0.66/0.71 ((~(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)))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.66/0.71 tff(159,plain,
% 0.66/0.71 (~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))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[158, 96])).
% 0.66/0.71 tff(160,plain,
% 0.66/0.71 (^[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))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(161,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[160])).
% 0.66/0.71 tff(162,plain,
% 0.66/0.71 (^[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)))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(163,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[162])).
% 0.66/0.71 tff(164,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(165,plain,
% 0.66/0.71 (^[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)))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(166,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[165])).
% 0.66/0.71 tff(167,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')).
% 0.66/0.71 tff(168,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.66/0.71 tff(169,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.66/0.71 tff(170,plain,(
% 0.66/0.71 ![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)))),
% 0.66/0.71 inference(skolemize,[status(sab)],[169])).
% 0.66/0.71 tff(171,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.66/0.71 tff(172,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.66/0.71 tff(173,plain,
% 0.66/0.71 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(174,plain,
% 0.66/0.71 ((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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(175,plain,
% 0.66/0.71 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.66/0.71 inference(monotonicity,[status(thm)],[174])).
% 0.66/0.71 tff(176,plain,
% 0.66/0.71 (((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.66/0.71 inference(transitivity,[status(thm)],[175, 173])).
% 0.66/0.71 tff(177,plain,
% 0.66/0.71 ((~![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)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(178,plain,
% 0.66/0.71 ((~![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) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.66/0.71 tff(179,plain,
% 0.66/0.71 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[178, 41, 64, 63, 62, 23, 172])).
% 0.66/0.71 tff(180,plain,
% 0.66/0.71 (((~![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))))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(181,plain,
% 0.66/0.71 ((~![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))))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(182,plain,
% 0.66/0.71 ((~![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)))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.66/0.71 tff(183,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[182, 90, 179, 48])).
% 0.66/0.71 tff(184,plain,
% 0.66/0.71 ((~![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)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(185,plain,
% 0.66/0.71 (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))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.66/0.71 tff(186,plain,
% 0.66/0.71 (((~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))),
% 0.66/0.71 inference(tautology,[status(thm)],[])).
% 0.66/0.71 tff(187,plain,
% 0.66/0.71 (r2_hidden(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[186, 139])).
% 0.66/0.71 tff(188,plain,
% 0.66/0.71 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(189,plain,
% 0.66/0.71 (![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))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[188])).
% 0.66/0.71 tff(190,plain,
% 0.66/0.71 (![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))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(191,plain,
% 0.66/0.71 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(192,plain,
% 0.66/0.71 (![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))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[191])).
% 0.66/0.71 tff(193,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.66/0.71 tff(194,plain,
% 0.66/0.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.66/0.71 tff(195,plain,
% 0.66/0.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.66/0.71 tff(196,plain,(
% 0.66/0.71 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.66/0.71 inference(skolemize,[status(sab)],[195])).
% 0.66/0.71 tff(197,plain,
% 0.66/0.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.66/0.71 tff(198,plain,
% 0.66/0.71 (((~![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)))),
% 0.66/0.71 inference(rewrite,[status(thm)],[])).
% 0.66/0.71 tff(199,plain,
% 0.66/0.71 ((~![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)))),
% 0.66/0.71 inference(quant_inst,[status(thm)],[])).
% 0.66/0.71 tff(200,plain,
% 0.66/0.71 ((~![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))),
% 0.66/0.71 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.66/0.71 tff(201,plain,
% 0.66/0.71 (m1_subset_1(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[200, 197, 187])).
% 0.66/0.71 tff(202,plain,
% 0.66/0.71 ((~(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)))),
% 0.66/0.71 inference(tautology,[status(thm)],[])).
% 0.66/0.71 tff(203,plain,
% 0.66/0.71 ((~(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))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.66/0.71 tff(204,plain,
% 0.66/0.71 (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))),
% 0.66/0.71 inference(unit_resolution,[status(thm)],[203, 185])).
% 0.66/0.71 tff(205,plain,
% 0.66/0.71 (^[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)))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(206,plain,
% 0.66/0.71 (![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))))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[205])).
% 0.66/0.71 tff(207,plain,
% 0.66/0.71 (^[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))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(208,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[207])).
% 0.66/0.71 tff(209,plain,
% 0.66/0.71 (^[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))))),
% 0.66/0.71 inference(bind,[status(th)],[])).
% 0.66/0.71 tff(210,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(quant_intro,[status(thm)],[209])).
% 0.66/0.71 tff(211,plain,
% 0.66/0.71 (![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)))),
% 0.66/0.71 inference(transitivity,[status(thm)],[210, 208])).
% 0.66/0.71 tff(212,plain,
% 0.66/0.71 (^[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)))))),
% 0.66/0.72 inference(bind,[status(th)],[])).
% 0.66/0.72 tff(213,plain,
% 0.66/0.72 (![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)))),
% 0.66/0.72 inference(quant_intro,[status(thm)],[212])).
% 0.66/0.72 tff(214,plain,
% 0.66/0.72 (![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))))),
% 0.66/0.72 inference(rewrite,[status(thm)],[])).
% 0.66/0.72 tff(215,plain,
% 0.66/0.72 (^[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))))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(216,plain,
% 0.74/0.72 (![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))))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[215])).
% 0.74/0.72 tff(217,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')).
% 0.74/0.72 tff(218,plain,
% 0.74/0.72 (![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))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.74/0.72 tff(219,plain,
% 0.74/0.72 (![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))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.74/0.72 tff(220,plain,(
% 0.74/0.72 ![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))))),
% 0.74/0.72 inference(skolemize,[status(sab)],[219])).
% 0.74/0.72 tff(221,plain,
% 0.74/0.72 (![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)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.74/0.72 tff(222,plain,
% 0.74/0.72 (![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)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[221, 211])).
% 0.74/0.72 tff(223,plain,
% 0.74/0.72 (![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))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[222, 206])).
% 0.74/0.72 tff(224,plain,
% 0.74/0.72 (((~![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) | (~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))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(225,plain,
% 0.74/0.72 ((~![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))))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(226,plain,
% 0.74/0.72 ((~![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)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.74/0.72 tff(227,plain,
% 0.74/0.72 (![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)))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[226, 41, 64, 63, 62, 23, 223])).
% 0.74/0.72 tff(228,plain,
% 0.74/0.72 (((~![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)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(229,plain,
% 0.74/0.72 ((~![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)))),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(230,plain,
% 0.74/0.73 ((~![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) | (~m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | m2_fraenkel(tptp_fun_C_1(k1_autgroup(A!0), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.74/0.73 tff(231,plain,
% 0.74/0.73 ($false),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[230, 227, 204, 159])).
% 0.74/0.73 % SZS output end Proof
%------------------------------------------------------------------------------