TSTP Solution File: GRP622+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP622+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 22:28:52 EDT 2022
% Result : Theorem 0.54s 0.58s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP622+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Aug 31 18:12:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.54/0.58 % SZS status Theorem
% 0.54/0.58 % SZS output start Proof
% 0.54/0.58 tff(m2_relset_1_type, type, (
% 0.54/0.58 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.54/0.58 tff(u1_struct_0_type, type, (
% 0.54/0.58 u1_struct_0: $i > $i)).
% 0.54/0.58 tff(tptp_fun_A_0_type, type, (
% 0.54/0.58 tptp_fun_A_0: $i)).
% 0.54/0.58 tff(tptp_fun_C_1_type, type, (
% 0.54/0.58 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.54/0.58 tff(k4_autgroup_type, type, (
% 0.54/0.58 k4_autgroup: $i > $i)).
% 0.54/0.58 tff(k1_fraenkel_type, type, (
% 0.54/0.58 k1_fraenkel: ( $i * $i ) > $i)).
% 0.54/0.58 tff(v1_funct_2_type, type, (
% 0.54/0.58 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.54/0.58 tff(v1_funct_1_type, type, (
% 0.54/0.58 v1_funct_1: $i > $o)).
% 0.54/0.58 tff(m2_fraenkel_type, type, (
% 0.54/0.58 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 0.54/0.58 tff(m1_subset_1_type, type, (
% 0.54/0.58 m1_subset_1: ( $i * $i ) > $o)).
% 0.54/0.58 tff(m1_fraenkel_type, type, (
% 0.54/0.58 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 0.54/0.58 tff(v4_group_1_type, type, (
% 0.54/0.58 v4_group_1: $i > $o)).
% 0.54/0.58 tff(v3_group_1_type, type, (
% 0.54/0.58 v3_group_1: $i > $o)).
% 0.54/0.58 tff(l1_group_1_type, type, (
% 0.54/0.58 l1_group_1: $i > $o)).
% 0.54/0.58 tff(v1_group_1_type, type, (
% 0.54/0.58 v1_group_1: $i > $o)).
% 0.54/0.58 tff(v3_struct_0_type, type, (
% 0.54/0.58 v3_struct_0: $i > $o)).
% 0.54/0.58 tff(r1_tarski_type, type, (
% 0.54/0.58 r1_tarski: ( $i * $i ) > $o)).
% 0.54/0.58 tff(v1_xboole_0_type, type, (
% 0.54/0.58 v1_xboole_0: $i > $o)).
% 0.54/0.58 tff(l1_struct_0_type, type, (
% 0.54/0.58 l1_struct_0: $i > $o)).
% 0.54/0.58 tff(r2_hidden_type, type, (
% 0.54/0.58 r2_hidden: ( $i * $i ) > $o)).
% 0.54/0.58 tff(k1_funct_2_type, type, (
% 0.54/0.58 k1_funct_2: ( $i * $i ) > $i)).
% 0.54/0.58 tff(1,plain,
% 0.54/0.58 (^[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))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(2,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![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)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.58 tff(3,plain,
% 0.54/0.58 (^[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)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(4,plain,
% 0.54/0.58 (![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)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[3])).
% 0.54/0.58 tff(5,plain,
% 0.54/0.58 (![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)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(6,plain,
% 0.54/0.58 (^[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)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(7,plain,
% 0.54/0.58 (![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)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[6])).
% 0.54/0.58 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_autgroup')).
% 0.54/0.58 tff(9,plain,
% 0.54/0.58 (![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)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.54/0.58 tff(10,plain,
% 0.54/0.58 (![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)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.54/0.58 tff(11,plain,(
% 0.54/0.58 ![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)))),
% 0.54/0.58 inference(skolemize,[status(sab)],[10])).
% 0.54/0.58 tff(12,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.54/0.58 tff(13,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.54/0.58 tff(14,plain,
% 0.54/0.58 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(15,plain,
% 0.54/0.58 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A)))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(16,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_autgroup')).
% 0.54/0.58 tff(17,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.54/0.58 tff(18,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.54/0.58 tff(19,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.54/0.58 tff(20,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.54/0.58 tff(21,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.54/0.58 tff(22,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.54/0.58 tff(23,plain,
% 0.54/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | r1_tarski(k4_autgroup(A), k1_fraenkel(u1_struct_0(A), u1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[22, 14])).
% 0.54/0.58 tff(24,plain,(
% 0.54/0.58 ~((~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))) | r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.58 inference(skolemize,[status(sab)],[23])).
% 0.54/0.58 tff(25,plain,
% 0.54/0.58 ((~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)),
% 0.54/0.58 inference(or_elim,[status(thm)],[24])).
% 0.54/0.58 tff(26,plain,
% 0.54/0.58 (l1_group_1(A!0)),
% 0.54/0.58 inference(and_elim,[status(thm)],[25])).
% 0.54/0.58 tff(27,plain,
% 0.54/0.58 (v4_group_1(A!0)),
% 0.54/0.58 inference(and_elim,[status(thm)],[25])).
% 0.54/0.58 tff(28,plain,
% 0.54/0.58 (v3_group_1(A!0)),
% 0.54/0.58 inference(and_elim,[status(thm)],[25])).
% 0.54/0.58 tff(29,plain,
% 0.54/0.58 (v1_group_1(A!0)),
% 0.54/0.58 inference(and_elim,[status(thm)],[25])).
% 0.54/0.58 tff(30,plain,
% 0.54/0.58 (~v3_struct_0(A!0)),
% 0.54/0.58 inference(and_elim,[status(thm)],[25])).
% 0.54/0.58 tff(31,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(32,plain,
% 0.54/0.58 ((v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(33,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))))),
% 0.54/0.58 inference(monotonicity,[status(thm)],[32])).
% 0.54/0.58 tff(34,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.54/0.58 inference(transitivity,[status(thm)],[33, 31])).
% 0.54/0.58 tff(35,plain,
% 0.54/0.58 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v1_group_1(A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 0.54/0.58 inference(quant_inst,[status(thm)],[])).
% 0.54/0.58 tff(36,plain,
% 0.54/0.58 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k4_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~v1_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.54/0.58 tff(37,plain,
% 0.54/0.58 (m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.58 inference(unit_resolution,[status(thm)],[36, 30, 29, 28, 27, 26, 13])).
% 0.54/0.58 tff(38,plain,
% 0.54/0.58 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(39,plain,
% 0.54/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[38])).
% 0.54/0.58 tff(40,plain,
% 0.54/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(41,plain,
% 0.54/0.58 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(42,plain,
% 0.54/0.58 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[41])).
% 0.54/0.58 tff(43,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 0.54/0.58 tff(44,plain,
% 0.54/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.54/0.58 tff(45,plain,
% 0.54/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.54/0.58 tff(46,plain,(
% 0.54/0.58 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(skolemize,[status(sab)],[45])).
% 0.54/0.58 tff(47,plain,
% 0.54/0.58 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.54/0.58 tff(48,plain,
% 0.54/0.58 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(49,plain,
% 0.54/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 0.54/0.58 inference(quant_inst,[status(thm)],[])).
% 0.54/0.58 tff(50,plain,
% 0.54/0.58 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.54/0.58 tff(51,plain,
% 0.54/0.58 (l1_struct_0(A!0)),
% 0.54/0.58 inference(unit_resolution,[status(thm)],[50, 26, 47])).
% 0.54/0.58 tff(52,plain,
% 0.54/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(53,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[52])).
% 0.54/0.58 tff(54,plain,
% 0.54/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(55,plain,
% 0.54/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[54])).
% 0.54/0.58 tff(56,plain,
% 0.54/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(57,plain,
% 0.54/0.58 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(58,plain,
% 0.54/0.58 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[57])).
% 0.54/0.58 tff(59,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')).
% 0.54/0.58 tff(60,plain,
% 0.54/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.54/0.58 tff(61,plain,
% 0.54/0.58 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.54/0.58 tff(62,plain,(
% 0.54/0.58 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.54/0.58 inference(skolemize,[status(sab)],[61])).
% 0.54/0.58 tff(63,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.54/0.58 tff(64,plain,
% 0.54/0.58 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.54/0.58 tff(65,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(66,plain,
% 0.54/0.58 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(67,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.54/0.58 inference(monotonicity,[status(thm)],[66])).
% 0.54/0.58 tff(68,plain,
% 0.54/0.58 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.54/0.58 inference(transitivity,[status(thm)],[67, 65])).
% 0.54/0.58 tff(69,plain,
% 0.54/0.58 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.54/0.58 inference(quant_inst,[status(thm)],[])).
% 0.54/0.58 tff(70,plain,
% 0.54/0.58 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.54/0.58 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.54/0.58 tff(71,plain,
% 0.54/0.58 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.54/0.58 inference(unit_resolution,[status(thm)],[70, 30, 64])).
% 0.54/0.58 tff(72,plain,
% 0.54/0.58 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.54/0.58 inference(unit_resolution,[status(thm)],[71, 51])).
% 0.54/0.58 tff(73,plain,
% 0.54/0.58 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(74,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[73])).
% 0.54/0.58 tff(75,plain,
% 0.54/0.58 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(76,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[75])).
% 0.54/0.58 tff(77,plain,
% 0.54/0.58 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(78,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[77])).
% 0.54/0.58 tff(79,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.54/0.58 inference(transitivity,[status(thm)],[78, 76])).
% 0.54/0.58 tff(80,plain,
% 0.54/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(81,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[80])).
% 0.54/0.58 tff(82,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.58 inference(rewrite,[status(thm)],[])).
% 0.54/0.58 tff(83,plain,
% 0.54/0.58 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 0.54/0.58 inference(bind,[status(th)],[])).
% 0.54/0.58 tff(84,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.58 inference(quant_intro,[status(thm)],[83])).
% 0.54/0.58 tff(85,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')).
% 0.54/0.58 tff(86,plain,
% 0.54/0.58 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.54/0.59 tff(87,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.54/0.59 tff(88,plain,(
% 0.54/0.59 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.59 inference(skolemize,[status(sab)],[87])).
% 0.54/0.59 tff(89,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.54/0.59 tff(90,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.54/0.59 tff(91,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[90, 74])).
% 0.54/0.59 tff(92,plain,
% 0.54/0.59 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> 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))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(93,plain,
% 0.54/0.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> 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))))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(94,plain,
% 0.54/0.59 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> 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)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.54/0.59 tff(95,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[94, 91, 72, 37])).
% 0.54/0.59 tff(96,plain,
% 0.54/0.59 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(D, k4_autgroup(A!0)))) | (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(97,plain,
% 0.54/0.59 (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.54/0.59 tff(98,plain,
% 0.54/0.59 (^[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))))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(99,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[98])).
% 0.54/0.59 tff(100,plain,
% 0.54/0.59 (^[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))))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(101,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[100])).
% 0.54/0.59 tff(102,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(transitivity,[status(thm)],[101, 99])).
% 0.54/0.59 tff(103,plain,
% 0.54/0.59 (^[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)))))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(104,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[103])).
% 0.54/0.59 tff(105,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(106,plain,
% 0.54/0.59 (^[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))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(107,plain,
% 0.54/0.59 (![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)))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[106])).
% 0.54/0.59 tff(108,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')).
% 0.54/0.59 tff(109,plain,
% 0.54/0.59 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.54/0.59 tff(110,plain,
% 0.54/0.59 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.54/0.59 tff(111,plain,(
% 0.54/0.59 ![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)))))),
% 0.54/0.59 inference(skolemize,[status(sab)],[110])).
% 0.54/0.59 tff(112,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.54/0.59 tff(113,plain,
% 0.54/0.59 (![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)))))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.54/0.59 tff(114,plain,
% 0.54/0.59 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_1(B, A), A)) | r2_hidden(tptp_fun_C_1(B, A), B)))))))) | (~((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))))))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(115,plain,
% 0.54/0.59 (~((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.54/0.59 tff(116,plain,
% 0.54/0.59 (((~((~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | ![C: $i] : ((~r2_hidden(C, k4_autgroup(A!0))) | r2_hidden(C, k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))))) | (r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(117,plain,
% 0.54/0.59 (r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.54/0.59 tff(118,plain,
% 0.54/0.59 (~r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.59 inference(or_elim,[status(thm)],[24])).
% 0.54/0.59 tff(119,plain,
% 0.54/0.59 ((~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))) | r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(120,plain,
% 0.54/0.59 ((~(r1_tarski(k4_autgroup(A!0), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.54/0.59 tff(121,plain,
% 0.54/0.59 (~((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.54/0.59 tff(122,plain,
% 0.54/0.59 (((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(123,plain,
% 0.54/0.59 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.54/0.59 tff(124,plain,
% 0.54/0.59 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(125,plain,
% 0.54/0.59 (![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))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[124])).
% 0.54/0.59 tff(126,plain,
% 0.54/0.59 (![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))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(127,plain,
% 0.54/0.59 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(128,plain,
% 0.54/0.59 (![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))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[127])).
% 0.54/0.59 tff(129,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 0.54/0.59 tff(130,plain,
% 0.54/0.59 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.54/0.59 tff(131,plain,
% 0.54/0.59 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.54/0.59 tff(132,plain,(
% 0.54/0.59 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.54/0.59 inference(skolemize,[status(sab)],[131])).
% 0.54/0.59 tff(133,plain,
% 0.54/0.59 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.54/0.59 tff(134,plain,
% 0.54/0.59 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(135,plain,
% 0.54/0.59 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.54/0.59 inference(quant_inst,[status(thm)],[])).
% 0.54/0.59 tff(136,plain,
% 0.54/0.59 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.54/0.59 tff(137,plain,
% 0.54/0.59 (m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 0.54/0.59 tff(138,plain,
% 0.54/0.59 ((~(m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) | (~m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))),
% 0.54/0.59 inference(tautology,[status(thm)],[])).
% 0.54/0.59 tff(139,plain,
% 0.54/0.59 ((~(m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0)) <=> m1_subset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0)))) | m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.54/0.59 tff(140,plain,
% 0.54/0.59 (m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))),
% 0.54/0.59 inference(unit_resolution,[status(thm)],[139, 97])).
% 0.54/0.59 tff(141,plain,
% 0.54/0.59 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(142,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[141])).
% 0.54/0.59 tff(143,plain,
% 0.54/0.59 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(144,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[143])).
% 0.54/0.59 tff(145,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.59 inference(transitivity,[status(thm)],[144, 142])).
% 0.54/0.59 tff(146,plain,
% 0.54/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), quant_intro(proof_bind(^[D: $i] : rewrite(((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B)))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(147,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[146])).
% 0.54/0.59 tff(148,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.54/0.59 inference(rewrite,[status(thm)],[])).
% 0.54/0.59 tff(149,plain,
% 0.54/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> (m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), rewrite((m2_fraenkel(D, A, B, C) => (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))), ((m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), (![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))) <=> ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))))), rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))), ((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))))),
% 0.54/0.59 inference(bind,[status(th)],[])).
% 0.54/0.59 tff(150,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.54/0.59 inference(quant_intro,[status(thm)],[149])).
% 0.54/0.59 tff(151,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) => ((v1_funct_1(D) & v1_funct_2(D, A, B)) & m2_relset_1(D, A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_fraenkel')).
% 0.54/0.59 tff(152,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.54/0.59 tff(153,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.54/0.59 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.54/0.59 tff(154,plain,(
% 0.54/0.59 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (v1_funct_1(D) & v1_funct_2(D, A, B) & m2_relset_1(D, A, B))))),
% 0.54/0.59 inference(skolemize,[status(sab)],[153])).
% 0.54/0.59 tff(155,plain,
% 0.54/0.59 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.54/0.60 tff(156,plain,
% 0.54/0.60 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.54/0.60 tff(157,plain,
% 0.54/0.60 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(158,plain,
% 0.54/0.60 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(159,plain,
% 0.54/0.60 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : ((~m2_fraenkel(D, A, B, C)) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m2_relset_1(D, A, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k4_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.54/0.60 tff(160,plain,
% 0.54/0.60 (![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[159, 156, 72, 37])).
% 0.54/0.60 tff(161,plain,
% 0.54/0.60 (((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(162,plain,
% 0.54/0.60 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(163,plain,
% 0.54/0.60 ((~![D: $i] : ((~m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0), k4_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.54/0.60 tff(164,plain,
% 0.54/0.60 (~((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[163, 160, 140])).
% 0.54/0.60 tff(165,plain,
% 0.54/0.60 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(tautology,[status(thm)],[])).
% 0.54/0.60 tff(166,plain,
% 0.54/0.60 (m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.54/0.60 tff(167,plain,
% 0.54/0.60 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(168,plain,
% 0.54/0.60 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[167])).
% 0.54/0.60 tff(169,plain,
% 0.54/0.60 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(170,plain,
% 0.54/0.60 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(171,plain,
% 0.54/0.60 (![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[170])).
% 0.54/0.60 tff(172,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(B)) => (k1_fraenkel(A, B) = k1_funct_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_fraenkel')).
% 0.54/0.60 tff(173,plain,
% 0.54/0.60 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.54/0.60 tff(174,plain,
% 0.54/0.60 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.54/0.60 tff(175,plain,(
% 0.54/0.60 ![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(skolemize,[status(sab)],[174])).
% 0.54/0.60 tff(176,plain,
% 0.54/0.60 (![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.54/0.60 tff(177,plain,
% 0.54/0.60 (((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(178,plain,
% 0.54/0.60 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(179,plain,
% 0.54/0.60 ((~![A: $i, B: $i] : (v1_xboole_0(B) | (k1_fraenkel(A, B) = k1_funct_2(A, B)))) | v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.54/0.60 tff(180,plain,
% 0.54/0.60 (v1_xboole_0(u1_struct_0(A!0)) | (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.54/0.60 tff(181,plain,
% 0.54/0.60 (k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[180, 72])).
% 0.54/0.60 tff(182,plain,
% 0.54/0.60 (k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)) = k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(symmetry,[status(thm)],[181])).
% 0.54/0.60 tff(183,plain,
% 0.54/0.60 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) <=> r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[182])).
% 0.54/0.60 tff(184,plain,
% 0.54/0.60 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))) <=> r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(symmetry,[status(thm)],[183])).
% 0.54/0.60 tff(185,plain,
% 0.54/0.60 ((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[184])).
% 0.54/0.60 tff(186,plain,
% 0.54/0.60 (((~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k4_autgroup(A!0))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))) | (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.60 inference(tautology,[status(thm)],[])).
% 0.54/0.60 tff(187,plain,
% 0.54/0.60 (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[186, 121])).
% 0.54/0.60 tff(188,plain,
% 0.54/0.60 (~r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[187, 185])).
% 0.54/0.60 tff(189,plain,
% 0.54/0.60 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 0.54/0.60 inference(tautology,[status(thm)],[])).
% 0.54/0.60 tff(190,plain,
% 0.54/0.60 (v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[189, 164])).
% 0.54/0.60 tff(191,plain,
% 0.54/0.60 (((~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(tautology,[status(thm)],[])).
% 0.54/0.60 tff(192,plain,
% 0.54/0.60 (v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[191, 164])).
% 0.54/0.60 tff(193,plain,
% 0.54/0.60 (^[A: $i, B: $i] : refl((r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(194,plain,
% 0.54/0.60 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) <=> ![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[193])).
% 0.54/0.60 tff(195,plain,
% 0.54/0.60 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))), ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))), ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))))), (((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))), (((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(196,plain,
% 0.54/0.60 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[195])).
% 0.54/0.60 tff(197,plain,
% 0.54/0.60 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(198,plain,
% 0.54/0.60 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) <=> (v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))), ((((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))), ((((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(199,plain,
% 0.54/0.60 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[198])).
% 0.54/0.60 tff(200,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, A, A)) & m2_relset_1(B, A, A)) => r2_hidden(B, k1_funct_2(A, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_funct_2')).
% 0.54/0.60 tff(201,plain,
% 0.54/0.60 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.54/0.60 tff(202,plain,
% 0.54/0.60 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.54/0.60 tff(203,plain,(
% 0.54/0.60 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, A, A) & m2_relset_1(B, A, A))) | r2_hidden(B, k1_funct_2(A, A)))),
% 0.54/0.60 inference(skolemize,[status(sab)],[202])).
% 0.54/0.60 tff(204,plain,
% 0.54/0.60 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.54/0.60 tff(205,plain,
% 0.54/0.60 (![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.54/0.60 tff(206,plain,
% 0.54/0.60 (((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(207,plain,
% 0.54/0.61 ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(208,plain,
% 0.54/0.61 ((~![A: $i, B: $i] : (r2_hidden(B, k1_funct_2(A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, A, A)) | (~m2_relset_1(B, A, A)))) | r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.54/0.61 tff(209,plain,
% 0.54/0.61 (r2_hidden(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), k1_funct_2(u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)))) | (~v1_funct_2(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_1(k1_fraenkel(u1_struct_0(A!0), u1_struct_0(A!0)), k4_autgroup(A!0)), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[208, 205])).
% 0.54/0.61 tff(210,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[209, 192, 190, 188, 166])).
% 0.54/0.61 % SZS output end Proof
%------------------------------------------------------------------------------