TSTP Solution File: SET909+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Tue Sep 20 05:08:35 EDT 2022
% Result : Theorem 14.72s 9.79s
% Output : Proof 14.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 08:53:37 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 14.72/9.79 % SZS status Theorem
% 14.72/9.79 % SZS output start Proof
% 14.72/9.79 tff(in_type, type, (
% 14.72/9.79 in: ( $i * $i ) > $o)).
% 14.72/9.79 tff(empty_set_type, type, (
% 14.72/9.79 empty_set: $i)).
% 14.72/9.79 tff(set_union2_type, type, (
% 14.72/9.79 set_union2: ( $i * $i ) > $i)).
% 14.72/9.79 tff(tptp_fun_C_5_type, type, (
% 14.72/9.79 tptp_fun_C_5: $i)).
% 14.72/9.79 tff(tptp_fun_B_6_type, type, (
% 14.72/9.79 tptp_fun_B_6: $i)).
% 14.72/9.79 tff(tptp_fun_D_2_type, type, (
% 14.72/9.79 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 14.72/9.79 tff(tptp_fun_B_0_type, type, (
% 14.72/9.79 tptp_fun_B_0: $i > $i)).
% 14.72/9.79 tff(unordered_pair_type, type, (
% 14.72/9.79 unordered_pair: ( $i * $i ) > $i)).
% 14.72/9.79 tff(tptp_fun_A_7_type, type, (
% 14.72/9.79 tptp_fun_A_7: $i)).
% 14.72/9.79 tff(tptp_fun_D_1_type, type, (
% 14.72/9.79 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 14.72/9.79 tff(tptp_fun_A_3_type, type, (
% 14.72/9.79 tptp_fun_A_3: $i)).
% 14.72/9.79 tff(1,assumption,((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))), introduced(assumption)).
% 14.72/9.79 tff(2,assumption,(~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)), introduced(assumption)).
% 14.72/9.79 tff(3,plain,
% 14.72/9.79 ((~((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6) | (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))),
% 14.72/9.79 inference(tautology,[status(thm)],[])).
% 14.72/9.79 tff(4,plain,
% 14.72/9.79 (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)),
% 14.72/9.79 inference(unit_resolution,[status(thm)],[3, 2, 1])).
% 14.72/9.79 tff(5,assumption,(in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)), introduced(assumption)).
% 14.72/9.79 tff(6,plain,
% 14.72/9.79 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 14.72/9.79 inference(bind,[status(th)],[])).
% 14.72/9.79 tff(7,plain,
% 14.72/9.79 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[6])).
% 14.72/9.80 tff(8,plain,
% 14.72/9.80 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(pull_quant,[status(thm)],[])).
% 14.72/9.80 tff(9,plain,
% 14.72/9.80 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(10,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[9])).
% 14.72/9.80 tff(11,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[10, 8])).
% 14.72/9.80 tff(12,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[11, 7])).
% 14.72/9.80 tff(13,plain,
% 14.72/9.80 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(14,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[13])).
% 14.72/9.80 tff(15,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[14, 12])).
% 14.72/9.80 tff(16,plain,
% 14.72/9.80 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(17,plain,
% 14.72/9.80 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[16])).
% 14.72/9.80 tff(18,plain,
% 14.72/9.80 (^[A: $i] : rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(19,plain,
% 14.72/9.80 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[18])).
% 14.72/9.80 tff(20,plain,
% 14.72/9.80 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(21,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 14.72/9.80 tff(22,plain,
% 14.72/9.80 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[21, 20])).
% 14.72/9.80 tff(23,plain,(
% 14.72/9.80 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | (~(~in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(skolemize,[status(sab)],[22])).
% 14.72/9.80 tff(24,plain,
% 14.72/9.80 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[23, 19])).
% 14.72/9.80 tff(25,plain,
% 14.72/9.80 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[24, 17])).
% 14.72/9.80 tff(26,plain,
% 14.72/9.80 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[25, 15])).
% 14.72/9.80 tff(27,plain,
% 14.72/9.80 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(28,plain,
% 14.72/9.80 ((~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set))))) <=> (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(29,plain,
% 14.72/9.80 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))),
% 14.72/9.80 inference(monotonicity,[status(thm)],[28])).
% 14.72/9.80 tff(30,plain,
% 14.72/9.80 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))),
% 14.72/9.80 inference(transitivity,[status(thm)],[29, 27])).
% 14.72/9.80 tff(31,plain,
% 14.72/9.80 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))),
% 14.72/9.80 inference(quant_inst,[status(thm)],[])).
% 14.72/9.80 tff(32,plain,
% 14.72/9.80 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[31, 30])).
% 14.72/9.80 tff(33,plain,
% 14.72/9.80 ($false),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[32, 26, 5])).
% 14.72/9.80 tff(34,plain,(~in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 14.72/9.80 tff(35,plain,
% 14.72/9.80 ((~(in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))) | in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)),
% 14.72/9.80 inference(tautology,[status(thm)],[])).
% 14.72/9.80 tff(36,plain,
% 14.72/9.80 ((~(in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[35, 34])).
% 14.72/9.80 tff(37,plain,
% 14.72/9.80 ($false),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[36, 4, 2])).
% 14.72/9.80 tff(38,plain,(in(tptp_fun_D_2(B!6, B!6, empty_set), B!6) | (~((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))))), inference(lemma,lemma(discharge,[]))).
% 14.72/9.80 tff(39,plain,
% 14.72/9.80 (in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[38, 1])).
% 14.72/9.80 tff(40,plain,
% 14.72/9.80 ((in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))),
% 14.72/9.80 inference(tautology,[status(thm)],[])).
% 14.72/9.80 tff(41,plain,
% 14.72/9.80 (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[40, 39])).
% 14.72/9.80 tff(42,plain,
% 14.72/9.80 ((~((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))) | (~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) | (~(in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))),
% 14.72/9.80 inference(tautology,[status(thm)],[])).
% 14.72/9.80 tff(43,plain,
% 14.72/9.80 ($false),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[42, 41, 39, 1])).
% 14.72/9.80 tff(44,plain,(~((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))), inference(lemma,lemma(discharge,[]))).
% 14.72/9.80 tff(45,plain,
% 14.72/9.80 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(46,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[45])).
% 14.72/9.80 tff(47,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(pull_quant,[status(thm)],[])).
% 14.72/9.80 tff(48,plain,
% 14.72/9.80 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(49,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[48])).
% 14.72/9.80 tff(50,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[49, 47])).
% 14.72/9.80 tff(51,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[50, 46])).
% 14.72/9.80 tff(52,plain,
% 14.72/9.80 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(53,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[52])).
% 14.72/9.80 tff(54,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[53, 51])).
% 14.72/9.80 tff(55,plain,
% 14.72/9.80 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), monotonicity(rewrite(((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))) <=> ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))), (((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))) <=> ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(56,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[55])).
% 14.72/9.80 tff(57,plain,
% 14.72/9.80 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))),
% 14.72/9.80 inference(bind,[status(th)],[])).
% 14.72/9.80 tff(58,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))),
% 14.72/9.80 inference(quant_intro,[status(thm)],[57])).
% 14.72/9.80 tff(59,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(60,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 14.72/9.80 tff(61,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[60, 59])).
% 14.72/9.80 tff(62,plain,(
% 14.72/9.80 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B))))))),
% 14.72/9.80 inference(skolemize,[status(sab)],[61])).
% 14.72/9.80 tff(63,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[62, 58])).
% 14.72/9.80 tff(64,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[63, 56])).
% 14.72/9.80 tff(65,plain,
% 14.72/9.80 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))),
% 14.72/9.80 inference(modus_ponens,[status(thm)],[64, 54])).
% 14.72/9.80 tff(66,plain,
% 14.72/9.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(B!6 = set_union2(empty_set, B!6))) | (in(tptp_fun_D_2(empty_set, B!6, C!5), B!6) <=> (in(tptp_fun_D_2(empty_set, B!6, C!5), empty_set) | in(tptp_fun_D_2(empty_set, B!6, C!5), B!6))))) | (~((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))))))),
% 14.72/9.80 inference(quant_inst,[status(thm)],[])).
% 14.72/9.80 tff(67,plain,
% 14.72/9.80 (~((~((~(B!6 = set_union2(empty_set, B!6))) | (in(tptp_fun_D_2(empty_set, B!6, C!5), B!6) <=> (in(tptp_fun_D_2(empty_set, B!6, C!5), empty_set) | in(tptp_fun_D_2(empty_set, B!6, C!5), B!6))))) | (~((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))))))),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[66, 65])).
% 14.72/9.80 tff(68,plain,
% 14.72/9.80 (((~((~(B!6 = set_union2(empty_set, B!6))) | (in(tptp_fun_D_2(empty_set, B!6, C!5), B!6) <=> (in(tptp_fun_D_2(empty_set, B!6, C!5), empty_set) | in(tptp_fun_D_2(empty_set, B!6, C!5), B!6))))) | (~((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))))) | ((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))))),
% 14.72/9.80 inference(tautology,[status(thm)],[])).
% 14.72/9.80 tff(69,plain,
% 14.72/9.80 ((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[68, 67])).
% 14.72/9.80 tff(70,plain,
% 14.72/9.80 ((~((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6))))) | (B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))),
% 14.72/9.80 inference(tautology,[status(thm)],[])).
% 14.72/9.80 tff(71,plain,
% 14.72/9.80 ((B!6 = set_union2(empty_set, B!6)) | ((~in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)) <=> (in(tptp_fun_D_2(B!6, B!6, empty_set), empty_set) | in(tptp_fun_D_2(B!6, B!6, empty_set), B!6)))),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[70, 69])).
% 14.72/9.80 tff(72,plain,
% 14.72/9.80 (B!6 = set_union2(empty_set, B!6)),
% 14.72/9.80 inference(unit_resolution,[status(thm)],[71, 44])).
% 14.72/9.80 tff(73,plain,
% 14.72/9.80 (set_union2(empty_set, B!6) = B!6),
% 14.72/9.80 inference(symmetry,[status(thm)],[72])).
% 14.72/9.80 tff(74,plain,
% 14.72/9.80 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))))))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(75,plain,
% 14.72/9.80 ((~((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5))))) | (~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))))) <=> (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))))))),
% 14.72/9.80 inference(rewrite,[status(thm)],[])).
% 14.72/9.80 tff(76,plain,
% 14.72/9.80 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5))))) | (~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))))))),
% 14.72/9.80 inference(monotonicity,[status(thm)],[75])).
% 14.72/9.80 tff(77,plain,
% 14.72/9.80 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5))))) | (~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))))))),
% 14.72/9.80 inference(transitivity,[status(thm)],[76, 74])).
% 14.72/9.80 tff(78,plain,
% 14.72/9.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5))))) | (~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5)))))))),
% 14.72/9.80 inference(quant_inst,[status(thm)],[])).
% 14.72/9.80 tff(79,plain,
% 14.72/9.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[78, 77])).
% 14.72/9.81 tff(80,plain,
% 14.72/9.81 (~((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))))),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[79, 65])).
% 14.72/9.81 tff(81,plain,
% 14.72/9.81 (((~((empty_set = set_union2(empty_set, C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, empty_set), empty_set) | in(tptp_fun_D_2(empty_set, C!5, empty_set), C!5))))) | (~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))))) | ((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))),
% 14.72/9.81 inference(tautology,[status(thm)],[])).
% 14.72/9.81 tff(82,plain,
% 14.72/9.81 ((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[81, 80])).
% 14.72/9.81 tff(83,plain,
% 14.72/9.81 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(84,plain,
% 14.72/9.81 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[83])).
% 14.72/9.81 tff(85,plain,
% 14.72/9.81 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(86,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 14.72/9.81 tff(87,plain,
% 14.72/9.81 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[86, 85])).
% 14.72/9.81 tff(88,plain,(
% 14.72/9.81 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 14.72/9.81 inference(skolemize,[status(sab)],[87])).
% 14.72/9.81 tff(89,plain,
% 14.72/9.81 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[88, 84])).
% 14.72/9.81 tff(90,plain,
% 14.72/9.81 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 14.72/9.81 inference(quant_inst,[status(thm)],[])).
% 14.72/9.81 tff(91,plain,
% 14.72/9.81 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[90, 89])).
% 14.72/9.81 tff(92,plain,
% 14.72/9.81 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 14.72/9.81 inference(symmetry,[status(thm)],[91])).
% 14.72/9.81 tff(93,assumption,((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))), introduced(assumption)).
% 14.72/9.81 tff(94,plain,
% 14.72/9.81 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(95,plain,
% 14.72/9.81 ((~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set))))) <=> (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(96,plain,
% 14.72/9.81 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 14.72/9.81 inference(monotonicity,[status(thm)],[95])).
% 14.72/9.81 tff(97,plain,
% 14.72/9.81 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))),
% 14.72/9.81 inference(transitivity,[status(thm)],[96, 94])).
% 14.72/9.81 tff(98,plain,
% 14.72/9.81 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))),
% 14.72/9.81 inference(quant_inst,[status(thm)],[])).
% 14.72/9.81 tff(99,plain,
% 14.72/9.81 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[98, 97])).
% 14.72/9.81 tff(100,plain,
% 14.72/9.81 (~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[99, 26])).
% 14.72/9.81 tff(101,plain,
% 14.72/9.81 ((~((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))) | in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) | ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))),
% 14.72/9.81 inference(tautology,[status(thm)],[])).
% 14.72/9.81 tff(102,plain,
% 14.72/9.81 ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[101, 100, 93])).
% 14.72/9.81 tff(103,assumption,((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))), introduced(assumption)).
% 14.72/9.81 tff(104,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(105,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[104])).
% 14.72/9.81 tff(106,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(pull_quant,[status(thm)],[])).
% 14.72/9.81 tff(107,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(108,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[107])).
% 14.72/9.81 tff(109,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(transitivity,[status(thm)],[108, 106])).
% 14.72/9.81 tff(110,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(transitivity,[status(thm)],[109, 105])).
% 14.72/9.81 tff(111,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(112,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[111])).
% 14.72/9.81 tff(113,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(transitivity,[status(thm)],[112, 110])).
% 14.72/9.81 tff(114,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(115,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[114])).
% 14.72/9.81 tff(116,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(117,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[116])).
% 14.72/9.81 tff(118,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(119,plain,
% 14.72/9.81 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 14.72/9.81 inference(bind,[status(th)],[])).
% 14.72/9.81 tff(120,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 14.72/9.81 inference(quant_intro,[status(thm)],[119])).
% 14.72/9.81 tff(121,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 14.72/9.81 tff(122,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[121, 120])).
% 14.72/9.81 tff(123,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[122, 118])).
% 14.72/9.81 tff(124,plain,(
% 14.72/9.81 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 14.72/9.81 inference(skolemize,[status(sab)],[123])).
% 14.72/9.81 tff(125,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[124, 117])).
% 14.72/9.81 tff(126,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[125, 115])).
% 14.72/9.81 tff(127,plain,
% 14.72/9.81 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[126, 113])).
% 14.72/9.81 tff(128,plain,
% 14.72/9.81 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(129,plain,
% 14.72/9.81 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = B!6) | (tptp_fun_D_1(empty_set, A!7, B!6) = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))) <=> (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 14.72/9.81 inference(rewrite,[status(thm)],[])).
% 14.72/9.81 tff(130,plain,
% 14.72/9.81 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = B!6) | (tptp_fun_D_1(empty_set, A!7, B!6) = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 14.72/9.81 inference(monotonicity,[status(thm)],[129])).
% 14.72/9.81 tff(131,plain,
% 14.72/9.81 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = B!6) | (tptp_fun_D_1(empty_set, A!7, B!6) = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 14.72/9.81 inference(transitivity,[status(thm)],[130, 128])).
% 14.72/9.81 tff(132,plain,
% 14.72/9.81 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = B!6) | (tptp_fun_D_1(empty_set, A!7, B!6) = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 14.72/9.81 inference(quant_inst,[status(thm)],[])).
% 14.72/9.81 tff(133,plain,
% 14.72/9.81 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))),
% 14.72/9.81 inference(modus_ponens,[status(thm)],[132, 131])).
% 14.72/9.81 tff(134,plain,
% 14.72/9.81 ($false),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[133, 127, 103])).
% 14.72/9.81 tff(135,plain,(~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))), inference(lemma,lemma(discharge,[]))).
% 14.72/9.81 tff(136,plain,
% 14.72/9.81 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7))) <=> ((tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_1(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))) | ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))),
% 14.72/9.81 inference(tautology,[status(thm)],[])).
% 14.72/9.81 tff(137,plain,
% 14.72/9.81 ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[136, 135])).
% 14.72/9.81 tff(138,plain,
% 14.72/9.81 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))),
% 14.72/9.81 inference(quant_inst,[status(thm)],[])).
% 14.72/9.81 tff(139,plain,
% 14.72/9.81 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[138, 89])).
% 14.72/9.81 tff(140,plain,
% 14.72/9.81 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.72/9.81 inference(tautology,[status(thm)],[])).
% 14.72/9.81 tff(141,plain,
% 14.72/9.81 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[140, 139])).
% 14.72/9.81 tff(142,plain,
% 14.72/9.81 (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))),
% 14.72/9.81 inference(unit_resolution,[status(thm)],[141, 137])).
% 14.72/9.81 tff(143,plain,
% 14.72/9.81 ((~(in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))) | in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | (~((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.72/9.82 inference(tautology,[status(thm)],[])).
% 14.72/9.82 tff(144,plain,
% 14.72/9.82 (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | (~((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[143, 142])).
% 14.72/9.82 tff(145,plain,
% 14.72/9.82 (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[144, 102])).
% 14.72/9.82 tff(146,plain,
% 14.72/9.82 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))) | (~((empty_set = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 14.72/9.82 inference(quant_inst,[status(thm)],[])).
% 14.72/9.82 tff(147,plain,
% 14.72/9.82 (~((~((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))) | (~((empty_set = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), C!5))))))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[146, 65])).
% 14.72/9.82 tff(148,plain,
% 14.72/9.82 (((~((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))) | (~((empty_set = set_union2(unordered_pair(B!6, A!7), C!5)) | ((~in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), empty_set)) <=> (in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_2(empty_set, C!5, unordered_pair(B!6, A!7)), C!5)))))) | ((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))),
% 14.72/9.82 inference(tautology,[status(thm)],[])).
% 14.72/9.82 tff(149,plain,
% 14.72/9.82 ((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[148, 147])).
% 14.72/9.82 tff(150,plain,
% 14.72/9.82 (set_union2(unordered_pair(B!6, A!7), C!5) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 14.72/9.82 inference(monotonicity,[status(thm)],[92])).
% 14.72/9.82 tff(151,plain,
% 14.72/9.82 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(unordered_pair(B!6, A!7), C!5)),
% 14.72/9.82 inference(symmetry,[status(thm)],[150])).
% 14.72/9.82 tff(152,plain,
% 14.72/9.82 ((~(~(set_union2(unordered_pair(A!7, B!6), C!5) = empty_set))) <=> (set_union2(unordered_pair(A!7, B!6), C!5) = empty_set)),
% 14.72/9.82 inference(rewrite,[status(thm)],[])).
% 14.72/9.82 tff(153,plain,
% 14.72/9.82 ((~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))) <=> (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set)))),
% 14.72/9.82 inference(rewrite,[status(thm)],[])).
% 14.72/9.82 tff(154,axiom,(~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t50_zfmisc_1')).
% 14.72/9.82 tff(155,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[154, 153])).
% 14.72/9.82 tff(156,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[155, 153])).
% 14.72/9.82 tff(157,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[156, 153])).
% 14.72/9.82 tff(158,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[157, 153])).
% 14.72/9.82 tff(159,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[158, 153])).
% 14.72/9.82 tff(160,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[159, 153])).
% 14.72/9.82 tff(161,plain,
% 14.72/9.82 (~![A: $i, B: $i, C: $i] : (~(set_union2(unordered_pair(A, B), C) = empty_set))),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[160, 153])).
% 14.72/9.82 tff(162,plain,(
% 14.72/9.82 ~(~(set_union2(unordered_pair(A!7, B!6), C!5) = empty_set))),
% 14.72/9.82 inference(skolemize,[status(sab)],[161])).
% 14.72/9.82 tff(163,plain,
% 14.72/9.82 (set_union2(unordered_pair(A!7, B!6), C!5) = empty_set),
% 14.72/9.82 inference(modus_ponens,[status(thm)],[162, 152])).
% 14.72/9.82 tff(164,plain,
% 14.72/9.82 (empty_set = set_union2(unordered_pair(A!7, B!6), C!5)),
% 14.72/9.82 inference(symmetry,[status(thm)],[163])).
% 14.72/9.82 tff(165,plain,
% 14.72/9.82 (empty_set = set_union2(unordered_pair(B!6, A!7), C!5)),
% 14.72/9.82 inference(transitivity,[status(thm)],[164, 151])).
% 14.72/9.82 tff(166,plain,
% 14.72/9.82 ((~((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))) | (~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)))),
% 14.72/9.82 inference(tautology,[status(thm)],[])).
% 14.72/9.82 tff(167,plain,
% 14.72/9.82 ((~((~(empty_set = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))))) | (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[166, 165])).
% 14.72/9.82 tff(168,plain,
% 14.72/9.82 (in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[167, 149])).
% 14.72/9.82 tff(169,plain,
% 14.72/9.82 ((~(in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) <=> (in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)))) | in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set) | (~(in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)))),
% 14.72/9.82 inference(tautology,[status(thm)],[])).
% 14.72/9.82 tff(170,plain,
% 14.72/9.82 (~(in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5))),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[169, 168, 100])).
% 14.72/9.82 tff(171,plain,
% 14.72/9.82 ((in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(empty_set, A!7, B!6), C!5)) | (~in(tptp_fun_D_1(empty_set, A!7, B!6), unordered_pair(B!6, A!7)))),
% 14.72/9.82 inference(tautology,[status(thm)],[])).
% 14.72/9.82 tff(172,plain,
% 14.72/9.82 ($false),
% 14.72/9.82 inference(unit_resolution,[status(thm)],[171, 170, 145])).
% 14.72/9.82 tff(173,plain,(~((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))), inference(lemma,lemma(discharge,[]))).
% 14.72/9.82 tff(174,plain,
% 14.72/9.82 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(B!6, A!7))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), empty_set) <=> ((tptp_fun_D_2(empty_set, A!3, A!7) = A!7) | (tptp_fun_D_2(empty_set, A!3, A!7) = B!6))))) | (~((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))))))),
% 14.86/9.82 inference(quant_inst,[status(thm)],[])).
% 14.86/9.82 tff(175,plain,
% 14.86/9.82 (~((~((~(empty_set = unordered_pair(B!6, A!7))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), empty_set) <=> ((tptp_fun_D_2(empty_set, A!3, A!7) = A!7) | (tptp_fun_D_2(empty_set, A!3, A!7) = B!6))))) | (~((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[174, 127])).
% 14.86/9.82 tff(176,plain,
% 14.86/9.82 (((~((~(empty_set = unordered_pair(B!6, A!7))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), empty_set) <=> ((tptp_fun_D_2(empty_set, A!3, A!7) = A!7) | (tptp_fun_D_2(empty_set, A!3, A!7) = B!6))))) | (~((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))))) | ((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(177,plain,
% 14.86/9.82 ((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[176, 175])).
% 14.86/9.82 tff(178,plain,
% 14.86/9.82 ((~((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6))))) | (empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(179,plain,
% 14.86/9.82 ((empty_set = unordered_pair(B!6, A!7)) | ((~in(tptp_fun_D_1(empty_set, A!7, B!6), empty_set)) <=> ((tptp_fun_D_1(empty_set, A!7, B!6) = A!7) | (tptp_fun_D_1(empty_set, A!7, B!6) = B!6)))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[178, 177])).
% 14.86/9.82 tff(180,plain,
% 14.86/9.82 (empty_set = unordered_pair(B!6, A!7)),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[179, 173])).
% 14.86/9.82 tff(181,plain,
% 14.86/9.82 (empty_set = unordered_pair(A!7, B!6)),
% 14.86/9.82 inference(transitivity,[status(thm)],[180, 92])).
% 14.86/9.82 tff(182,plain,
% 14.86/9.82 (set_union2(empty_set, C!5) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 14.86/9.82 inference(monotonicity,[status(thm)],[181])).
% 14.86/9.82 tff(183,plain,
% 14.86/9.82 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(empty_set, C!5)),
% 14.86/9.82 inference(symmetry,[status(thm)],[182])).
% 14.86/9.82 tff(184,plain,
% 14.86/9.82 (empty_set = set_union2(empty_set, C!5)),
% 14.86/9.82 inference(transitivity,[status(thm)],[164, 183])).
% 14.86/9.82 tff(185,plain,
% 14.86/9.82 ((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))) | (~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(186,plain,
% 14.86/9.82 ((~((~(empty_set = set_union2(empty_set, C!5))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))))) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[185, 184])).
% 14.86/9.82 tff(187,plain,
% 14.86/9.82 (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[186, 82])).
% 14.86/9.82 tff(188,assumption,(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)), introduced(assumption)).
% 14.86/9.82 tff(189,plain,
% 14.86/9.82 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(rewrite,[status(thm)],[])).
% 14.86/9.82 tff(190,plain,
% 14.86/9.82 ((~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set))))) <=> (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))),
% 14.86/9.82 inference(rewrite,[status(thm)],[])).
% 14.86/9.82 tff(191,plain,
% 14.86/9.82 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(monotonicity,[status(thm)],[190])).
% 14.86/9.82 tff(192,plain,
% 14.86/9.82 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(transitivity,[status(thm)],[191, 189])).
% 14.86/9.82 tff(193,plain,
% 14.86/9.82 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))),
% 14.86/9.82 inference(quant_inst,[status(thm)],[])).
% 14.86/9.82 tff(194,plain,
% 14.86/9.82 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))),
% 14.86/9.82 inference(modus_ponens,[status(thm)],[193, 192])).
% 14.86/9.82 tff(195,plain,
% 14.86/9.82 ($false),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[194, 26, 188])).
% 14.86/9.82 tff(196,plain,(~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)), inference(lemma,lemma(discharge,[]))).
% 14.86/9.82 tff(197,plain,
% 14.86/9.82 ((~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) | (~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(198,plain,
% 14.86/9.82 ((~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))) | (~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[197, 196])).
% 14.86/9.82 tff(199,plain,
% 14.86/9.82 (~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[198, 187])).
% 14.86/9.82 tff(200,plain,
% 14.86/9.82 ((in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)) | (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(201,plain,
% 14.86/9.82 (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[200, 199])).
% 14.86/9.82 tff(202,plain,
% 14.86/9.82 (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set) <=> in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))),
% 14.86/9.82 inference(monotonicity,[status(thm)],[180])).
% 14.86/9.82 tff(203,plain,
% 14.86/9.82 ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), empty_set)) <=> (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))),
% 14.86/9.82 inference(monotonicity,[status(thm)],[202])).
% 14.86/9.82 tff(204,plain,
% 14.86/9.82 (~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))),
% 14.86/9.82 inference(modus_ponens,[status(thm)],[196, 203])).
% 14.86/9.82 tff(205,plain,
% 14.86/9.82 ((~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(206,plain,
% 14.86/9.82 (~(in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[205, 201, 204])).
% 14.86/9.82 tff(207,plain,
% 14.86/9.82 ((~((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(208,plain,
% 14.86/9.82 (~((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[207, 206, 201])).
% 14.86/9.82 tff(209,plain,
% 14.86/9.82 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_2(C, B, A), C)) <=> (in(tptp_fun_D_2(C, B, A), A) | in(tptp_fun_D_2(C, B, A), B)))))))) | (~((~((~(C!5 = set_union2(C!5, unordered_pair(B!6, A!7)))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) <=> (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) | in(tptp_fun_D_2(empty_set, A!3, A!7), unordered_pair(B!6, A!7)))))) | (~((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))))))),
% 14.86/9.82 inference(quant_inst,[status(thm)],[])).
% 14.86/9.82 tff(210,plain,
% 14.86/9.82 (~((~((~(C!5 = set_union2(C!5, unordered_pair(B!6, A!7)))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) <=> (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) | in(tptp_fun_D_2(empty_set, A!3, A!7), unordered_pair(B!6, A!7)))))) | (~((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))))))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[209, 65])).
% 14.86/9.82 tff(211,plain,
% 14.86/9.82 (((~((~(C!5 = set_union2(C!5, unordered_pair(B!6, A!7)))) | (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) <=> (in(tptp_fun_D_2(empty_set, A!3, A!7), C!5) | in(tptp_fun_D_2(empty_set, A!3, A!7), unordered_pair(B!6, A!7)))))) | (~((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))))) | ((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(212,plain,
% 14.86/9.82 ((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[211, 210])).
% 14.86/9.82 tff(213,plain,
% 14.86/9.82 ((~((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7)))))) | (C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))),
% 14.86/9.82 inference(tautology,[status(thm)],[])).
% 14.86/9.82 tff(214,plain,
% 14.86/9.82 ((C!5 = set_union2(C!5, unordered_pair(B!6, A!7))) | ((~in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5)) <=> (in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), C!5) | in(tptp_fun_D_2(C!5, unordered_pair(B!6, A!7), C!5), unordered_pair(B!6, A!7))))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[213, 212])).
% 14.86/9.82 tff(215,plain,
% 14.86/9.82 (C!5 = set_union2(C!5, unordered_pair(B!6, A!7))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[214, 208])).
% 14.86/9.82 tff(216,plain,
% 14.86/9.82 (set_union2(C!5, unordered_pair(B!6, A!7)) = C!5),
% 14.86/9.82 inference(symmetry,[status(thm)],[215])).
% 14.86/9.82 tff(217,plain,
% 14.86/9.82 (set_union2(C!5, unordered_pair(B!6, A!7)) = set_union2(C!5, unordered_pair(A!7, B!6))),
% 14.86/9.82 inference(monotonicity,[status(thm)],[92])).
% 14.86/9.82 tff(218,plain,
% 14.86/9.82 (set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(C!5, unordered_pair(B!6, A!7))),
% 14.86/9.82 inference(symmetry,[status(thm)],[217])).
% 14.86/9.82 tff(219,plain,
% 14.86/9.82 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 14.86/9.82 inference(bind,[status(th)],[])).
% 14.86/9.82 tff(220,plain,
% 14.86/9.82 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 14.86/9.82 inference(quant_intro,[status(thm)],[219])).
% 14.86/9.82 tff(221,plain,
% 14.86/9.82 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 14.86/9.82 inference(rewrite,[status(thm)],[])).
% 14.86/9.82 tff(222,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 14.86/9.82 tff(223,plain,
% 14.86/9.82 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 14.86/9.82 inference(modus_ponens,[status(thm)],[222, 221])).
% 14.86/9.82 tff(224,plain,(
% 14.86/9.82 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 14.86/9.82 inference(skolemize,[status(sab)],[223])).
% 14.86/9.82 tff(225,plain,
% 14.86/9.82 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 14.86/9.82 inference(modus_ponens,[status(thm)],[224, 220])).
% 14.86/9.82 tff(226,plain,
% 14.86/9.82 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6)))),
% 14.86/9.82 inference(quant_inst,[status(thm)],[])).
% 14.86/9.82 tff(227,plain,
% 14.86/9.82 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6))),
% 14.86/9.82 inference(unit_resolution,[status(thm)],[226, 225])).
% 14.86/9.83 tff(228,plain,
% 14.86/9.83 (empty_set = C!5),
% 14.86/9.83 inference(transitivity,[status(thm)],[164, 227, 218, 216])).
% 14.86/9.83 tff(229,plain,
% 14.86/9.83 (set_union2(empty_set, B!6) = set_union2(C!5, B!6)),
% 14.86/9.83 inference(monotonicity,[status(thm)],[228])).
% 14.86/9.83 tff(230,plain,
% 14.86/9.83 (set_union2(C!5, B!6) = set_union2(empty_set, B!6)),
% 14.86/9.83 inference(symmetry,[status(thm)],[229])).
% 14.86/9.83 tff(231,plain,
% 14.86/9.83 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(C!5, B!6) = set_union2(B!6, C!5))),
% 14.86/9.83 inference(quant_inst,[status(thm)],[])).
% 14.86/9.83 tff(232,plain,
% 14.86/9.83 (set_union2(C!5, B!6) = set_union2(B!6, C!5)),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[231, 225])).
% 14.86/9.83 tff(233,plain,
% 14.86/9.83 (set_union2(B!6, C!5) = set_union2(C!5, B!6)),
% 14.86/9.83 inference(symmetry,[status(thm)],[232])).
% 14.86/9.83 tff(234,plain,
% 14.86/9.83 (set_union2(B!6, C!5) = B!6),
% 14.86/9.83 inference(transitivity,[status(thm)],[233, 230, 73])).
% 14.86/9.83 tff(235,plain,
% 14.86/9.83 (in(set_union2(B!6, C!5), empty_set) <=> in(B!6, empty_set)),
% 14.86/9.83 inference(monotonicity,[status(thm)],[234])).
% 14.86/9.83 tff(236,plain,
% 14.86/9.83 (in(B!6, empty_set) <=> in(set_union2(B!6, C!5), empty_set)),
% 14.86/9.83 inference(symmetry,[status(thm)],[235])).
% 14.86/9.83 tff(237,assumption,((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))), introduced(assumption)).
% 14.86/9.83 tff(238,plain,
% 14.86/9.83 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7))))))))),
% 14.86/9.83 inference(rewrite,[status(thm)],[])).
% 14.86/9.83 tff(239,plain,
% 14.86/9.83 ((~((~((~(empty_set = unordered_pair(A!7, B!6))) | (in(B!6, empty_set) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7))))))) <=> (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))),
% 14.86/9.83 inference(rewrite,[status(thm)],[])).
% 14.86/9.83 tff(240,plain,
% 14.86/9.83 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | (in(B!6, empty_set) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7))))))))),
% 14.86/9.83 inference(monotonicity,[status(thm)],[239])).
% 14.86/9.83 tff(241,plain,
% 14.86/9.83 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | (in(B!6, empty_set) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7))))))))),
% 14.86/9.83 inference(transitivity,[status(thm)],[240, 238])).
% 14.86/9.83 tff(242,plain,
% 14.86/9.83 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | (in(B!6, empty_set) <=> ((B!6 = B!6) | (B!6 = A!7))))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))),
% 14.86/9.83 inference(quant_inst,[status(thm)],[])).
% 14.86/9.83 tff(243,plain,
% 14.86/9.83 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))) | (~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))))),
% 14.86/9.83 inference(modus_ponens,[status(thm)],[242, 241])).
% 14.86/9.83 tff(244,plain,
% 14.86/9.83 ($false),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[243, 127, 237])).
% 14.86/9.83 tff(245,plain,(~((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7))))))), inference(lemma,lemma(discharge,[]))).
% 14.86/9.83 tff(246,plain,
% 14.86/9.83 (((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~((empty_set = unordered_pair(A!7, B!6)) | ((~in(tptp_fun_D_1(empty_set, B!6, A!7), empty_set)) <=> ((tptp_fun_D_1(empty_set, B!6, A!7) = B!6) | (tptp_fun_D_1(empty_set, B!6, A!7) = A!7)))))) | ((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))),
% 14.86/9.83 inference(tautology,[status(thm)],[])).
% 14.86/9.83 tff(247,plain,
% 14.86/9.83 ((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set)),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[246, 245])).
% 14.86/9.83 tff(248,plain,
% 14.86/9.83 ((set_union2(unordered_pair(B!6, A!7), C!5) = unordered_pair(B!6, A!7)) <=> (unordered_pair(B!6, A!7) = set_union2(unordered_pair(B!6, A!7), C!5))),
% 14.86/9.83 inference(commutativity,[status(thm)],[])).
% 14.86/9.83 tff(249,plain,
% 14.86/9.83 ((empty_set = unordered_pair(A!7, B!6)) <=> (set_union2(unordered_pair(B!6, A!7), C!5) = unordered_pair(B!6, A!7))),
% 14.86/9.83 inference(monotonicity,[status(thm)],[165, 91])).
% 14.86/9.83 tff(250,plain,
% 14.86/9.83 ((empty_set = unordered_pair(A!7, B!6)) <=> (unordered_pair(B!6, A!7) = set_union2(unordered_pair(B!6, A!7), C!5))),
% 14.86/9.83 inference(transitivity,[status(thm)],[249, 248])).
% 14.86/9.83 tff(251,plain,
% 14.86/9.83 ((unordered_pair(B!6, A!7) = set_union2(unordered_pair(B!6, A!7), C!5)) <=> (empty_set = unordered_pair(A!7, B!6))),
% 14.86/9.83 inference(symmetry,[status(thm)],[250])).
% 14.86/9.83 tff(252,plain,
% 14.86/9.83 ((empty_set = unordered_pair(B!6, A!7)) <=> (set_union2(unordered_pair(B!6, A!7), C!5) = unordered_pair(B!6, A!7))),
% 14.86/9.83 inference(monotonicity,[status(thm)],[165])).
% 14.86/9.83 tff(253,plain,
% 14.86/9.83 ((empty_set = unordered_pair(B!6, A!7)) <=> (unordered_pair(B!6, A!7) = set_union2(unordered_pair(B!6, A!7), C!5))),
% 14.86/9.83 inference(transitivity,[status(thm)],[252, 248])).
% 14.86/9.83 tff(254,plain,
% 14.86/9.83 ((empty_set = unordered_pair(B!6, A!7)) <=> (empty_set = unordered_pair(A!7, B!6))),
% 14.86/9.83 inference(transitivity,[status(thm)],[253, 251])).
% 14.86/9.83 tff(255,plain,
% 14.86/9.83 (empty_set = unordered_pair(A!7, B!6)),
% 14.86/9.83 inference(modus_ponens,[status(thm)],[180, 254])).
% 14.86/9.83 tff(256,plain,
% 14.86/9.83 ((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | (~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set)),
% 14.86/9.83 inference(tautology,[status(thm)],[])).
% 14.86/9.83 tff(257,plain,
% 14.86/9.83 ((~((~(empty_set = unordered_pair(A!7, B!6))) | in(B!6, empty_set))) | in(B!6, empty_set)),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[256, 255])).
% 14.86/9.83 tff(258,plain,
% 14.86/9.83 (in(B!6, empty_set)),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[257, 247])).
% 14.86/9.83 tff(259,plain,
% 14.86/9.83 (in(set_union2(B!6, C!5), empty_set)),
% 14.86/9.83 inference(modus_ponens,[status(thm)],[258, 236])).
% 14.86/9.83 tff(260,plain,
% 14.86/9.83 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(set_union2(B!6, C!5), empty_set))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(set_union2(B!6, C!5), empty_set)))),
% 14.86/9.83 inference(rewrite,[status(thm)],[])).
% 14.86/9.83 tff(261,plain,
% 14.86/9.83 ((~((~((~(empty_set = empty_set)) | (~in(set_union2(B!6, C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set))))) <=> (~in(set_union2(B!6, C!5), empty_set))),
% 14.86/9.83 inference(rewrite,[status(thm)],[])).
% 14.86/9.83 tff(262,plain,
% 14.86/9.83 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(set_union2(B!6, C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(set_union2(B!6, C!5), empty_set)))),
% 14.86/9.83 inference(monotonicity,[status(thm)],[261])).
% 14.86/9.83 tff(263,plain,
% 14.86/9.83 (((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(set_union2(B!6, C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))) <=> ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(set_union2(B!6, C!5), empty_set)))),
% 14.86/9.83 inference(transitivity,[status(thm)],[262, 260])).
% 14.86/9.83 tff(264,plain,
% 14.86/9.83 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(empty_set = empty_set)) | (~in(set_union2(B!6, C!5), empty_set)))) | (~((empty_set = empty_set) | in(tptp_fun_B_0(empty_set), empty_set)))))),
% 14.86/9.83 inference(quant_inst,[status(thm)],[])).
% 14.86/9.83 tff(265,plain,
% 14.86/9.83 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~in(set_union2(B!6, C!5), empty_set))),
% 14.86/9.83 inference(modus_ponens,[status(thm)],[264, 263])).
% 14.86/9.83 tff(266,plain,
% 14.86/9.83 ($false),
% 14.86/9.83 inference(unit_resolution,[status(thm)],[265, 26, 259])).
% 14.86/9.83 % SZS output end Proof
%------------------------------------------------------------------------------