TSTP Solution File: SEU124+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 07:27:35 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 09:34:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(in_type, type, (
% 0.19/0.38 in: ( $i * $i ) > $o)).
% 0.19/0.38 tff(set_union2_type, type, (
% 0.19/0.38 set_union2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_A_5_type, type, (
% 0.19/0.38 tptp_fun_A_5: $i)).
% 0.19/0.38 tff(tptp_fun_B_4_type, type, (
% 0.19/0.38 tptp_fun_B_4: $i)).
% 0.19/0.38 tff(tptp_fun_C_1_type, type, (
% 0.19/0.38 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.19/0.38 tff(subset_type, type, (
% 0.19/0.38 subset: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_D_0_type, type, (
% 0.19/0.38 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.38 tff(6,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(skolemize,[status(sab)],[5])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!5, B!4) = set_union2(B!4, A!5))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (set_union2(A!5, B!4) = set_union2(B!4, A!5)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (set_union2(B!4, A!5) = set_union2(A!5, B!4)),
% 0.19/0.38 inference(symmetry,[status(thm)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)) <=> in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))),
% 0.19/0.38 inference(symmetry,[status(thm)],[11])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))) <=> (~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.39 tff(24,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.39 tff(27,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[26])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!5, set_union2(A!5, B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_union2(A!5, B!4))))) | (~(subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (~((~((~subset(A!5, set_union2(A!5, B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_union2(A!5, B!4))))) | (~(subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (((~((~subset(A!5, set_union2(A!5, B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, set_union2(A!5, B!4))))) | (~(subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))))))) | (subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) <=> (~![A: $i, B: $i] : subset(A, set_union2(A, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,axiom,(~![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (~![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.39 tff(43,plain,(
% 0.19/0.39 ~subset(A!5, set_union2(A!5, B!4))),
% 0.19/0.39 inference(skolemize,[status(sab)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((~(subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))))) | subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~(subset(A!5, set_union2(A!5, B!4)) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))))) | (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[45, 33])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))) | (~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 13])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (^[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, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[55, 51])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[58, 56])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[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)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![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, B) | in(D, A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.40 tff(67,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/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.40 tff(70,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 59])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))) | $false) <=> ((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~$true) <=> $false),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (($true | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((set_union2(B!4, A!5) = set_union2(B!4, A!5)) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))) <=> ($true | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[82, 77])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~(in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> ((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (($false | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[86, 77])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> ($false | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[88, 85])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 ((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) <=> (~(in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) <=> ((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[90, 84])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))))) <=> (((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[91, 83])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))))) <=> ((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[92, 76])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4))))))) <=> (~((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4))))))) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[94, 75])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[96, 74])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (~((~((~(set_union2(B!4, A!5) = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))))) | (~((set_union2(B!4, A!5) = set_union2(B!4, A!5)) | ((~in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), set_union2(B!4, A!5))) <=> (in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), A!5) | in(tptp_fun_D_0(set_union2(B!4, A!5), A!5, B!4), B!4)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | ((~in(tptp_fun_D_0(C, B, A), C)) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) | (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 73])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (((~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(A!5, B!4))) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 46])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)) | (~in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 ((~(in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) | (~(in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 ((~(in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5)) <=> (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), A!5) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), B!4)))) | in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (in(tptp_fun_C_1(set_union2(A!5, B!4), A!5), set_union2(B!4, A!5))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[107, 49])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------