TSTP Solution File: SET941+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 05:08:42 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET941+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 08:33:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(in_type, type, (
% 0.20/0.40 in: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_B_6_type, type, (
% 0.20/0.40 tptp_fun_B_6: $i)).
% 0.20/0.40 tff(tptp_fun_D_1_type, type, (
% 0.20/0.40 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_A_7_type, type, (
% 0.20/0.40 tptp_fun_A_7: $i)).
% 0.20/0.40 tff(tptp_fun_C_0_type, type, (
% 0.20/0.40 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(union_type, type, (
% 0.20/0.40 union: $i > $i)).
% 0.20/0.40 tff(subset_type, type, (
% 0.20/0.40 subset: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_C_2_type, type, (
% 0.20/0.40 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_D_3_type, type, (
% 0.20/0.40 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.40 tff(14,plain,(
% 0.20/0.40 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6)))))) | ((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (~((~((~subset(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~((~subset(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))))) | (subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6))) <=> (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))) <=> (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : (![C: $i] : (in(C, A) => subset(C, B)) => subset(union(A), B))) <=> (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(28,axiom,(~![A: $i, B: $i] : (![C: $i] : (in(C, A) => subset(C, B)) => subset(union(A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t94_zfmisc_1')).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (~subset(union(A!7), B!6)),
% 0.20/0.40 inference(and_elim,[status(thm)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))) | subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[39, 24])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (^[A: $i, B: $i, D_8: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[A: $i, B: $i, D_8: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![A: $i, B: $i] : ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))) <=> ![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> (~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))))), pull_quant((~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), pull_quant(((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> (~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), pull_quant((~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))), ((~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))), ((~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), (((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), (((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), ((~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), ((~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> ?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> ?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> (~?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))))), pull_quant((~?[D_8: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[50, 46])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[53, 51])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) <=> ((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A)) <=> (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))))), rewrite((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))))), rewrite(((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), rewrite(((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(58,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_tarski')).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[59])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 44])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~(~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))) <=> ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | $false) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~$true) <=> $false),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (($true | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 ((~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))) <=> (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 ((union(A!7) = union(A!7)) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> ($true | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[70, 69])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> $true),
% 0.20/0.42 inference(transitivity,[status(thm)],[71, 68])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[73, 67])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))) <=> ((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | $false)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[75, 74])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[76, 66])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 ((~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))))) <=> (~(~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 ((~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))))) <=> ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[78, 65])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))) <=> ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[80, 64])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![A: $i, B: $i, D_8: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[83, 63, 42])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))) | in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (^[C: $i] : refl(((~in(C, A!7)) | subset(C, B!6)) <=> ((~in(C, A!7)) | subset(C, B!6)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) <=> ![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.20/0.44 inference(and_elim,[status(thm)],[36])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | ((~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))) <=> ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | ((~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[93, 90, 86])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 ((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[96, 20])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 84])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)) | (~in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (~in(tptp_fun_C_0(B!6, union(A!7)), B!6)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[100, 40])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))) <=> ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | (~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | (~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[104, 101, 99, 97])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------