TSTP Solution File: SET947+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:08:43 EDT 2022
% Result : Theorem 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Sep 3 08:39:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.23/0.41 % SZS status Theorem
% 0.23/0.41 % SZS output start Proof
% 0.23/0.41 tff(subset_type, type, (
% 0.23/0.41 subset: ( $i * $i ) > $o)).
% 0.23/0.41 tff(union_type, type, (
% 0.23/0.41 union: $i > $i)).
% 0.23/0.41 tff(tptp_fun_A_4_type, type, (
% 0.23/0.41 tptp_fun_A_4: $i)).
% 0.23/0.41 tff(tptp_fun_C_1_type, type, (
% 0.23/0.41 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.23/0.41 tff(powerset_type, type, (
% 0.23/0.41 powerset: $i > $i)).
% 0.23/0.41 tff(in_type, type, (
% 0.23/0.41 in: ( $i * $i ) > $o)).
% 0.23/0.41 tff(tptp_fun_C_0_type, type, (
% 0.23/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.23/0.41 tff(1,plain,
% 0.23/0.41 (^[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))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(2,plain,
% 0.23/0.41 (![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)))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 (^[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))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(4,plain,
% 0.23/0.41 (![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)))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.41 tff(5,plain,
% 0.23/0.41 (![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)))))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.23/0.41 tff(6,plain,
% 0.23/0.41 (^[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)))))))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(7,plain,
% 0.23/0.41 (![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)))))))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 (![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)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(9,plain,
% 0.23/0.41 (^[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))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(10,plain,
% 0.23/0.41 (![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)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.23/0.41 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')).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.23/0.41 tff(13,plain,
% 0.23/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.42 tff(14,plain,(
% 0.23/0.42 ![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)))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[13])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 (![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)))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 ((~![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!4, powerset(union(A!4)))) | ![C: $i] : ((~in(C, A!4)) | in(C, powerset(union(A!4)))))) | (~(subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))))))))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (~((~((~subset(A!4, powerset(union(A!4)))) | ![C: $i] : ((~in(C, A!4)) | in(C, powerset(union(A!4)))))) | (~(subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (((~((~subset(A!4, powerset(union(A!4)))) | ![C: $i] : ((~in(C, A!4)) | in(C, powerset(union(A!4)))))) | (~(subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))))))) | (subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 ((~![A: $i] : subset(A, powerset(union(A)))) <=> (~![A: $i] : subset(A, powerset(union(A))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(22,axiom,(~![A: $i] : subset(A, powerset(union(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t100_zfmisc_1')).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.23/0.42 tff(25,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.23/0.42 tff(30,plain,(
% 0.23/0.42 ~subset(A!4, powerset(union(A!4)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[29])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 ((~(subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))))) | subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 ((~(subset(A!4, powerset(union(A!4))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))))) | (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 (^[A: $i, B: $i] : refl(((~in(A, B)) | subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 (^[A: $i, B: $i] : rewrite((in(A, B) => subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 (![A: $i, B: $i] : (in(A, B) => subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.23/0.42 tff(41,axiom,(![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l50_zfmisc_1')).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.23/0.42 tff(44,plain,(
% 0.23/0.42 ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[43])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 (((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.42 tff(49,plain,
% 0.23/0.42 (subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 0.23/0.42 tff(50,plain,
% 0.23/0.42 (((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) | (~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(51,plain,
% 0.23/0.42 (~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[50, 33])).
% 0.23/0.42 tff(52,plain,
% 0.23/0.42 ((~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) | in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) | (~subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(53,plain,
% 0.23/0.42 (~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[52, 51, 49])).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(55,plain,
% 0.23/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(pull_quant,[status(thm)],[])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))), ((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) <=> (~![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))))), pull_quant((~![C: $i] : ((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) <=> ?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A))))), ((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) <=> ?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))))), (((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))) <=> (?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))), pull_quant((?[C: $i] : (~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))) <=> ?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))), (((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))) <=> ?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))), ((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> (~?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))))), pull_quant((~?[C: $i] : ((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))), ((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(58,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.23/0.42 tff(59,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[58, 56])).
% 0.23/0.42 tff(60,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[59, 55])).
% 0.23/0.42 tff(61,plain,
% 0.23/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(62,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.23/0.42 tff(63,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[62, 60])).
% 0.23/0.42 tff(64,plain,
% 0.23/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))), ((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))) <=> (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))), rewrite((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))), ((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))) <=> (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(65,plain,
% 0.23/0.42 (![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[64])).
% 0.23/0.42 tff(66,plain,
% 0.23/0.42 (^[A: $i, B: $i] : rewrite((((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(67,plain,
% 0.23/0.42 (![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))) <=> ![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.23/0.42 tff(68,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A))) <=> ![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(69,axiom,(![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_zfmisc_1')).
% 0.23/0.42 tff(70,plain,
% 0.23/0.42 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.23/0.42 tff(71,plain,(
% 0.23/0.42 ![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[70])).
% 0.23/0.42 tff(72,plain,
% 0.23/0.42 (![A: $i, B: $i] : (((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A))) & ((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.23/0.42 tff(73,plain,
% 0.23/0.42 (![A: $i, B: $i] : (~((~((~(B = powerset(A))) | ![C: $i] : (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.23/0.42 tff(74,plain,
% 0.23/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.23/0.42 tff(75,plain,
% 0.23/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(76,plain,
% 0.23/0.43 ((~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 ((((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))) | $false) <=> ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 ((~$true) <=> $false),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (($true | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))) <=> $true),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(80,plain,
% 0.23/0.43 ((powerset(union(A!4)) = powerset(union(A!4))) <=> $true),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 (((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))) <=> ($true | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.23/0.43 tff(82,plain,
% 0.23/0.43 (((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))) <=> $true),
% 0.23/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 ((~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))) <=> (~$true)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 ((~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))) <=> $false),
% 0.23/0.43 inference(transitivity,[status(thm)],[83, 78])).
% 0.23/0.43 tff(85,plain,
% 0.23/0.43 ((~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 (($false | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(87,plain,
% 0.23/0.43 ((~(powerset(union(A!4)) = powerset(union(A!4)))) <=> (~$true)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.23/0.43 tff(88,plain,
% 0.23/0.43 ((~(powerset(union(A!4)) = powerset(union(A!4)))) <=> $false),
% 0.23/0.43 inference(transitivity,[status(thm)],[87, 78])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 (((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> ($false | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[88])).
% 0.23/0.43 tff(90,plain,
% 0.23/0.43 (((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[89, 86])).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 ((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) <=> (~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[90])).
% 0.23/0.43 tff(92,plain,
% 0.23/0.43 ((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) <=> ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[91, 85])).
% 0.23/0.43 tff(93,plain,
% 0.23/0.43 (((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))) <=> (((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))) | $false)),
% 0.23/0.43 inference(monotonicity,[status(thm)],[92, 84])).
% 0.23/0.43 tff(94,plain,
% 0.23/0.43 (((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))) <=> ((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[93, 77])).
% 0.23/0.43 tff(95,plain,
% 0.23/0.43 ((~((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))))) <=> (~((~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.23/0.43 tff(96,plain,
% 0.23/0.43 ((~((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))))) <=> (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(transitivity,[status(thm)],[95, 76])).
% 0.23/0.43 tff(97,plain,
% 0.23/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (~((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[96])).
% 0.23/0.43 tff(98,plain,
% 0.23/0.43 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (~((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[97, 75])).
% 0.23/0.43 tff(99,plain,
% 0.23/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (~((~((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))) | (~((powerset(union(A!4)) = powerset(union(A!4))) | ((~in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4)))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(100,plain,
% 0.23/0.43 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | ((~in(tptp_fun_C_0(B, A), B)) <=> subset(tptp_fun_C_0(B, A), A))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.23/0.43 tff(101,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[100, 74, 53])).
% 0.23/0.43 % SZS output end Proof
%------------------------------------------------------------------------------