%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET947+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:26:42 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET947+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 05:51:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(subset_type, type, (
% 0.21/0.39 subset: ( $i * $i ) > $o)).
% 0.21/0.39 tff(union_type, type, (
% 0.21/0.39 union: $i > $i)).
% 0.21/0.39 tff(tptp_fun_A_4_type, type, (
% 0.21/0.39 tptp_fun_A_4: $i)).
% 0.21/0.39 tff(tptp_fun_C_1_type, type, (
% 0.21/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.21/0.39 tff(powerset_type, type, (
% 0.21/0.39 powerset: $i > $i)).
% 0.21/0.39 tff(in_type, type, (
% 0.21/0.39 in: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[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))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[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))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.39 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')).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.39 tff(14,plain,(
% 0.21/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!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)))))))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~((~((~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))))))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (((~((~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))))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (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)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 ((~![A: $i] : subset(A, powerset(union(A)))) <=> (~![A: $i] : subset(A, powerset(union(A))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(22,axiom,(~![A: $i] : subset(A, powerset(union(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t100_zfmisc_1')).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~![A: $i] : subset(A, powerset(union(A)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.39 ~subset(A!4, powerset(union(A!4)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~(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)))))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 ((~(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)))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (~((~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))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[29, 20])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (((~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)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (in(tptp_fun_C_1(powerset(union(A!4)), A!4), A!4)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (^[A: $i, B: $i] : refl(((~in(A, B)) | subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (^[A: $i, B: $i] : rewrite((in(A, B) => subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (![A: $i, B: $i] : (in(A, B) => subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.39 tff(38,axiom,(![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l50_zfmisc_1')).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.39 tff(41,plain,(
% 0.21/0.39 ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[40])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (((~![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)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![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)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((~![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))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[45, 42, 32])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (((~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))))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(48,plain,
% 0.21/0.40 (~in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[47, 30])).
% 0.21/0.40 tff(49,plain,
% 0.21/0.40 ((~(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)))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(50,plain,
% 0.21/0.40 (~(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)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[49, 48, 46])).
% 0.21/0.40 tff(51,plain,
% 0.21/0.40 (^[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))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(52,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.40 tff(53,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(pull_quant,[status(thm)],[])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (^[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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[55, 53])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[56, 52])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (^[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))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (^[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)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))), (((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))), rewrite(((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))) <=> ((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A))))), (((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), 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))))))), 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)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(64,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')).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((B = powerset(A)) <=> ![C: $i] : (in(C, B) <=> subset(C, A)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.40 tff(66,plain,(
% 0.21/0.40 ![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)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[65])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![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)))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (((~![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 ((~(~(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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (((~(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)))) | $false) <=> (~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 ((~$true) <=> $false),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 (($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),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~(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_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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((powerset(union(A!4)) = powerset(union(A!4))) <=> $true),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (((powerset(union(A!4)) = powerset(union(A!4))) | (~(in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4))))) <=> ($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)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[75, 74])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (((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))))) <=> $true),
% 0.21/0.40 inference(transitivity,[status(thm)],[76, 73])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 ((~((powerset(union(A!4)) = powerset(union(A!4))) | (~(in(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), powerset(union(A!4))) <=> subset(tptp_fun_C_0(powerset(union(A!4)), union(A!4)), union(A!4)))))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 ((~((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)))))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[78, 72])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 ((~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> (~(in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (($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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 ((~(powerset(union(A!4)) = powerset(union(A!4)))) <=> (~$true)),
% 0.21/0.40 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 ((~(powerset(union(A!4)) = powerset(union(A!4)))) <=> $false),
% 0.21/0.40 inference(transitivity,[status(thm)],[82, 72])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (((~(powerset(union(A!4)) = powerset(union(A!4)))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))) <=> ($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))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (((~(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)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[84, 81])).
% 0.21/0.40 tff(86,plain,
% 0.21/0.40 ((~((~(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))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[85])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 ((~((~(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))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[86, 80])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (((~((~(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)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[87, 79])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (((~((~(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))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[88, 71])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 ((~((~((~(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)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 ((~((~((~(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)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[90, 70])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[92, 69])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ((~![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))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(95,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = powerset(A))) | (in(C, B) <=> subset(C, A)))) | (~((B = powerset(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> subset(tptp_fun_C_0(B, A), A)))))))) | (in(tptp_fun_C_1(powerset(union(A!4)), A!4), powerset(union(A!4))) <=> subset(tptp_fun_C_1(powerset(union(A!4)), A!4), union(A!4)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[95, 68, 50])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------