TSTP Solution File: SEU171+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:27:58 EDT 2022
% Result : Theorem 0.84s 0.78s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 09:52:33 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.84/0.78 % SZS status Theorem
% 0.84/0.78 % SZS output start Proof
% 0.84/0.78 tff(empty_type, type, (
% 0.84/0.78 empty: $i > $o)).
% 0.84/0.78 tff(tptp_fun_A_25_type, type, (
% 0.84/0.78 tptp_fun_A_25: $i)).
% 0.84/0.78 tff(in_type, type, (
% 0.84/0.78 in: ( $i * $i ) > $o)).
% 0.84/0.78 tff(tptp_fun_C_27_type, type, (
% 0.84/0.78 tptp_fun_C_27: $i)).
% 0.84/0.78 tff(element_type, type, (
% 0.84/0.78 element: ( $i * $i ) > $o)).
% 0.84/0.78 tff(tptp_fun_B_26_type, type, (
% 0.84/0.78 tptp_fun_B_26: $i)).
% 0.84/0.78 tff(set_difference_type, type, (
% 0.84/0.78 set_difference: ( $i * $i ) > $i)).
% 0.84/0.78 tff(tptp_fun_D_15_type, type, (
% 0.84/0.78 tptp_fun_D_15: ( $i * $i * $i ) > $i)).
% 0.84/0.78 tff(subset_complement_type, type, (
% 0.84/0.78 subset_complement: ( $i * $i ) > $i)).
% 0.84/0.78 tff(powerset_type, type, (
% 0.84/0.78 powerset: $i > $i)).
% 0.84/0.78 tff(empty_set_type, type, (
% 0.84/0.78 empty_set: $i)).
% 0.84/0.78 tff(1,plain,
% 0.84/0.78 (^[A: $i, B: $i] : refl((~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(2,plain,
% 0.84/0.78 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.84/0.78 tff(3,plain,
% 0.84/0.78 (^[A: $i, B: $i] : rewrite(((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(4,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[3])).
% 0.84/0.78 tff(5,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.84/0.78 inference(rewrite,[status(thm)],[])).
% 0.84/0.78 tff(6,plain,
% 0.84/0.78 (^[A: $i, B: $i] : rewrite((((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))))),
% 0.84/0.78 inference(bind,[status(th)],[])).
% 0.84/0.78 tff(7,plain,
% 0.84/0.78 (![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.84/0.78 inference(quant_intro,[status(thm)],[6])).
% 0.84/0.78 tff(8,axiom,(![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_subset_1')).
% 0.84/0.78 tff(9,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.84/0.78 tff(10,plain,
% 0.84/0.78 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.84/0.78 tff(11,plain,(
% 0.84/0.78 ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.84/0.78 inference(skolemize,[status(sab)],[10])).
% 0.84/0.78 tff(12,plain,
% 0.84/0.78 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.84/0.78 tff(13,plain,
% 0.84/0.78 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.84/0.78 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.84/0.78 tff(14,plain,
% 0.84/0.78 ((~![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))) | (~((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27))))))),
% 0.84/0.79 inference(quant_inst,[status(thm)],[])).
% 0.84/0.79 tff(15,plain,
% 0.84/0.79 (~((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27)))))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.84/0.79 tff(16,plain,
% 0.84/0.79 (((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27))))) | (empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))),
% 0.84/0.79 inference(tautology,[status(thm)],[])).
% 0.84/0.79 tff(17,plain,
% 0.84/0.79 (empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25))),
% 0.84/0.79 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.84/0.79 tff(18,plain,
% 0.84/0.79 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(19,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[18])).
% 0.84/0.79 tff(20,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(pull_quant,[status(thm)],[])).
% 0.84/0.79 tff(21,plain,
% 0.84/0.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(22,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[21])).
% 0.84/0.79 tff(23,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[22, 20])).
% 0.84/0.79 tff(24,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[23, 19])).
% 0.84/0.79 tff(25,plain,
% 0.84/0.79 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(26,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[25])).
% 0.84/0.79 tff(27,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(transitivity,[status(thm)],[26, 24])).
% 0.84/0.79 tff(28,plain,
% 0.84/0.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(29,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[28])).
% 0.84/0.79 tff(30,plain,
% 0.84/0.79 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(bind,[status(th)],[])).
% 0.84/0.79 tff(31,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B))))))),
% 0.84/0.79 inference(quant_intro,[status(thm)],[30])).
% 0.84/0.79 tff(32,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(33,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.84/0.79 tff(34,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.84/0.79 tff(35,plain,(
% 0.84/0.79 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(skolemize,[status(sab)],[34])).
% 0.84/0.79 tff(36,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_15(C, B, A), C)) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B))))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.84/0.79 tff(37,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.84/0.79 tff(38,plain,
% 0.84/0.79 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.84/0.79 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.84/0.79 tff(39,plain,
% 0.84/0.79 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(40,plain,
% 0.84/0.79 ((~(in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))) <=> ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.84/0.79 inference(rewrite,[status(thm)],[])).
% 0.84/0.79 tff(41,plain,
% 0.84/0.79 (((in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26))) | $false) <=> (in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(42,plain,
% 0.84/0.80 ((~$true) <=> $false),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(43,plain,
% 0.84/0.80 (($true | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))) <=> $true),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(44,plain,
% 0.84/0.80 ((set_difference(A!25, B!26) = set_difference(A!25, B!26)) <=> $true),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(45,plain,
% 0.84/0.80 (((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))) <=> ($true | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[44])).
% 0.84/0.80 tff(46,plain,
% 0.84/0.80 (((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))) <=> $true),
% 0.84/0.80 inference(transitivity,[status(thm)],[45, 43])).
% 0.84/0.80 tff(47,plain,
% 0.84/0.80 ((~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26))))) <=> (~$true)),
% 0.84/0.80 inference(monotonicity,[status(thm)],[46])).
% 0.84/0.80 tff(48,plain,
% 0.84/0.80 ((~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26))))) <=> $false),
% 0.84/0.80 inference(transitivity,[status(thm)],[47, 42])).
% 0.84/0.80 tff(49,plain,
% 0.84/0.80 ((~(in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))) <=> (in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(50,plain,
% 0.84/0.80 (($false | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))) <=> (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.84/0.80 inference(rewrite,[status(thm)],[])).
% 0.84/0.80 tff(51,plain,
% 0.84/0.80 ((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) <=> (~$true)),
% 0.84/0.80 inference(monotonicity,[status(thm)],[44])).
% 0.84/0.80 tff(52,plain,
% 0.84/0.80 ((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) <=> $false),
% 0.84/0.80 inference(transitivity,[status(thm)],[51, 42])).
% 0.84/0.80 tff(53,plain,
% 0.84/0.80 (((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))) <=> ($false | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[52])).
% 0.84/0.80 tff(54,plain,
% 0.84/0.80 (((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))) <=> (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.84/0.80 inference(transitivity,[status(thm)],[53, 50])).
% 0.84/0.80 tff(55,plain,
% 0.84/0.80 ((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) <=> (~(in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))),
% 0.84/0.80 inference(monotonicity,[status(thm)],[54])).
% 0.90/0.80 tff(56,plain,
% 0.90/0.80 ((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) <=> (in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.90/0.80 inference(transitivity,[status(thm)],[55, 49])).
% 0.90/0.80 tff(57,plain,
% 0.90/0.80 (((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))))) <=> ((in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26))) | $false)),
% 0.90/0.80 inference(monotonicity,[status(thm)],[56, 48])).
% 0.90/0.80 tff(58,plain,
% 0.90/0.80 (((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))))) <=> (in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.90/0.80 inference(transitivity,[status(thm)],[57, 41])).
% 0.90/0.80 tff(59,plain,
% 0.90/0.80 ((~((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26))))))) <=> (~(in(C!27, set_difference(A!25, B!26)) <=> ((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.90/0.80 inference(monotonicity,[status(thm)],[58])).
% 0.90/0.80 tff(60,plain,
% 0.90/0.80 ((~((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26))))))) <=> ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.90/0.80 inference(transitivity,[status(thm)],[59, 40])).
% 0.90/0.80 tff(61,plain,
% 0.90/0.80 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | (~((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.90/0.80 inference(monotonicity,[status(thm)],[60])).
% 0.90/0.80 tff(62,plain,
% 0.90/0.80 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | (~((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26))))),
% 0.90/0.80 inference(transitivity,[status(thm)],[61, 39])).
% 0.90/0.80 tff(63,plain,
% 0.90/0.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | (~((~((~(set_difference(A!25, B!26) = set_difference(A!25, B!26))) | (in(C!27, set_difference(A!25, B!26)) <=> (~((~in(C!27, A!25)) | in(C!27, B!26)))))) | (~((set_difference(A!25, B!26) = set_difference(A!25, B!26)) | (in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), set_difference(A!25, B!26)) <=> ((~in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), A!25)) | in(tptp_fun_D_15(set_difference(A!25, B!26), B!26, A!25), B!26)))))))),
% 0.90/0.80 inference(quant_inst,[status(thm)],[])).
% 0.90/0.80 tff(64,plain,
% 0.90/0.80 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_15(C, B, A), C) <=> ((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)))))))) | ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))),
% 0.90/0.80 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.90/0.80 tff(65,plain,
% 0.90/0.80 ((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26))),
% 0.90/0.80 inference(unit_resolution,[status(thm)],[64, 38])).
% 0.90/0.80 tff(66,plain,
% 0.90/0.80 (((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 0.90/0.80 inference(rewrite,[status(thm)],[])).
% 0.90/0.80 tff(67,plain,
% 0.90/0.80 (((~(~element(B!26, powerset(A!25)))) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))) <=> (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 0.90/0.80 inference(rewrite,[status(thm)],[])).
% 0.90/0.80 tff(68,plain,
% 0.90/0.80 (((~(A!25 = empty_set)) & ((~(~element(B!26, powerset(A!25)))) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))))),
% 0.90/0.80 inference(monotonicity,[status(thm)],[67])).
% 0.90/0.80 tff(69,plain,
% 0.90/0.80 (((~(A!25 = empty_set)) & ((~(~element(B!26, powerset(A!25)))) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 0.90/0.80 inference(transitivity,[status(thm)],[68, 66])).
% 0.90/0.80 tff(70,plain,
% 0.90/0.80 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.90/0.80 inference(rewrite,[status(thm)],[])).
% 0.90/0.80 tff(71,plain,
% 0.90/0.81 ((~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(72,axiom,(~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t50_subset_1')).
% 0.90/0.81 tff(73,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.90/0.81 tff(74,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.90/0.81 tff(75,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.90/0.81 tff(76,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.90/0.81 tff(77,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[76, 70])).
% 0.90/0.81 tff(78,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.90/0.81 tff(79,plain,
% 0.90/0.81 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.90/0.81 tff(80,plain,
% 0.90/0.81 ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.90/0.81 tff(81,plain,
% 0.90/0.81 (element(B!26, powerset(A!25))),
% 0.90/0.81 inference(and_elim,[status(thm)],[80])).
% 0.90/0.81 tff(82,plain,
% 0.90/0.81 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(83,plain,
% 0.90/0.81 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[82])).
% 0.90/0.81 tff(84,plain,
% 0.90/0.81 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(85,plain,
% 0.90/0.81 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 0.90/0.81 inference(bind,[status(th)],[])).
% 0.90/0.81 tff(86,plain,
% 0.90/0.81 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(quant_intro,[status(thm)],[85])).
% 0.90/0.81 tff(87,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_subset_1')).
% 0.90/0.81 tff(88,plain,
% 0.90/0.81 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.90/0.81 tff(89,plain,
% 0.90/0.81 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.90/0.81 tff(90,plain,(
% 0.90/0.81 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(skolemize,[status(sab)],[89])).
% 0.90/0.81 tff(91,plain,
% 0.90/0.81 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.90/0.81 tff(92,plain,
% 0.90/0.81 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))),
% 0.90/0.81 inference(rewrite,[status(thm)],[])).
% 0.90/0.81 tff(93,plain,
% 0.90/0.81 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))),
% 0.90/0.81 inference(quant_inst,[status(thm)],[])).
% 0.90/0.81 tff(94,plain,
% 0.90/0.81 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.90/0.81 tff(95,plain,
% 0.90/0.81 (subset_complement(A!25, B!26) = set_difference(A!25, B!26)),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[94, 91, 81])).
% 0.90/0.81 tff(96,plain,
% 0.90/0.81 (set_difference(A!25, B!26) = subset_complement(A!25, B!26)),
% 0.90/0.81 inference(symmetry,[status(thm)],[95])).
% 0.90/0.81 tff(97,plain,
% 0.90/0.81 (in(C!27, set_difference(A!25, B!26)) <=> in(C!27, subset_complement(A!25, B!26))),
% 0.90/0.81 inference(monotonicity,[status(thm)],[96])).
% 0.90/0.81 tff(98,plain,
% 0.90/0.81 (in(C!27, subset_complement(A!25, B!26)) <=> in(C!27, set_difference(A!25, B!26))),
% 0.90/0.81 inference(symmetry,[status(thm)],[97])).
% 0.90/0.81 tff(99,plain,
% 0.90/0.81 ((~in(C!27, subset_complement(A!25, B!26))) <=> (~in(C!27, set_difference(A!25, B!26)))),
% 0.90/0.81 inference(monotonicity,[status(thm)],[98])).
% 0.90/0.81 tff(100,plain,
% 0.90/0.81 (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))),
% 0.90/0.81 inference(and_elim,[status(thm)],[80])).
% 0.90/0.81 tff(101,plain,
% 0.90/0.81 (~in(C!27, subset_complement(A!25, B!26))),
% 0.90/0.81 inference(or_elim,[status(thm)],[100])).
% 0.90/0.81 tff(102,plain,
% 0.90/0.81 (~in(C!27, set_difference(A!25, B!26))),
% 0.90/0.81 inference(modus_ponens,[status(thm)],[101, 99])).
% 0.90/0.81 tff(103,plain,
% 0.90/0.81 ((~((~in(C!27, set_difference(A!25, B!26))) <=> ((~in(C!27, A!25)) | in(C!27, B!26)))) | in(C!27, set_difference(A!25, B!26)) | ((~in(C!27, A!25)) | in(C!27, B!26))),
% 0.90/0.81 inference(tautology,[status(thm)],[])).
% 0.90/0.81 tff(104,plain,
% 0.90/0.81 ((~in(C!27, A!25)) | in(C!27, B!26)),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[103, 102, 65])).
% 0.90/0.81 tff(105,plain,
% 0.90/0.81 (~in(C!27, B!26)),
% 0.90/0.81 inference(or_elim,[status(thm)],[100])).
% 0.90/0.81 tff(106,plain,
% 0.90/0.81 ((~((~in(C!27, A!25)) | in(C!27, B!26))) | (~in(C!27, A!25)) | in(C!27, B!26)),
% 0.90/0.81 inference(tautology,[status(thm)],[])).
% 0.90/0.81 tff(107,plain,
% 0.90/0.81 ((~((~in(C!27, A!25)) | in(C!27, B!26))) | (~in(C!27, A!25))),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.90/0.81 tff(108,plain,
% 0.90/0.81 (~in(C!27, A!25)),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.90/0.81 tff(109,plain,
% 0.90/0.81 (element(C!27, A!25)),
% 0.90/0.81 inference(or_elim,[status(thm)],[100])).
% 0.90/0.81 tff(110,plain,
% 0.90/0.81 ((~(element(C!27, A!25) <=> in(C!27, A!25))) | (~element(C!27, A!25)) | in(C!27, A!25)),
% 0.90/0.81 inference(tautology,[status(thm)],[])).
% 0.90/0.81 tff(111,plain,
% 0.90/0.81 ((~(element(C!27, A!25) <=> in(C!27, A!25))) | in(C!27, A!25)),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.90/0.81 tff(112,plain,
% 0.90/0.81 (~(element(C!27, A!25) <=> in(C!27, A!25))),
% 0.90/0.81 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.90/0.81 tff(113,plain,
% 0.90/0.81 ((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25))),
% 0.90/0.82 inference(tautology,[status(thm)],[])).
% 0.90/0.82 tff(114,plain,
% 0.90/0.82 (empty(A!25)),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[113, 112, 17])).
% 0.90/0.82 tff(115,plain,
% 0.90/0.82 (^[A: $i, B: $i] : refl(((A = B) | (~empty(A)) | (~empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(116,plain,
% 0.90/0.82 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[115])).
% 0.90/0.82 tff(117,plain,
% 0.90/0.82 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(A)) | (~empty(B))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(A)) | (~empty(B))))))), rewrite((~(~((A = B) | (~empty(A)) | (~empty(B))))) <=> ((A = B) | (~empty(A)) | (~empty(B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(A)) | (~empty(B)))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(118,plain,
% 0.90/0.82 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[117])).
% 0.90/0.82 tff(119,plain,
% 0.90/0.82 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(120,plain,
% 0.90/0.82 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.90/0.82 inference(bind,[status(th)],[])).
% 0.90/0.82 tff(121,plain,
% 0.90/0.82 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.90/0.82 inference(quant_intro,[status(thm)],[120])).
% 0.90/0.82 tff(122,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.90/0.82 tff(123,plain,
% 0.90/0.82 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.90/0.82 tff(124,plain,
% 0.90/0.82 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.90/0.82 tff(125,plain,(
% 0.90/0.82 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.90/0.82 inference(skolemize,[status(sab)],[124])).
% 0.90/0.82 tff(126,plain,
% 0.90/0.82 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.90/0.82 tff(127,plain,
% 0.90/0.82 (![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.90/0.82 tff(128,plain,
% 0.90/0.82 (~(A!25 = empty_set)),
% 0.90/0.82 inference(and_elim,[status(thm)],[80])).
% 0.90/0.82 tff(129,plain,
% 0.90/0.82 (empty(empty_set) <=> empty(empty_set)),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(130,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.90/0.82 tff(131,plain,
% 0.90/0.82 (empty(empty_set)),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.90/0.82 tff(132,plain,
% 0.90/0.82 (((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((A!25 = empty_set) | (~empty(A!25)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (A!25 = empty_set) | (~empty(A!25)) | (~empty(empty_set)))),
% 0.90/0.82 inference(rewrite,[status(thm)],[])).
% 0.90/0.82 tff(133,plain,
% 0.90/0.82 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | ((A!25 = empty_set) | (~empty(A!25)) | (~empty(empty_set)))),
% 0.90/0.82 inference(quant_inst,[status(thm)],[])).
% 0.90/0.82 tff(134,plain,
% 0.90/0.82 ((~![A: $i, B: $i] : ((A = B) | (~empty(A)) | (~empty(B)))) | (A!25 = empty_set) | (~empty(A!25)) | (~empty(empty_set))),
% 0.90/0.82 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.90/0.82 tff(135,plain,
% 0.90/0.82 ($false),
% 0.90/0.82 inference(unit_resolution,[status(thm)],[134, 131, 128, 127, 114])).
% 0.90/0.82 % SZS output end Proof
%------------------------------------------------------------------------------