TSTP Solution File: SET616+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 05:07:20 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET616+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 07:12:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(member_type, type, (
% 0.20/0.40 member: ( $i * $i ) > $o)).
% 0.20/0.40 tff(difference_type, type, (
% 0.20/0.40 difference: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_C_2_type, type, (
% 0.20/0.40 tptp_fun_C_2: $i)).
% 0.20/0.40 tff(tptp_fun_B_3_type, type, (
% 0.20/0.40 tptp_fun_B_3: $i)).
% 0.20/0.40 tff(tptp_fun_D_0_type, type, (
% 0.20/0.40 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))) <=> (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((~![B: $i, C: $i] : ((difference(B, C) = difference(C, B)) => (B = C))) <=> (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,axiom,(~![B: $i, C: $i] : ((difference(B, C) = difference(C, B)) => (B = C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th90')).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.40 tff(11,plain,(
% 0.20/0.40 ~((~(difference(B!3, C!2) = difference(C!2, B!3))) | (B!3 = C!2))),
% 0.20/0.40 inference(skolemize,[status(sab)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (difference(B!3, C!2) = difference(C!2, B!3)),
% 0.20/0.40 inference(or_elim,[status(thm)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (difference(C!2, B!3) = difference(B!3, C!2)),
% 0.20/0.40 inference(symmetry,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) <=> member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 ((~member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))) <=> (~member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(21,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.41 tff(23,plain,(
% 0.20/0.41 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) <=> member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.41 inference(symmetry,[status(thm)],[14])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((~member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))) <=> (~member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[30, 25])).
% 0.20/0.41 tff(32,assumption,(~member(tptp_fun_D_0(B!3, C!2), B!3)), introduced(assumption)).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((~(member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))))) | (~member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 34, 31])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[43, 39])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(53,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_member_defn')).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.41 tff(55,plain,(
% 0.20/0.41 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_0(C, B), B)) <=> member(tptp_fun_D_0(C, B), C))))))) | (~((~((~(C!2 = B!3)) | (member(tptp_fun_D_0(C!2, B!3), C!2) <=> member(tptp_fun_D_0(C!2, B!3), B!3)))) | (~((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (~((~((~(C!2 = B!3)) | (member(tptp_fun_D_0(C!2, B!3), C!2) <=> member(tptp_fun_D_0(C!2, B!3), B!3)))) | (~((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (((~((~(C!2 = B!3)) | (member(tptp_fun_D_0(C!2, B!3), C!2) <=> member(tptp_fun_D_0(C!2, B!3), B!3)))) | (~((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))))) | ((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((C!2 = B!3) <=> (B!3 = C!2)),
% 0.20/0.41 inference(commutativity,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((B!3 = C!2) <=> (C!2 = B!3)),
% 0.20/0.41 inference(symmetry,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~(B!3 = C!2)) <=> (~(C!2 = B!3))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (~(B!3 = C!2)),
% 0.20/0.41 inference(or_elim,[status(thm)],[11])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (~(C!2 = B!3)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~((C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)))) | (C!2 = B!3) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[68, 67, 62])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((~((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))) | member(tptp_fun_D_0(B!3, C!2), C!2) | member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!3, C!2), C!2) | member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (member(tptp_fun_D_0(B!3, C!2), C!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[71, 32])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 ((~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))) | (~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[73, 72, 32])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~(member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))))) | member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) | ((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 74, 27])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 37])).
% 0.20/0.42 tff(78,plain,(member(tptp_fun_D_0(B!3, C!2), B!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)) | (~member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 ((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~(member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3))))) | (~member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))) | (~((~member(tptp_fun_D_0(B!3, C!2), C!2)) | member(tptp_fun_D_0(B!3, C!2), B!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (~member(tptp_fun_D_0(B!3, C!2), difference(C!2, B!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[81, 80, 27])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 15])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~((~member(tptp_fun_D_0(B!3, C!2), C!2)) <=> member(tptp_fun_D_0(B!3, C!2), B!3))) | (~member(tptp_fun_D_0(B!3, C!2), C!2)) | (~member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~member(tptp_fun_D_0(B!3, C!2), C!2)) | (~member(tptp_fun_D_0(B!3, C!2), B!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 69])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (~member(tptp_fun_D_0(B!3, C!2), C!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 78])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 ((~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))) | (~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[87, 86, 78])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~(member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))))) | member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2)) | ((~member(tptp_fun_D_0(B!3, C!2), B!3)) | member(tptp_fun_D_0(B!3, C!2), C!2))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (member(tptp_fun_D_0(B!3, C!2), difference(B!3, C!2))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[89, 88, 31])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 83])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------