TSTP Solution File: SET603+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 05:07:15 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 06:48:47 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(member_type, type, (
% 0.21/0.41 member: ( $i * $i ) > $o)).
% 0.21/0.41 tff(empty_set_type, type, (
% 0.21/0.41 empty_set: $i)).
% 0.21/0.41 tff(tptp_fun_D_0_type, type, (
% 0.21/0.41 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(difference_type, type, (
% 0.21/0.41 difference: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_B_3_type, type, (
% 0.21/0.41 tptp_fun_B_3: $i)).
% 0.21/0.41 tff(1,assumption,(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (^[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)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(pull_quant,[status(thm)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[7, 3])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (^[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)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[10, 8])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (![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))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(17,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.42 tff(19,plain,(
% 0.21/0.42 ![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)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[18])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![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))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 ((~![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))))))) | (~((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), B!3)))) | (~((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (~((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), B!3)))) | (~((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~((~(difference(B!3, empty_set) = B!3)) | (member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), difference(B!3, empty_set)) <=> member(tptp_fun_D_0(difference(B!3, empty_set), empty_set), B!3)))) | (~((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))))) | ((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 ((~![B: $i] : (difference(B, empty_set) = B)) <=> (~![B: $i] : (difference(B, empty_set) = B))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,axiom,(~![B: $i] : (difference(B, empty_set) = B)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th74')).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (~![B: $i] : (difference(B, empty_set) = B)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.21/0.42 tff(36,plain,(
% 0.21/0.42 ~(difference(B!3, empty_set) = B!3)),
% 0.21/0.42 inference(skolemize,[status(sab)],[35])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))) | (difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 ((~((difference(B!3, empty_set) = B!3) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)))) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[38, 26])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 ((~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(48,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','difference_defn')).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.21/0.42 tff(50,plain,(
% 0.21/0.42 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[49])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 ((~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) | (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[56, 1])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[58, 57, 42])).
% 0.21/0.42 tff(60,plain,(~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(61,assumption,(~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)), introduced(assumption)).
% 0.21/0.42 tff(62,assumption,(~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))), introduced(assumption)).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 ((~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set))) <=> member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3))) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 39])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) <=> (~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))))) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[66, 54])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 ((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 62])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ((~((~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), B!3)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[69, 68, 65, 61])).
% 0.21/0.43 tff(71,plain,(member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), difference(B!3, empty_set)) | member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[71, 60])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(76,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.43 tff(78,plain,(
% 0.21/0.43 ![B: $i] : (~member(B, empty_set))),
% 0.21/0.43 inference(skolemize,[status(sab)],[77])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![B: $i] : (~member(B, empty_set))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(B!3, difference(B!3, empty_set)), empty_set))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[80, 79, 72])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------