TSTP Solution File: SET577+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:07:05 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET577+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 06:45:48 EDT 2022
% 0.19/0.33 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(union_type, type, (
% 0.19/0.40 union: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_C_3_type, type, (
% 0.19/0.40 tptp_fun_C_3: $i)).
% 0.19/0.40 tff(tptp_fun_D_2_type, type, (
% 0.19/0.40 tptp_fun_D_2: $i)).
% 0.19/0.40 tff(tptp_fun_D_1_type, type, (
% 0.19/0.40 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_B_4_type, type, (
% 0.19/0.40 tptp_fun_B_4: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (^[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_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[6, 2])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[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_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[B: $i, C: $i] : rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C))))) <=> ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,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')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,(
% 0.19/0.40 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_1(C, B), B) <=> member(tptp_fun_D_1(C, B), C)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | ((~member(tptp_fun_D_1(C, B), B)) <=> member(tptp_fun_D_1(C, B), C))))))) | (~((~((~(B!4 = union(D!2, C!3))) | (member(tptp_fun_D_1(union(D!2, C!3), C!3), B!4) <=> member(tptp_fun_D_1(union(D!2, C!3), C!3), union(D!2, C!3))))) | (~((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~((~((~(B!4 = union(D!2, C!3))) | (member(tptp_fun_D_1(union(D!2, C!3), C!3), B!4) <=> member(tptp_fun_D_1(union(D!2, C!3), C!3), union(D!2, C!3))))) | (~((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~((~(B!4 = union(D!2, C!3))) | (member(tptp_fun_D_1(union(D!2, C!3), C!3), B!4) <=> member(tptp_fun_D_1(union(D!2, C!3), C!3), union(D!2, C!3))))) | (~((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))))) | ((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (^[B: $i, C: $i] : refl((union(B, C) = union(C, B)) <=> (union(B, C) = union(C, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B)) <=> ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,axiom,(![B: $i, C: $i] : (union(B, C) = union(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_union')).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.41 tff(31,plain,(
% 0.19/0.41 ![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[30])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![B: $i, C: $i] : (union(B, C) = union(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![B: $i, C: $i] : (union(B, C) = union(C, B))) | (union(C!3, D!2) = union(D!2, C!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (union(C!3, D!2) = union(D!2, C!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (union(D!2, C!3) = union(C!3, D!2)),
% 0.19/0.41 inference(symmetry,[status(thm)],[34])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 ((B!4 = union(D!2, C!3)) <=> (B!4 = union(C!3, D!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((B!4 = union(C!3, D!2)) <=> (B!4 = union(D!2, C!3))),
% 0.19/0.41 inference(symmetry,[status(thm)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~(B!4 = union(C!3, D!2))) <=> (~(B!4 = union(D!2, C!3)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2)))) <=> (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) | member(E, D))) => (B = union(C, D)))) <=> (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,axiom,(~![B: $i, C: $i, D: $i] : (![E: $i] : (member(E, B) <=> (member(E, C) | member(E, D))) => (B = union(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th18')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (~![B: $i, C: $i, D: $i] : ((~![E: $i] : (member(E, B) <=> (member(E, D) | member(E, C)))) | (B = union(C, D)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) & (~(B!4 = union(C!3, D!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~(B!4 = union(C!3, D!2))),
% 0.19/0.41 inference(and_elim,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~(B!4 = union(D!2, C!3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~((B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))))) | (B!4 = union(D!2, C!3)) | ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 ((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 52, 25])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[B: $i, C: $i, D: $i] : refl((member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (^[B: $i, C: $i, D: $i] : rewrite((member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> (member(D, union(B, C)) <=> (member(D, C) | member(D, B))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.41 tff(60,axiom,(![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, B) | member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','union_defn')).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.41 tff(63,plain,(
% 0.19/0.41 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.19/0.41 tff(67,assumption,(~(member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))), introduced(assumption)).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((~(member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))) | (~member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (~member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 67, 66])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[E: $i] : refl((member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) <=> (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3))) <=> ![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.42 inference(and_elim,[status(thm)],[50])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))) <=> ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 ((member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2) | member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3))) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2) | member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3)))) <=> ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2) | member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3)))) <=> ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2) | member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ((~![E: $i] : (member(E, B!4) <=> (member(E, D!2) | member(E, C!3)))) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[79, 73])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((~(member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))) | (~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) | (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[81, 67, 80])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))) | member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) | member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[83, 82, 69, 54])).
% 0.19/0.42 tff(85,plain,(member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~(member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))) | member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)) | (~(member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 85, 66])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 ((~(member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) <=> (member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))) | member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4) | (~(member(tptp_fun_D_1(union(D!2, C!3), B!4), C!3) | member(tptp_fun_D_1(union(D!2, C!3), B!4), D!2)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[88, 85, 80])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ((~((~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) <=> member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))) | (~member(tptp_fun_D_1(union(D!2, C!3), B!4), B!4)) | (~member(tptp_fun_D_1(union(D!2, C!3), B!4), union(D!2, C!3)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 89, 87, 54])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------