TSTP Solution File: SET593+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 05:07:11 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 06:47:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(member_type, type, (
% 0.13/0.40 member: ( $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_B_4_type, type, (
% 0.13/0.40 tptp_fun_B_4: $i)).
% 0.13/0.40 tff(tptp_fun_D_0_type, type, (
% 0.13/0.40 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.40 tff(difference_type, type, (
% 0.13/0.40 difference: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_D_2_type, type, (
% 0.13/0.40 tptp_fun_D_2: $i)).
% 0.13/0.40 tff(tptp_fun_C_3_type, type, (
% 0.13/0.40 tptp_fun_C_3: $i)).
% 0.13/0.40 tff(subset_type, type, (
% 0.13/0.40 subset: ( $i * $i ) > $o)).
% 0.13/0.40 tff(union_type, type, (
% 0.13/0.40 union: ( $i * $i ) > $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,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')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40 tff(8,plain,(
% 0.13/0.40 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2)) <=> (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2)) <=> (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))), rewrite((subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (^[B: $i, C: $i] : rewrite((subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C))) <=> ![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.40 tff(23,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.41 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.13/0.41 tff(26,plain,(
% 0.13/0.41 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(difference(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, difference(B!4, D!2))) | member(D, C!3)))) | (~(subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (~((~((~subset(difference(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, difference(B!4, D!2))) | member(D, C!3)))) | (~(subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (((~((~subset(difference(B!4, D!2), C!3)) | ![D: $i] : ((~member(D, difference(B!4, D!2))) | member(D, C!3)))) | (~(subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))))) | (subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.41 tff(33,assumption,((~((~subset(difference(B!4, C!3), D!2)) | ![D: $i] : ((~member(D, difference(B!4, C!3))) | member(D, D!2)))) | (~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)))))), introduced(assumption)).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(difference(B!4, C!3), D!2)) | ![D: $i] : ((~member(D, difference(B!4, C!3))) | member(D, D!2)))) | (~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.13/0.41 tff(36,plain,(~((~((~subset(difference(B!4, C!3), D!2)) | ![D: $i] : ((~member(D, difference(B!4, C!3))) | member(D, D!2)))) | (~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (((~((~subset(difference(B!4, C!3), D!2)) | ![D: $i] : ((~member(D, difference(B!4, C!3))) | member(D, D!2)))) | (~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)))))) | (subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 10])).
% 0.21/0.41 tff(41,assumption,(~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))), introduced(assumption)).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))))) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))))) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 40])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[49, 41])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 ((~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 52, 50])).
% 0.21/0.41 tff(55,assumption,(~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))), introduced(assumption)).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.41 tff(61,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')).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.41 tff(64,plain,(
% 0.21/0.41 ![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[66, 65, 55])).
% 0.21/0.41 tff(68,plain,(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~(member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3)))) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2))) | (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2))) | (member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), C!3))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 54])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (~((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2)))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[72, 28])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~(subset(B!4, union(C!3, D!2)) | (~((~member(tptp_fun_D_0(union(C!3, D!2), B!4), B!4)) | member(tptp_fun_D_0(union(C!3, D!2), B!4), union(C!3, D!2))))))) | ((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~![B: $i, C: $i, D: $i] : (subset(B, union(C, D)) => (subset(difference(B, C), D) & subset(difference(B, D), C)))) <=> (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(78,axiom,(~![B: $i, C: $i, D: $i] : (subset(B, union(C, D)) => (subset(difference(B, C), D) & subset(difference(B, D), C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th52')).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 76])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[82, 76])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (~![B: $i, C: $i, D: $i] : ((~subset(B, union(C, D))) | (subset(difference(B, C), D) & subset(difference(B, D), C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[84, 76])).
% 0.21/0.42 tff(86,plain,(
% 0.21/0.42 ~((~subset(B!4, union(C!3, D!2))) | (subset(difference(B!4, C!3), D!2) & subset(difference(B!4, D!2), C!3)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[85])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (subset(B!4, union(C!3, D!2))),
% 0.21/0.42 inference(or_elim,[status(thm)],[86])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 ((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | (~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 ((~((~subset(B!4, union(C!3, D!2))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2))))) | ![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[89, 75])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | ((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | ((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | (~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), B!4)) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), union(C!3, D!2))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[93, 90, 71, 48])).
% 0.21/0.42 tff(95,plain,((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ((~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))))) | subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 ((~(subset(difference(B!4, C!3), D!2) | (~((~member(tptp_fun_D_0(D!2, difference(B!4, C!3)), difference(B!4, C!3))) | member(tptp_fun_D_0(D!2, difference(B!4, C!3)), D!2))))) | subset(difference(B!4, C!3), D!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (subset(difference(B!4, C!3), D!2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[97, 38])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~(~((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3))))) <=> ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((subset(difference(B!4, C!3), D!2) & subset(difference(B!4, D!2), C!3)) <=> (~((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~(subset(difference(B!4, C!3), D!2) & subset(difference(B!4, D!2), C!3))) <=> (~(~((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ((~(subset(difference(B!4, C!3), D!2) & subset(difference(B!4, D!2), C!3))) <=> ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[101, 99])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~(subset(difference(B!4, C!3), D!2) & subset(difference(B!4, D!2), C!3))),
% 0.21/0.42 inference(or_elim,[status(thm)],[86])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~subset(difference(B!4, C!3), D!2)) | (~subset(difference(B!4, D!2), C!3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (~subset(difference(B!4, D!2), C!3)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~(subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))))) | subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~(subset(difference(B!4, D!2), C!3) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))))) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[107, 32])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2)) <=> (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2)) <=> (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))) | (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 (~((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[112, 12])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), difference(B!4, D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[116, 108])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 (((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[120, 119, 117])).
% 0.21/0.43 tff(122,assumption,(~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))), introduced(assumption)).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 ((member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3))) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[124])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))) <=> ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[125, 123])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 ((~![B: $i, C: $i, D: $i] : (member(D, union(B, C)) <=> (member(D, C) | member(D, B)))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[128, 65, 122])).
% 0.21/0.43 tff(130,plain,(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 ((~(member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)) <=> (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2)))) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2))) | (member(tptp_fun_D_0(C!3, difference(B!4, D!2)), C!3) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[132, 121])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | ((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)))) <=> ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | ((~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 ((~![D: $i] : ((~member(D, B!4)) | member(D, union(C!3, D!2)))) | (~member(tptp_fun_D_0(C!3, difference(B!4, D!2)), B!4)) | member(tptp_fun_D_0(C!3, difference(B!4, D!2)), union(C!3, D!2))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[136, 90, 133, 115])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------