TSTP Solution File: SET008+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 05:04:40 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Sep 3 01:01:55 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.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(member_type, type, (
% 0.20/0.44 member: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_C_3_type, type, (
% 0.20/0.44 tptp_fun_C_3: $i)).
% 0.20/0.44 tff(tptp_fun_D_0_type, type, (
% 0.20/0.44 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.20/0.44 tff(intersection_type, type, (
% 0.20/0.44 intersection: ( $i * $i ) > $i)).
% 0.20/0.44 tff(difference_type, type, (
% 0.20/0.44 difference: ( $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_B_4_type, type, (
% 0.20/0.44 tptp_fun_B_4: $i)).
% 0.20/0.44 tff(empty_set_type, type, (
% 0.20/0.44 empty_set: $i)).
% 0.20/0.44 tff(subset_type, type, (
% 0.20/0.44 subset: ( $i * $i ) > $o)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 (^[B: $i, C: $i, D: $i] : refl((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (^[B: $i, C: $i, D: $i] : rewrite((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersection_defn')).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,(
% 0.20/0.44 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[7])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3))) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3))) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (^[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))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 (^[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)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.44 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')).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.44 tff(26,plain,(
% 0.20/0.44 ![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)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[25])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 (![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)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 ((~![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(intersection(C!3, difference(B!4, C!3)), empty_set)) | ![D: $i] : ((~member(D, intersection(C!3, difference(B!4, C!3)))) | member(D, empty_set)))) | (~(subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (~((~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | ![D: $i] : ((~member(D, intersection(C!3, difference(B!4, C!3)))) | member(D, empty_set)))) | (~(subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (((~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | ![D: $i] : ((~member(D, intersection(C!3, difference(B!4, C!3)))) | member(D, empty_set)))) | (~(subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)))))) | (subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.44 tff(33,assumption,((~((~subset(empty_set, intersection(C!3, difference(B!4, C!3)))) | ![D: $i] : ((~member(D, empty_set)) | member(D, intersection(C!3, difference(B!4, C!3)))))) | (~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))))))), introduced(assumption)).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ((~![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(empty_set, intersection(C!3, difference(B!4, C!3)))) | ![D: $i] : ((~member(D, empty_set)) | member(D, intersection(C!3, difference(B!4, C!3)))))) | (~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[34, 28, 33])).
% 0.20/0.44 tff(36,plain,(~((~((~subset(empty_set, intersection(C!3, difference(B!4, C!3)))) | ![D: $i] : ((~member(D, empty_set)) | member(D, intersection(C!3, difference(B!4, C!3)))))) | (~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (((~((~subset(empty_set, intersection(C!3, difference(B!4, C!3)))) | ![D: $i] : ((~member(D, empty_set)) | member(D, intersection(C!3, difference(B!4, C!3)))))) | (~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))))))) | (subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.44 tff(39,assumption,(member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)), introduced(assumption)).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(43,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','empty_set_defn')).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.44 tff(45,plain,(
% 0.20/0.44 ![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(skolemize,[status(sab)],[44])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![B: $i] : (~member(B, empty_set))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.20/0.44 tff(49,plain,(~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 ((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 ((~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3))))))) | subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~(subset(empty_set, intersection(C!3, difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), empty_set)) | member(tptp_fun_D_0(intersection(C!3, difference(B!4, C!3)), empty_set), intersection(C!3, difference(B!4, C!3))))))) | subset(empty_set, intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 (subset(empty_set, intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[53, 38])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (^[B: $i, C: $i] : refl(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (^[B: $i, C: $i] : rewrite(((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(60,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.45 tff(62,plain,(
% 0.20/0.45 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[61])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B)))))) | ((intersection(C!3, difference(B!4, C!3)) = empty_set) <=> (~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 ((intersection(C!3, difference(B!4, C!3)) = empty_set) <=> (~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(68,plain,
% 0.20/0.45 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(70,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.45 tff(72,plain,(
% 0.20/0.45 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[71])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(difference(B!4, C!3), C!3) = intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (intersection(difference(B!4, C!3), C!3) = intersection(C!3, difference(B!4, C!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (intersection(C!3, difference(B!4, C!3)) = intersection(difference(B!4, C!3), C!3)),
% 0.20/0.45 inference(symmetry,[status(thm)],[75])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((intersection(C!3, difference(B!4, C!3)) = empty_set) <=> (intersection(difference(B!4, C!3), C!3) = empty_set)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ((intersection(difference(B!4, C!3), C!3) = empty_set) <=> (intersection(C!3, difference(B!4, C!3)) = empty_set)),
% 0.20/0.45 inference(symmetry,[status(thm)],[77])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 ((~(intersection(difference(B!4, C!3), C!3) = empty_set)) <=> (~(intersection(C!3, difference(B!4, C!3)) = empty_set))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 ((~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)) <=> (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(81,axiom,(~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_difference_empty_set')).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 80])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[85, 80])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 80])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (~![B: $i, C: $i] : (intersection(difference(B, C), C) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.45 tff(89,plain,(
% 0.20/0.45 ~(intersection(difference(B!4, C!3), C!3) = empty_set)),
% 0.20/0.45 inference(skolemize,[status(sab)],[88])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (~(intersection(C!3, difference(B!4, C!3)) = empty_set)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 ((~((intersection(C!3, difference(B!4, C!3)) = empty_set) <=> (~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3)))))))) | (intersection(C!3, difference(B!4, C!3)) = empty_set) | ((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 ((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[91, 90, 66])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 ((~((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3)))))) | (~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 ((~subset(intersection(C!3, difference(B!4, C!3)), empty_set)) | (~subset(empty_set, intersection(C!3, difference(B!4, C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (~subset(intersection(C!3, difference(B!4, C!3)), empty_set)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[94, 54])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ((~(subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set))))) | subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 ((~(subset(intersection(C!3, difference(B!4, C!3)), empty_set) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set))))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[97, 32])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), empty_set)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3))) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)))))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3)))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), intersection(C!3, difference(B!4, C!3))) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)))))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[102, 12])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 ((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 ((~(member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))) | (~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3))) | (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (~(member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[110, 109, 107])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (^[B: $i, C: $i, D: $i] : refl((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (^[B: $i, C: $i, D: $i] : rewrite((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(117,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')).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.46 tff(119,plain,(
% 0.20/0.46 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[118])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C))))) | (member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), difference(B!4, C!3)) <=> (~((~member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), B!4)) | member(tptp_fun_D_0(empty_set, intersection(C!3, difference(B!4, C!3))), C!3))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[122, 121, 111])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------