TSTP Solution File: SET627+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 05:07:24 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET627+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Sep 3 07:04:40 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 tff(member_type, type, (
% 0.14/0.38 member: ( $i * $i ) > $o)).
% 0.14/0.38 tff(empty_set_type, type, (
% 0.14/0.38 empty_set: $i)).
% 0.14/0.38 tff(tptp_fun_D_0_type, type, (
% 0.14/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.14/0.38 tff(tptp_fun_B_2_type, type, (
% 0.14/0.38 tptp_fun_B_2: $i)).
% 0.14/0.38 tff(intersect_type, type, (
% 0.14/0.38 intersect: ( $i * $i ) > $o)).
% 0.14/0.38 tff(disjoint_type, type, (
% 0.14/0.38 disjoint: ( $i * $i ) > $o)).
% 0.14/0.38 tff(1,plain,
% 0.14/0.38 (^[B: $i, C: $i] : refl((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(2,plain,
% 0.14/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.38 tff(3,plain,
% 0.14/0.38 (^[B: $i, C: $i] : rewrite((~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(4,plain,
% 0.14/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.38 tff(5,plain,
% 0.14/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.14/0.38 tff(6,plain,
% 0.14/0.38 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) <=> ((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))), rewrite((intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))) <=> (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))))), rewrite((((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C))))) & (intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))), ((((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(7,plain,
% 0.14/0.38 (![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C))))) <=> ![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.38 tff(8,plain,
% 0.14/0.38 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C))) <=> ![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(9,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.14/0.38 tff(10,plain,
% 0.14/0.38 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.14/0.38 tff(11,plain,(
% 0.14/0.38 ![B: $i, C: $i] : (((~intersect(B, C)) | (member(tptp_fun_D_0(C, B), B) & member(tptp_fun_D_0(C, B), C))) & (intersect(B, C) | ![D: $i] : (~(member(D, B) & member(D, C)))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[10])).
% 0.14/0.38 tff(12,plain,
% 0.14/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.14/0.38 tff(13,plain,
% 0.14/0.38 (![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.38 tff(14,plain,
% 0.14/0.38 ((~![B: $i, C: $i] : (~((~((~intersect(B, C)) | (~((~member(tptp_fun_D_0(C, B), B)) | (~member(tptp_fun_D_0(C, B), C)))))) | (~(intersect(B, C) | ![D: $i] : ((~member(D, C)) | (~member(D, B)))))))) | (~((~((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))) | (~(intersect(B!2, empty_set) | ![D: $i] : ((~member(D, empty_set)) | (~member(D, B!2)))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(15,plain,
% 0.14/0.38 (~((~((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))) | (~(intersect(B!2, empty_set) | ![D: $i] : ((~member(D, empty_set)) | (~member(D, B!2))))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.14/0.38 tff(16,plain,
% 0.14/0.38 (((~((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))) | (~(intersect(B!2, empty_set) | ![D: $i] : ((~member(D, empty_set)) | (~member(D, B!2)))))) | ((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(17,plain,
% 0.14/0.38 ((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.14/0.38 tff(18,plain,
% 0.14/0.38 (^[B: $i, C: $i] : refl((disjoint(B, C) <=> (~intersect(B, C))) <=> (disjoint(B, C) <=> (~intersect(B, C))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(19,plain,
% 0.14/0.38 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.38 tff(20,plain,
% 0.14/0.38 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(21,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','disjoint_defn')).
% 0.14/0.38 tff(22,plain,
% 0.14/0.38 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.38 tff(23,plain,(
% 0.14/0.38 ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.14/0.39 inference(skolemize,[status(sab)],[22])).
% 0.14/0.39 tff(24,plain,
% 0.14/0.39 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.39 tff(25,plain,
% 0.14/0.39 ((~![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))) | (disjoint(B!2, empty_set) <=> (~intersect(B!2, empty_set)))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(26,plain,
% 0.14/0.39 (disjoint(B!2, empty_set) <=> (~intersect(B!2, empty_set))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.14/0.39 tff(27,plain,
% 0.14/0.39 ((~![B: $i] : disjoint(B, empty_set)) <=> (~![B: $i] : disjoint(B, empty_set))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(28,axiom,(~![B: $i] : disjoint(B, empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th104')).
% 0.14/0.39 tff(29,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.39 tff(30,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.14/0.39 tff(31,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.14/0.39 tff(32,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.14/0.39 tff(33,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.14/0.39 tff(34,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.14/0.39 tff(35,plain,
% 0.14/0.39 (~![B: $i] : disjoint(B, empty_set)),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.14/0.39 tff(36,plain,(
% 0.14/0.39 ~disjoint(B!2, empty_set)),
% 0.14/0.39 inference(skolemize,[status(sab)],[35])).
% 0.14/0.39 tff(37,plain,
% 0.14/0.39 ((~(disjoint(B!2, empty_set) <=> (~intersect(B!2, empty_set)))) | disjoint(B!2, empty_set) | intersect(B!2, empty_set)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(38,plain,
% 0.14/0.39 ((~(disjoint(B!2, empty_set) <=> (~intersect(B!2, empty_set)))) | intersect(B!2, empty_set)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.14/0.39 tff(39,plain,
% 0.14/0.39 (intersect(B!2, empty_set)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[38, 26])).
% 0.14/0.39 tff(40,plain,
% 0.14/0.39 ((~((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))) | (~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(41,plain,
% 0.14/0.39 ((~((~intersect(B!2, empty_set)) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))))) | (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.14/0.39 tff(42,plain,
% 0.14/0.39 (~((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[41, 17])).
% 0.14/0.39 tff(43,plain,
% 0.14/0.39 (((~member(tptp_fun_D_0(empty_set, B!2), B!2)) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set))) | member(tptp_fun_D_0(empty_set, B!2), empty_set)),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(44,plain,
% 0.14/0.39 (member(tptp_fun_D_0(empty_set, B!2), empty_set)),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.14/0.39 tff(45,plain,
% 0.14/0.39 (^[B: $i] : refl((~member(B, empty_set)) <=> (~member(B, empty_set)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(46,plain,
% 0.14/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.39 tff(47,plain,
% 0.14/0.39 (![B: $i] : (~member(B, empty_set)) <=> ![B: $i] : (~member(B, empty_set))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(48,axiom,(![B: $i] : (~member(B, empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','empty_set_defn')).
% 0.14/0.39 tff(49,plain,
% 0.14/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.39 tff(50,plain,(
% 0.14/0.39 ![B: $i] : (~member(B, empty_set))),
% 0.14/0.39 inference(skolemize,[status(sab)],[49])).
% 0.14/0.39 tff(51,plain,
% 0.14/0.39 (![B: $i] : (~member(B, empty_set))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.39 tff(52,plain,
% 0.14/0.39 ((~![B: $i] : (~member(B, empty_set))) | (~member(tptp_fun_D_0(empty_set, B!2), empty_set))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(53,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[52, 51, 44])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------