TSTP Solution File: SET629+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 05:07:25 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SET629+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 06:25:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(member_type, type, (
% 0.13/0.38 member: ( $i * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_C_2_type, type, (
% 0.13/0.38 tptp_fun_C_2: $i)).
% 0.13/0.38 tff(tptp_fun_D_0_type, type, (
% 0.13/0.38 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.13/0.38 tff(intersection_type, type, (
% 0.13/0.38 intersection: ( $i * $i ) > $i)).
% 0.13/0.38 tff(tptp_fun_B_3_type, type, (
% 0.13/0.38 tptp_fun_B_3: $i)).
% 0.13/0.38 tff(difference_type, type, (
% 0.13/0.38 difference: ( $i * $i ) > $i)).
% 0.13/0.38 tff(intersect_type, type, (
% 0.13/0.38 intersect: ( $i * $i ) > $o)).
% 0.13/0.38 tff(disjoint_type, type, (
% 0.13/0.38 disjoint: ( $i * $i ) > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (^[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))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (![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)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (^[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))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![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)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(6,axiom,(![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_defn')).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.38 tff(8,plain,(
% 0.13/0.38 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[7])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((~![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B)))))) | (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (^[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))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (^[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))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (^[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)))))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![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)))))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (![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)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(21,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')).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.13/0.38 tff(23,plain,(
% 0.13/0.38 ![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)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![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)))))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~![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(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))))) | (~(intersect(intersection(C!2, B!3), difference(B!3, C!2)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | (~member(D, intersection(C!2, B!3))))))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (~((~((~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))))) | (~(intersect(intersection(C!2, B!3), difference(B!3, C!2)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | (~member(D, intersection(C!2, B!3)))))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (((~((~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))))) | (~(intersect(intersection(C!2, B!3), difference(B!3, C!2)) | ![D: $i] : ((~member(D, difference(B!3, C!2))) | (~member(D, intersection(C!2, B!3))))))) | ((~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,(
% 0.13/0.39 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.13/0.39 inference(skolemize,[status(sab)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.13/0.39 inference(symmetry,[status(thm)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (intersect(intersection(C!2, B!3), difference(B!3, C!2)) <=> intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> intersect(intersection(C!2, B!3), difference(B!3, C!2))),
% 0.13/0.39 inference(symmetry,[status(thm)],[40])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (^[B: $i, C: $i] : refl((disjoint(B, C) <=> (~intersect(B, C))) <=> (disjoint(B, C) <=> (~intersect(B, C))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(45,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','disjoint_defn')).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39 tff(47,plain,(
% 0.13/0.39 ![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[46])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))) | (disjoint(intersection(B!3, C!2), difference(B!3, C!2)) <=> (~intersect(intersection(B!3, C!2), difference(B!3, C!2))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (disjoint(intersection(B!3, C!2), difference(B!3, C!2)) <=> (~intersect(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))) <=> (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(52,axiom,(~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_intersection_and_difference_disjoint')).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[53, 51])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[56, 51])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.13/0.39 tff(60,plain,(
% 0.13/0.39 ~disjoint(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.13/0.39 inference(skolemize,[status(sab)],[59])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((~(disjoint(intersection(B!3, C!2), difference(B!3, C!2)) <=> (~intersect(intersection(B!3, C!2), difference(B!3, C!2))))) | disjoint(intersection(B!3, C!2), difference(B!3, C!2)) | intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~(disjoint(intersection(B!3, C!2), difference(B!3, C!2)) <=> (~intersect(intersection(B!3, C!2), difference(B!3, C!2))))) | intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 (intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[62, 50])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 (intersect(intersection(C!2, B!3), difference(B!3, C!2))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[63, 41])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 ((~((~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))))) | (~intersect(intersection(C!2, B!3), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(66,plain,
% 0.13/0.39 (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[65, 64, 29])).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)))) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 ((~(member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 ((~(member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.13/0.39 tff(71,plain,
% 0.13/0.39 (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[70, 12])).
% 0.13/0.39 tff(72,plain,
% 0.13/0.39 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(73,plain,
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.39 tff(74,plain,
% 0.13/0.39 (^[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)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(75,plain,
% 0.13/0.39 (![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)],[74])).
% 0.13/0.40 tff(76,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(77,axiom,(![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','difference_defn')).
% 0.13/0.40 tff(78,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)],[77, 76])).
% 0.13/0.40 tff(79,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)],[78])).
% 0.13/0.40 tff(80,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)],[79, 75])).
% 0.13/0.40 tff(81,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)],[80, 73])).
% 0.13/0.40 tff(82,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(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(83,plain,
% 0.13/0.40 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.13/0.40 tff(84,plain,
% 0.13/0.40 (((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)))) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(85,plain,
% 0.13/0.40 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[84, 66])).
% 0.13/0.40 tff(86,plain,
% 0.13/0.40 ((~(member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(87,plain,
% 0.13/0.40 ((~(member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)) <=> (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))))) | (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.13/0.40 tff(88,plain,
% 0.13/0.40 (~((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[87, 83])).
% 0.13/0.40 tff(89,plain,
% 0.13/0.40 (((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(90,plain,
% 0.13/0.40 (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.13/0.40 tff(91,plain,
% 0.13/0.40 (((~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), B!3)) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2))) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(92,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[91, 90, 71])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------