%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET629+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:26:03 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SET629+3 : TPTP v9.0.0. Released v2.2.0.
% 0.01/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:32:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(member_type, type, (
% 0.19/0.36 member: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_C_2_type, type, (
% 0.19/0.36 tptp_fun_C_2: $i)).
% 0.19/0.36 tff(tptp_fun_D_0_type, type, (
% 0.19/0.36 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.36 tff(intersection_type, type, (
% 0.19/0.36 intersection: ( $i * $i ) > $i)).
% 0.19/0.36 tff(tptp_fun_B_3_type, type, (
% 0.19/0.36 tptp_fun_B_3: $i)).
% 0.19/0.36 tff(difference_type, type, (
% 0.19/0.36 difference: ( $i * $i ) > $i)).
% 0.19/0.36 tff(intersect_type, type, (
% 0.19/0.36 intersect: ( $i * $i ) > $o)).
% 0.19/0.36 tff(disjoint_type, type, (
% 0.19/0.36 disjoint: ( $i * $i ) > $o)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & (~member(D, C))) <=> (~((~member(D, B)) | member(D, C)))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))))), rewrite((member(D, difference(B, C)) <=> (~((~member(D, B)) | member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))))), rewrite((~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))), ((member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C)))) <=> (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![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, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (![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))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 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')).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.36 tff(8,plain,(
% 0.19/0.36 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.36 inference(skolemize,[status(sab)],[7])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~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))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (~(((~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)))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 (^[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))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[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))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (^[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)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(21,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersect_defn')).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.37 tff(23,plain,(
% 0.19/0.37 ![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)))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[22])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![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)))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~![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)) | ![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)), 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)))))))))) <=> ((~![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)) | ![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)), 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))))))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~((~((~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)) | ![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)), 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)))))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (((~![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))))))))) <=> ((~![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)) | ![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)), 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))))))))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (((~![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))))))))) <=> ((~![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)) | ![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)), 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))))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[28, 26])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((~![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))))))))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((~![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)) | ![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)), 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)))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~((~(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)), 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))))))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 25])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (((~(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)), 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)))))))) | ((~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)), 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))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~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)), 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)))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((intersection(B, C) = intersection(C, B)) <=> (intersection(B, C) = intersection(C, B)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B)) <=> ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(38,axiom,(![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_of_intersection')).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.37 tff(40,plain,(
% 0.19/0.37 ![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(skolemize,[status(sab)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 ((~![B: $i, C: $i] : (intersection(B, C) = intersection(C, B))) | (intersection(B!3, C!2) = intersection(C!2, B!3))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (intersection(B!3, C!2) = intersection(C!2, B!3)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (intersection(C!2, B!3) = intersection(B!3, C!2)),
% 0.19/0.37 inference(symmetry,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (intersect(intersection(C!2, B!3), difference(B!3, C!2)) <=> intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 (intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> intersect(intersection(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.37 inference(symmetry,[status(thm)],[45])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 (^[B: $i, C: $i] : refl((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (^[B: $i, C: $i] : trans(rewrite((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), rewrite((~(intersect(B, C) <=> disjoint(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))), ((disjoint(B, C) <=> (~intersect(B, C))) <=> (~(intersect(B, C) <=> disjoint(B, C)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C))) <=> ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.37 tff(52,axiom,(![B: $i, C: $i] : (disjoint(B, C) <=> (~intersect(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','disjoint_defn')).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.38 tff(55,plain,(
% 0.19/0.38 ![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[54])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 ((~![B: $i, C: $i] : (~(intersect(B, C) <=> disjoint(B, C)))) | (~(intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (~(intersect(intersection(B!3, C!2), difference(B!3, C!2)) <=> disjoint(intersection(B!3, C!2), difference(B!3, C!2)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 ((~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))) <=> (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,axiom,(~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_intersection_and_difference_disjoint')).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[61, 59])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 59])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (~![B: $i, C: $i] : disjoint(intersection(B, C), difference(B, C))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.38 tff(65,plain,(
% 0.19/0.38 ~disjoint(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.19/0.38 inference(skolemize,[status(sab)],[64])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 ((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)) | disjoint(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ((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))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (intersect(intersection(B!3, C!2), difference(B!3, C!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[67, 58])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (intersect(intersection(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[68, 46])).
% 0.19/0.38 tff(70,plain,
% 0.19/0.38 ((~((~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)), 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))))))) | (~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)), 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)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (~((~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))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[70, 69, 34])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (((~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)))) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(73,plain,
% 0.19/0.38 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 ((((~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))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), difference(B!3, C!2)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 ((((~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)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 (~((~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))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[75, 12])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, C)) | (~member(D, B))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, C)) | (~member(D, B))))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (![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, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[79])).
% 0.19/0.38 tff(81,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(82,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')).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.38 tff(84,plain,(
% 0.19/0.38 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[83])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, C)) | (~member(D, B))) <=> member(D, intersection(B, C))))) | (~(((~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))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 (~(((~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)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (((~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)))) | member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[89, 71])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 ((((~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)))) | (~member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), intersection(C!2, B!3)))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 ((((~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))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 (~((~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)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.19/0.38 tff(94,plain,
% 0.19/0.38 (((~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)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(95,plain,
% 0.19/0.38 (member(tptp_fun_D_0(difference(B!3, C!2), intersection(C!2, B!3)), C!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.19/0.38 tff(96,plain,
% 0.19/0.38 (((~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))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(97,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[96, 95, 76])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------