%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET183+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:25:25 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET183+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:30:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(member_type, type, (
% 0.18/0.37 member: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_C_2_type, type, (
% 0.18/0.37 tptp_fun_C_2: $i)).
% 0.18/0.37 tff(tptp_fun_D_0_type, type, (
% 0.18/0.37 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_B_3_type, type, (
% 0.18/0.37 tptp_fun_B_3: $i)).
% 0.18/0.37 tff(intersection_type, type, (
% 0.18/0.37 intersection: ( $i * $i ) > $i)).
% 0.18/0.37 tff(subset_type, type, (
% 0.18/0.37 subset: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[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))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (^[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)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![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)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.18/0.37 tff(11,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subset_defn')).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.18/0.37 tff(14,plain,(
% 0.18/0.37 ![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)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[13])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, intersection(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, intersection(B!3, C!2))))) | (~(subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (~((~((~subset(B!3, intersection(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, intersection(B!3, C!2))))) | (~(subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (((~((~subset(B!3, intersection(B!3, C!2))) | ![D: $i] : ((~member(D, B!3)) | member(D, intersection(B!3, C!2))))) | (~(subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))))) | (subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[21])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (^[B: $i, C: $i] : trans(trans(monotonicity(rewrite((subset(B, C) & subset(C, B)) <=> (~((~subset(B, C)) | (~subset(C, B))))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> ((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))))), rewrite(((B = C) <=> (~((~subset(B, C)) | (~subset(C, B))))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))), rewrite((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))), (((B = C) <=> (subset(B, C) & subset(C, B))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_defn')).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.37 tff(28,plain,(
% 0.18/0.37 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[27])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)))) <=> ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 ((~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))) <=> (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 ((((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3)) <=> (((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 ((~(((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3))) <=> (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 ((~(((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3))) <=> (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)))),
% 0.18/0.37 inference(transitivity,[status(thm)],[34, 32])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3)))) <=> ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[35])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3)))) <=> ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[36, 31])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(intersection(B!3, C!2), B!3)) | (~subset(B!3, intersection(B!3, C!2)))) <=> (intersection(B!3, C!2) = B!3)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (~(((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[39, 30])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 ((~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((~![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B))) <=> (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(43,axiom,(~![B: $i, C: $i] : (subset(B, C) => (intersection(B, C) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_subset_intersection')).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~subset(B, C)) | (intersection(B, C) = B))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.18/0.37 tff(48,plain,(
% 0.18/0.37 ~((~subset(B!3, C!2)) | (intersection(B!3, C!2) = B!3))),
% 0.18/0.37 inference(skolemize,[status(sab)],[47])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (~(intersection(B!3, C!2) = B!3)),
% 0.18/0.37 inference(or_elim,[status(thm)],[48])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 ((((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)) | ((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) | (intersection(B!3, C!2) = B!3)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 ((((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))) <=> (intersection(B!3, C!2) = B!3)) | ((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 ((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[51, 40])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (^[B: $i, C: $i] : refl(subset(intersection(B, C), B) <=> subset(intersection(B, C), B))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B) <=> ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(56,axiom,(![B: $i, C: $i] : subset(intersection(B, C), B)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersection_is_subset')).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.38 tff(58,plain,(
% 0.18/0.38 ![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.18/0.38 inference(skolemize,[status(sab)],[57])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (![B: $i, C: $i] : subset(intersection(B, C), B)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : subset(intersection(B, C), B)) | subset(intersection(B!3, C!2), B!3)),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (subset(intersection(B!3, C!2), B!3)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 ((~((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3)))) | (~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 ((~((~subset(B!3, intersection(B!3, C!2))) | (~subset(intersection(B!3, C!2), B!3)))) | (~subset(B!3, intersection(B!3, C!2)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (~subset(B!3, intersection(B!3, C!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[63, 52])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 ((~(subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))))) | subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 ((~(subset(B!3, intersection(B!3, C!2)) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))))) | (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[66, 20])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_0(C, B), B)) | member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2))))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[70, 16])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_0(C!2, B!3), B!3)) | member(tptp_fun_D_0(C!2, B!3), C!2)))))) | ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 ((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (subset(B!3, C!2)),
% 0.18/0.38 inference(or_elim,[status(thm)],[48])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 ((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (![D: $i] : ((~member(D, B!3)) | member(D, C!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 (((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) <=> ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | ((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 ((~![D: $i] : ((~member(D, B!3)) | member(D, C!2))) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[80, 77, 69])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (^[B: $i, C: $i, D: $i] : refl((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> ![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (^[B: $i, C: $i, D: $i] : trans(trans(monotonicity(rewrite((member(D, B) & member(D, C)) <=> (~((~member(D, B)) | (~member(D, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))))), rewrite((member(D, intersection(B, C)) <=> (~((~member(D, B)) | (~member(D, C))))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))))), rewrite((~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C)))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))), ((member(D, intersection(B, C)) <=> (member(D, B) & member(D, C))) <=> (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (![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, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 (![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)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(87,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')).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.38 tff(89,plain,(
% 0.18/0.38 ![B: $i, C: $i, D: $i] : (member(D, intersection(B, C)) <=> (member(D, B) & member(D, C)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[88])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | (~member(D, C))) <=> member(D, intersection(B, C))))) | (~(((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) <=> member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (~(((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) <=> member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[94, 67])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 ((((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) <=> member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))) | ((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) | member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 ((((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))) <=> member(tptp_fun_D_0(intersection(B!3, C!2), B!3), intersection(B!3, C!2))) | ((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.18/0.38 tff(98,plain,
% 0.18/0.38 ((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[97, 93])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2)))) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 ((~((~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), B!3)) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2)))) | (~member(tptp_fun_D_0(intersection(B!3, C!2), B!3), C!2))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[99, 69])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[100, 98, 81])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------