%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET575+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:25:53 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
% 0.00/0.12 % Problem : SET575+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 05:29:50 EDT 2025
% 0.11/0.33 % 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_1_type, type, (
% 0.18/0.37 tptp_fun_C_1: $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_2_type, type, (
% 0.18/0.37 tptp_fun_B_2: $i)).
% 0.18/0.37 tff(intersect_type, type, (
% 0.18/0.37 intersect: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[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, 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, B)) | (~member(D, C))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![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, B)) | (~member(D, 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((~((~((~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, B)) | (~member(D, C))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![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, B)) | (~member(D, 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] : (~((~((~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, B)) | (~member(D, 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(((~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, 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, 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, B)) | (~member(D, C))))))), 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, 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, 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, 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, B)) | (~member(D, C)))))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![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, B)) | (~member(D, 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] : (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)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(9,axiom,(![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','intersect_defn')).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (![B: $i, C: $i] : (intersect(B, C) <=> ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.37 tff(11,plain,(
% 0.18/0.37 ![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)))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[10])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (![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)))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (((~![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)))))))) | (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))))))) <=> ((~![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)))))))) | (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 ((~((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))))) <=> (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (((~![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)))))))) | (~((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))))))) <=> ((~![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)))))))) | (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))))))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (((~![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)))))))) | (~((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))))))) <=> ((~![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)))))))) | (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))))))),
% 0.18/0.37 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((~![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)))))))) | (~((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 ((~![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)))))))) | (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (~((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (((~(intersect(B!2, C!1) | ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))))) | (~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))))) | ((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 ((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 ((intersect(B!2, C!1) & ![D: $i] : (~(member(D, B!2) & member(D, C!1)))) <=> (intersect(B!2, C!1) & ![D: $i] : (~(member(D, B!2) & member(D, C!1))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 ((~![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))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 ((~![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))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(26,axiom,(~![B: $i, C: $i] : (intersect(B, C) => ?[D: $i] : (member(D, B) & member(D, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_th15')).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~intersect(B, C)) | ?[D: $i] : (member(D, B) & member(D, C)))),
% 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] : ((~intersect(B, C)) | ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (~![B: $i, C: $i] : ((~intersect(B, C)) | ?[D: $i] : (member(D, B) & member(D, 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] : ((~intersect(B, C)) | ?[D: $i] : (member(D, B) & member(D, C)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (intersect(B!2, C!1) & ![D: $i] : (~(member(D, B!2) & member(D, C!1)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (intersect(B!2, C!1)),
% 0.18/0.38 inference(and_elim,[status(thm)],[31])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 ((~((~intersect(B!2, C!1)) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))))) | (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (~((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[34, 22])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))) | member(tptp_fun_D_0(C!1, B!2), C!1)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (member(tptp_fun_D_0(C!1, B!2), C!1)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))) | member(tptp_fun_D_0(C!1, B!2), B!2)),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (member(tptp_fun_D_0(C!1, B!2), B!2)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[38, 35])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (^[D: $i] : refl(((~member(D, B!2)) | (~member(D, C!1))) <=> ((~member(D, B!2)) | (~member(D, C!1))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (![D: $i] : ((~member(D, B!2)) | (~member(D, C!1))) <=> ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (^[D: $i] : trans(monotonicity(rewrite((member(D, B!2) & member(D, C!1)) <=> (~((~member(D, B!2)) | (~member(D, C!1))))), ((~(member(D, B!2) & member(D, C!1))) <=> (~(~((~member(D, B!2)) | (~member(D, C!1))))))), rewrite((~(~((~member(D, B!2)) | (~member(D, C!1))))) <=> ((~member(D, B!2)) | (~member(D, C!1)))), ((~(member(D, B!2) & member(D, C!1))) <=> ((~member(D, B!2)) | (~member(D, C!1)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (![D: $i] : (~(member(D, B!2) & member(D, C!1))) <=> ![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (![D: $i] : (~(member(D, B!2) & member(D, C!1)))),
% 0.18/0.38 inference(and_elim,[status(thm)],[31])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (((~![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))) | ((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))) <=> ((~![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))) | (~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 ((~![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))) | ((~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 ((~![D: $i] : ((~member(D, B!2)) | (~member(D, C!1)))) | (~member(tptp_fun_D_0(C!1, B!2), B!2)) | (~member(tptp_fun_D_0(C!1, B!2), C!1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[49, 46, 39, 37])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------