%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET616+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 05:26:01 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET616+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 05:31:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(member_type, type, (
% 0.19/0.44 member: ( $i * $i ) > $o)).
% 0.19/0.44 tff(difference_type, type, (
% 0.19/0.44 difference: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_C_2_type, type, (
% 0.19/0.44 tptp_fun_C_2: $i)).
% 0.19/0.44 tff(tptp_fun_B_3_type, type, (
% 0.19/0.44 tptp_fun_B_3: $i)).
% 0.19/0.44 tff(tptp_fun_D_1_type, type, (
% 0.19/0.44 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_D_0_type, type, (
% 0.19/0.44 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.19/0.44 tff(subset_type, type, (
% 0.19/0.44 subset: ( $i * $i ) > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))) <=> (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((~![B: $i, C: $i] : ((difference(B, C) = difference(C, B)) => (B = C))) <=> (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,axiom,(~![B: $i, C: $i] : ((difference(B, C) = difference(C, B)) => (B = C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_th90')).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (~![B: $i, C: $i] : ((~(difference(B, C) = difference(C, B))) | (B = C))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.44 tff(8,plain,(
% 0.19/0.44 ~((~(difference(B!3, C!2) = difference(C!2, B!3))) | (B!3 = C!2))),
% 0.19/0.44 inference(skolemize,[status(sab)],[7])).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (difference(B!3, C!2) = difference(C!2, B!3)),
% 0.19/0.44 inference(or_elim,[status(thm)],[8])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[9])).
% 0.19/0.44 tff(11,plain,
% 0.19/0.44 (member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2))),
% 0.19/0.44 inference(symmetry,[status(thm)],[10])).
% 0.19/0.44 tff(12,assumption,(~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))), introduced(assumption)).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.44 tff(15,plain,
% 0.19/0.44 (^[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))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(16,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.44 tff(17,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(18,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')).
% 0.19/0.44 tff(19,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.44 tff(20,plain,(
% 0.19/0.44 ![B: $i, C: $i, D: $i] : (member(D, difference(B, C)) <=> (member(D, B) & (~member(D, C))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[19])).
% 0.19/0.44 tff(21,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.44 tff(22,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.44 tff(23,plain,
% 0.19/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(24,plain,
% 0.19/0.44 ((~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)))) <=> (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(25,plain,
% 0.19/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.44 tff(26,plain,
% 0.19/0.44 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.44 tff(27,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(28,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 ((member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[30, 29, 12])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[31, 11])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[33, 22])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 (~(((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[35, 22])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 ((((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (~((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[37, 31, 36])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 ((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 ((((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2))) | (~((~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), B!3)) | member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), C!2))) | (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (~member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(B!3, C!2))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[43, 42, 34])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[44, 32])).
% 0.19/0.44 tff(46,plain,(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (^[B: $i, C: $i, D: $i] : refl((~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(pull_quant,[status(thm)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (^[B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> (~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))))), pull_quant((~![D: $i] : ((~(B = C)) | (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C))))), ((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) <=> ?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> (?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), pull_quant((?[D: $i] : (~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), (((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))) <=> ?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))), pull_quant((~?[D: $i] : ((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : ![D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[51, 49])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[52, 48])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (^[B: $i, C: $i] : rewrite((~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))) <=> ![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (^[B: $i, C: $i] : trans(monotonicity(rewrite(((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) <=> ((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))), trans(monotonicity(rewrite((~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))) <=> (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), rewrite(((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))), (((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))) <=> ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))))), rewrite((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))), ((((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C))))) <=> ![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.45 tff(59,plain,
% 0.19/0.45 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C))) <=> ![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(60,axiom,(![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_member_defn')).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![B: $i, C: $i] : ((B = C) <=> ![D: $i] : (member(D, B) <=> member(D, C)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.45 tff(62,plain,(
% 0.19/0.45 ![B: $i, C: $i] : (((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C))) & ((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[61])).
% 0.19/0.45 tff(63,plain,
% 0.19/0.45 (![B: $i, C: $i] : (~((~((~(B = C)) | ![D: $i] : (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.45 tff(64,plain,
% 0.19/0.45 (![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.45 tff(65,plain,
% 0.19/0.45 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(66,plain,
% 0.19/0.45 ((~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((difference(C!2, C!2) = difference(C!2, B!3)) | (~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))))))) <=> (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(67,plain,
% 0.19/0.45 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((difference(C!2, C!2) = difference(C!2, B!3)) | (~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.45 tff(68,plain,
% 0.19/0.45 (((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((difference(C!2, C!2) = difference(C!2, B!3)) | (~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))))))))) <=> ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.45 tff(69,plain,
% 0.19/0.45 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((difference(C!2, C!2) = difference(C!2, B!3)) | (~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(70,plain,
% 0.19/0.45 ((~![B: $i, C: $i, D: $i] : (~((~((~(B = C)) | (member(D, B) <=> member(D, C)))) | (~((B = C) | (~(member(tptp_fun_D_0(C, B), B) <=> member(tptp_fun_D_0(C, B), C)))))))) | (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (~((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[70, 64])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (((~((~(difference(C!2, C!2) = difference(C!2, B!3))) | (member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(C!2, difference(C!2, C!2)), difference(C!2, B!3))))) | (~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))))) | ((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 ((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 ((~((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3)))) | (~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 ((~(member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, C!2)) <=> member(tptp_fun_D_0(difference(C!2, B!3), difference(C!2, C!2)), difference(C!2, B!3)))) | (difference(C!2, C!2) = difference(C!2, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (difference(C!2, C!2) = difference(C!2, B!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[75, 46])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (difference(C!2, B!3) = difference(C!2, C!2)),
% 0.19/0.46 inference(symmetry,[status(thm)],[76])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (difference(B!3, C!2) = difference(C!2, C!2)),
% 0.19/0.46 inference(transitivity,[status(thm)],[9, 77])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[78])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.46 inference(symmetry,[status(thm)],[79])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 ((~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))) <=> (~member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.46 tff(82,assumption,((~((~subset(C!2, B!3)) | ![D: $i] : ((~member(D, C!2)) | member(D, B!3)))) | (~(subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)))))), introduced(assumption)).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 (^[B: $i, C: $i] : refl((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(84,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.46 tff(85,plain,
% 0.19/0.46 (^[B: $i, C: $i] : rewrite((~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(86,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.46 tff(87,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.46 tff(88,plain,
% 0.19/0.46 (^[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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))) <=> (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))))), rewrite((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))), ((((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C))))) <=> (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(89,plain,
% 0.19/0.46 (![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.46 tff(90,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(91,plain,
% 0.19/0.46 (^[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))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(92,plain,
% 0.19/0.46 (![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)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.46 tff(93,axiom,(![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : (member(D, B) => member(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','subset_defn')).
% 0.19/0.46 tff(94,plain,
% 0.19/0.46 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.46 tff(95,plain,
% 0.19/0.46 (![B: $i, C: $i] : (subset(B, C) <=> ![D: $i] : ((~member(D, B)) | member(D, C)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.46 tff(96,plain,(
% 0.19/0.46 ![B: $i, C: $i] : (((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C))) & (subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[95])).
% 0.19/0.46 tff(97,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.19/0.46 tff(98,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.19/0.46 tff(99,plain,
% 0.19/0.46 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(C!2, B!3)) | ![D: $i] : ((~member(D, C!2)) | member(D, B!3)))) | (~(subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(100,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[99, 98, 82])).
% 0.19/0.46 tff(101,plain,(~((~((~subset(C!2, B!3)) | ![D: $i] : ((~member(D, C!2)) | member(D, B!3)))) | (~(subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(102,plain,
% 0.19/0.46 (((~((~subset(C!2, B!3)) | ![D: $i] : ((~member(D, C!2)) | member(D, B!3)))) | (~(subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)))))) | (subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(103,plain,
% 0.19/0.46 (subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.19/0.46 tff(104,plain,
% 0.19/0.46 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(105,plain,
% 0.19/0.46 (~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[104, 22])).
% 0.19/0.46 tff(106,plain,
% 0.19/0.46 (member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[77])).
% 0.19/0.46 tff(107,plain,
% 0.19/0.46 (member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3))),
% 0.19/0.46 inference(symmetry,[status(thm)],[106])).
% 0.19/0.46 tff(108,plain,
% 0.19/0.46 ((~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))) <=> (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3)))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.46 tff(109,assumption,(member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))), introduced(assumption)).
% 0.19/0.46 tff(110,plain,
% 0.19/0.46 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(111,plain,
% 0.19/0.46 ((~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), C!2)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2)))) <=> (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(112,plain,
% 0.19/0.46 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), C!2)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.46 tff(113,plain,
% 0.19/0.46 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), C!2)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.46 tff(114,plain,
% 0.19/0.46 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), C!2)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(115,plain,
% 0.19/0.46 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.46 tff(116,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[115, 22, 109])).
% 0.19/0.46 tff(117,plain,(~member(tptp_fun_D_1(B!3, C!2), difference(C!2, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(118,plain,
% 0.19/0.46 (~member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[117, 108])).
% 0.19/0.46 tff(119,plain,
% 0.19/0.46 ((((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)) <=> member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3))) | ((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)) | member(tptp_fun_D_1(B!3, C!2), difference(C!2, B!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(120,plain,
% 0.19/0.46 ((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[119, 118, 105])).
% 0.19/0.46 tff(121,plain,
% 0.19/0.46 ((~(subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3))))) | subset(C!2, B!3) | (~((~member(tptp_fun_D_1(B!3, C!2), C!2)) | member(tptp_fun_D_1(B!3, C!2), B!3)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(122,plain,
% 0.19/0.46 (subset(C!2, B!3)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[121, 120, 103])).
% 0.19/0.46 tff(123,plain,
% 0.19/0.46 (^[B: $i, C: $i] : refl((~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(124,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.46 tff(125,plain,
% 0.19/0.46 (^[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)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(126,plain,
% 0.19/0.46 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[125])).
% 0.19/0.46 tff(127,plain,
% 0.19/0.46 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B))) <=> ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(128,axiom,(![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','equal_defn')).
% 0.19/0.46 tff(129,plain,
% 0.19/0.46 (![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.46 tff(130,plain,(
% 0.19/0.46 ![B: $i, C: $i] : ((B = C) <=> (subset(B, C) & subset(C, B)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[129])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 (![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 ((~![B: $i, C: $i] : (~(((~subset(B, C)) | (~subset(C, B))) <=> (B = C)))) | (~(((~subset(B!3, C!2)) | (~subset(C!2, B!3))) <=> (B!3 = C!2)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (~(((~subset(B!3, C!2)) | (~subset(C!2, B!3))) <=> (B!3 = C!2))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (~(B!3 = C!2)),
% 0.19/0.46 inference(or_elim,[status(thm)],[8])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 ((((~subset(B!3, C!2)) | (~subset(C!2, B!3))) <=> (B!3 = C!2)) | ((~subset(B!3, C!2)) | (~subset(C!2, B!3))) | (B!3 = C!2)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((((~subset(B!3, C!2)) | (~subset(C!2, B!3))) <=> (B!3 = C!2)) | ((~subset(B!3, C!2)) | (~subset(C!2, B!3)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~subset(B!3, C!2)) | (~subset(C!2, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 ((~((~subset(B!3, C!2)) | (~subset(C!2, B!3)))) | (~subset(B!3, C!2)) | (~subset(C!2, B!3))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 ((~subset(B!3, C!2)) | (~subset(C!2, B!3))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (~subset(B!3, C!2)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[140, 122])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(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_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (~((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[142, 98])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (((~((~subset(B!3, C!2)) | ![D: $i] : ((~member(D, B!3)) | member(D, C!2)))) | (~(subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))))) | (subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2))))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 ((~(subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2))))) | subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (subset(B!3, C!2) | (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (~((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[147, 141])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) | (~member(tptp_fun_D_1(C!2, B!3), C!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (~member(tptp_fun_D_1(C!2, B!3), C!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.19/0.47 tff(151,assumption,(member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))), introduced(assumption)).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2)))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 ((~(((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2)))) <=> (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[153])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))) <=> ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[154, 152])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) <=> member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[157, 22, 151])).
% 0.19/0.47 tff(159,plain,(~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 (((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 ((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 ((~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~(subset(difference(C!2, C!2), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))))))) <=> (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~(subset(difference(C!2, C!2), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[163])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~(subset(difference(C!2, C!2), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)))))))) <=> ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[164, 162])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~(subset(difference(C!2, C!2), C!2) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2)))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 ((~![B: $i, C: $i] : (~((~((~subset(B, C)) | ![D: $i] : ((~member(D, B)) | member(D, C)))) | (~(subset(B, C) | (~((~member(tptp_fun_D_1(C, B), B)) | member(tptp_fun_D_1(C, B), C)))))))) | (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 (~((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[167, 98])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)))) | ((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 ((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 ((~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2))) | (~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 ((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (subset(difference(C!2, C!2), C!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[172, 161])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~((~((~member(tptp_fun_D_1(C!2, difference(C!2, C!2)), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, difference(C!2, C!2)), C!2))) | subset(difference(C!2, C!2), C!2)))) | ((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 ((~((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2)))) | (~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 ((~subset(difference(C!2, C!2), C!2)) | ![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 (![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 (((~![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))) | ((~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, B!3), C!2))) <=> ((~![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))) | (~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, B!3), C!2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 ((~![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))) | ((~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, B!3), C!2))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 ((~![D: $i] : ((~member(D, difference(C!2, C!2))) | member(D, C!2))) | (~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))) | member(tptp_fun_D_1(C!2, B!3), C!2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (~member(tptp_fun_D_1(C!2, B!3), difference(C!2, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[181, 178, 150])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (~member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[182, 81])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 ((~![B: $i, C: $i, D: $i] : (~(((~member(D, B)) | member(D, C)) <=> member(D, difference(B, C))))) | (~(((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(185,plain,
% 0.19/0.47 (~(((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[184, 22])).
% 0.19/0.47 tff(186,plain,
% 0.19/0.47 ((((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))) | ((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) | member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(187,plain,
% 0.19/0.47 ((((~member(tptp_fun_D_1(C!2, B!3), B!3)) | member(tptp_fun_D_1(C!2, B!3), C!2)) <=> member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))) | member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[186, 148])).
% 0.19/0.47 tff(188,plain,
% 0.19/0.47 (member(tptp_fun_D_1(C!2, B!3), difference(B!3, C!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[187, 185])).
% 0.19/0.47 tff(189,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[188, 183])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------