%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU264+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:27:26 AM UTC 2025
% Result : Theorem 3.54s 3.79s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU264+2 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 06:36:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.54/3.79 % SZS status Theorem
% 3.54/3.79 % SZS output start Proof
% 3.54/3.79 tff(subset_type, type, (
% 3.54/3.79 subset: ( $i * $i ) > $o)).
% 3.54/3.79 tff(set_union2_type, type, (
% 3.54/3.79 set_union2: ( $i * $i ) > $i)).
% 3.54/3.79 tff(set_difference_type, type, (
% 3.54/3.79 set_difference: ( $i * $i ) > $i)).
% 3.54/3.79 tff(tptp_fun_A_110_type, type, (
% 3.54/3.79 tptp_fun_A_110: $i)).
% 3.54/3.79 tff(tptp_fun_B_109_type, type, (
% 3.54/3.79 tptp_fun_B_109: $i)).
% 3.54/3.79 tff(relation_rng_type, type, (
% 3.54/3.79 relation_rng: $i > $i)).
% 3.54/3.79 tff(tptp_fun_D_107_type, type, (
% 3.54/3.79 tptp_fun_D_107: $i)).
% 3.54/3.79 tff(relation_of2_as_subset_type, type, (
% 3.54/3.79 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 3.54/3.79 tff(tptp_fun_C_108_type, type, (
% 3.54/3.79 tptp_fun_C_108: $i)).
% 3.54/3.79 tff(relation_dom_type, type, (
% 3.54/3.79 relation_dom: $i > $i)).
% 3.54/3.79 tff(1,plain,
% 3.54/3.79 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(2,plain,
% 3.54/3.79 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[1])).
% 3.54/3.79 tff(3,plain,
% 3.54/3.79 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(4,plain,
% 3.54/3.79 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(5,plain,
% 3.54/3.79 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[4])).
% 3.54/3.79 tff(6,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 3.54/3.79 tff(7,plain,
% 3.54/3.79 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[6, 5])).
% 3.54/3.79 tff(8,plain,
% 3.54/3.79 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[7, 3])).
% 3.54/3.79 tff(9,plain,(
% 3.54/3.79 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(skolemize,[status(sab)],[8])).
% 3.54/3.79 tff(10,plain,
% 3.54/3.79 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[9, 2])).
% 3.54/3.79 tff(11,plain,
% 3.54/3.79 ((~(relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(A!110, B!109)))) <=> (~(relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(A!110, B!109))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(12,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(13,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B)))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(14,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_relset_1')).
% 3.54/3.79 tff(15,plain,
% 3.54/3.79 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[14, 13])).
% 3.54/3.79 tff(16,plain,
% 3.54/3.79 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[15, 12])).
% 3.54/3.79 tff(17,plain,
% 3.54/3.79 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[16, 12])).
% 3.54/3.79 tff(18,plain,
% 3.54/3.79 (~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~relation_of2_as_subset(D, C, A)) | (~subset(A, B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[17, 12])).
% 3.54/3.79 tff(19,plain,(
% 3.54/3.79 ~(relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(A!110, B!109)))),
% 3.54/3.79 inference(skolemize,[status(sab)],[18])).
% 3.54/3.79 tff(20,plain,
% 3.54/3.79 (~(relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(A!110, B!109)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[19, 11])).
% 3.54/3.79 tff(21,plain,
% 3.54/3.79 (subset(A!110, B!109)),
% 3.54/3.79 inference(or_elim,[status(thm)],[20])).
% 3.54/3.79 tff(22,plain,
% 3.54/3.79 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!110, B!109)) | (B!109 = set_union2(A!110, set_difference(B!109, A!110))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!110, B!109)) | (B!109 = set_union2(A!110, set_difference(B!109, A!110))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(23,plain,
% 3.54/3.79 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(A!110, B!109)) | (B!109 = set_union2(A!110, set_difference(B!109, A!110))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(24,plain,
% 3.54/3.79 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(A!110, B!109)) | (B!109 = set_union2(A!110, set_difference(B!109, A!110)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.54/3.79 tff(25,plain,
% 3.54/3.79 (B!109 = set_union2(A!110, set_difference(B!109, A!110))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[24, 21, 10])).
% 3.54/3.79 tff(26,plain,
% 3.54/3.79 (set_union2(A!110, set_difference(B!109, A!110)) = B!109),
% 3.54/3.79 inference(symmetry,[status(thm)],[25])).
% 3.54/3.79 tff(27,plain,
% 3.54/3.79 (subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) <=> subset(relation_rng(D!107), B!109)),
% 3.54/3.79 inference(monotonicity,[status(thm)],[26])).
% 3.54/3.79 tff(28,plain,
% 3.54/3.79 (subset(relation_rng(D!107), B!109) <=> subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110)))),
% 3.54/3.79 inference(symmetry,[status(thm)],[27])).
% 3.54/3.79 tff(29,plain,
% 3.54/3.79 ((~subset(relation_rng(D!107), B!109)) <=> (~subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[28])).
% 3.54/3.79 tff(30,plain,
% 3.54/3.79 (relation_of2_as_subset(D!107, C!108, A!110)),
% 3.54/3.79 inference(or_elim,[status(thm)],[20])).
% 3.54/3.79 tff(31,plain,
% 3.54/3.79 (~relation_of2_as_subset(D!107, C!108, B!109)),
% 3.54/3.79 inference(or_elim,[status(thm)],[20])).
% 3.54/3.79 tff(32,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i, D: $i] : refl((relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(33,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[32])).
% 3.54/3.79 tff(34,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(35,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)) <=> ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))), ((relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, A) => ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))))), rewrite((relation_of2_as_subset(D, C, A) => ((~subset(relation_rng(D), B)) | relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))), ((relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(36,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[35])).
% 3.54/3.79 tff(37,axiom,(![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(relation_rng(D), B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t14_relset_1')).
% 3.54/3.79 tff(38,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.54/3.79 tff(39,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[38, 34])).
% 3.54/3.79 tff(40,plain,(
% 3.54/3.79 ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(skolemize,[status(sab)],[39])).
% 3.54/3.79 tff(41,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[40, 33])).
% 3.54/3.79 tff(42,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109)))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(43,plain,
% 3.54/3.79 ((relation_of2_as_subset(D!107, C!108, B!109) | (~subset(relation_rng(D!107), B!109)) | (~relation_of2_as_subset(D!107, C!108, A!110))) <=> (relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109)))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(44,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!107, C!108, B!109) | (~subset(relation_rng(D!107), B!109)) | (~relation_of2_as_subset(D!107, C!108, A!110)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[43])).
% 3.54/3.79 tff(45,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!107, C!108, B!109) | (~subset(relation_rng(D!107), B!109)) | (~relation_of2_as_subset(D!107, C!108, A!110)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109)))),
% 3.54/3.79 inference(transitivity,[status(thm)],[44, 42])).
% 3.54/3.79 tff(46,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!107, C!108, B!109) | (~subset(relation_rng(D!107), B!109)) | (~relation_of2_as_subset(D!107, C!108, A!110)))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(47,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(relation_rng(D), B)) | (~relation_of2_as_subset(D, C, A)))) | relation_of2_as_subset(D!107, C!108, B!109) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~subset(relation_rng(D!107), B!109))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.54/3.79 tff(48,plain,
% 3.54/3.79 (~subset(relation_rng(D!107), B!109)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[47, 41, 31, 30])).
% 3.54/3.79 tff(49,plain,
% 3.54/3.79 (~subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[48, 29])).
% 3.54/3.79 tff(50,plain,
% 3.54/3.79 (subset(A!110, set_union2(A!110, set_difference(B!109, A!110))) <=> subset(A!110, B!109)),
% 3.54/3.79 inference(monotonicity,[status(thm)],[26])).
% 3.54/3.79 tff(51,plain,
% 3.54/3.79 (subset(A!110, B!109) <=> subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))),
% 3.54/3.79 inference(symmetry,[status(thm)],[50])).
% 3.54/3.79 tff(52,plain,
% 3.54/3.79 (subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[21, 51])).
% 3.54/3.79 tff(53,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(54,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[53])).
% 3.54/3.79 tff(55,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i] : rewrite(((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B))))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(56,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[55])).
% 3.54/3.79 tff(57,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(58,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(59,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[58])).
% 3.54/3.79 tff(60,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => (subset(relation_dom(C), A) & subset(relation_rng(C), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_relset_1')).
% 3.54/3.79 tff(61,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[60, 59])).
% 3.54/3.79 tff(62,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[61, 57])).
% 3.54/3.79 tff(63,plain,(
% 3.54/3.79 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (subset(relation_dom(C), A) & subset(relation_rng(C), B)))),
% 3.54/3.79 inference(skolemize,[status(sab)],[62])).
% 3.54/3.79 tff(64,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[63, 56])).
% 3.54/3.79 tff(65,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[64, 54])).
% 3.54/3.79 tff(66,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!107, C!108, A!110)) | (~((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110)))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(67,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | ((~relation_of2_as_subset(D!107, C!108, A!110)) | (~((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110)))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(68,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~subset(relation_dom(C), A)) | (~subset(relation_rng(C), B)))))) | (~relation_of2_as_subset(D!107, C!108, A!110)) | (~((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110))))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[67, 66])).
% 3.54/3.79 tff(69,plain,
% 3.54/3.79 (~((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110)))),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[68, 65, 30])).
% 3.54/3.79 tff(70,plain,
% 3.54/3.79 (((~subset(relation_dom(D!107), C!108)) | (~subset(relation_rng(D!107), A!110))) | subset(relation_rng(D!107), A!110)),
% 3.54/3.79 inference(tautology,[status(thm)],[])).
% 3.54/3.79 tff(71,plain,
% 3.54/3.79 (subset(relation_rng(D!107), A!110)),
% 3.54/3.79 inference(unit_resolution,[status(thm)],[70, 69])).
% 3.54/3.79 tff(72,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(73,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(A, B)) | (~subset(B, C))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(A, B)) | (~subset(B, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(B, C))))) <=> ((~subset(A, B)) | (~subset(B, C)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(A, B)) | (~subset(B, C))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(A, B)) | (~subset(B, C))) | subset(A, C)))), rewrite((((~subset(A, B)) | (~subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(74,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[73])).
% 3.54/3.79 tff(75,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(76,plain,
% 3.54/3.79 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 3.54/3.79 inference(bind,[status(th)],[])).
% 3.54/3.79 tff(77,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 3.54/3.79 inference(quant_intro,[status(thm)],[76])).
% 3.54/3.79 tff(78,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 3.54/3.79 tff(79,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[78, 77])).
% 3.54/3.79 tff(80,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[79, 75])).
% 3.54/3.79 tff(81,plain,(
% 3.54/3.79 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 3.54/3.79 inference(skolemize,[status(sab)],[80])).
% 3.54/3.79 tff(82,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[81, 74])).
% 3.54/3.79 tff(83,plain,
% 3.54/3.79 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 3.54/3.79 inference(modus_ponens,[status(thm)],[82, 72])).
% 3.54/3.79 tff(84,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(85,plain,
% 3.54/3.79 ((subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(relation_rng(D!107), A!110)) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110))))) <=> ((~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))),
% 3.54/3.79 inference(rewrite,[status(thm)],[])).
% 3.54/3.79 tff(86,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(relation_rng(D!107), A!110)) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110))))))),
% 3.54/3.79 inference(monotonicity,[status(thm)],[85])).
% 3.54/3.79 tff(87,plain,
% 3.54/3.79 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(relation_rng(D!107), A!110)) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))),
% 3.54/3.79 inference(transitivity,[status(thm)],[86, 84])).
% 3.54/3.79 tff(88,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(relation_rng(D!107), A!110)) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110)))))),
% 3.54/3.79 inference(quant_inst,[status(thm)],[])).
% 3.54/3.79 tff(89,plain,
% 3.54/3.79 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(relation_rng(D!107), A!110)) | subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110))))),
% 3.54/3.81 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.54/3.81 tff(90,plain,
% 3.54/3.81 (subset(relation_rng(D!107), set_union2(A!110, set_difference(B!109, A!110))) | (~subset(A!110, set_union2(A!110, set_difference(B!109, A!110))))),
% 3.54/3.81 inference(unit_resolution,[status(thm)],[89, 83, 71])).
% 3.54/3.81 tff(91,plain,
% 3.54/3.81 ($false),
% 3.54/3.81 inference(unit_resolution,[status(thm)],[90, 52, 49])).
% 3.54/3.81 % SZS output end Proof
% 3.65/3.82 % E exiting
%------------------------------------------------------------------------------