%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET010-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:24:45 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.55s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET010-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:00:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.55 % SZS status Unsatisfiable
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 tff(difference_type, type, (
% 0.19/0.55 difference: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(aIb_type, type, (
% 0.19/0.55 aIb: $i)).
% 0.19/0.55 tff(cD_aIb_type, type, (
% 0.19/0.55 cD_aIb: $i)).
% 0.19/0.55 tff(member_type, type, (
% 0.19/0.55 member: ( $i * $i ) > $o)).
% 0.19/0.55 tff(k_type, type, (
% 0.19/0.55 k: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(c_type, type, (
% 0.19/0.55 c: $i)).
% 0.19/0.55 tff(g_type, type, (
% 0.19/0.55 g: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(cDb_type, type, (
% 0.19/0.55 cDb: $i)).
% 0.19/0.55 tff(cDa_type, type, (
% 0.19/0.55 cDa: $i)).
% 0.19/0.55 tff(union_type, type, (
% 0.19/0.55 union: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(b_type, type, (
% 0.19/0.55 b: $i)).
% 0.19/0.55 tff(intersection_type, type, (
% 0.19/0.55 intersection: ( $i * $i * $i ) > $o)).
% 0.19/0.55 tff(h_type, type, (
% 0.19/0.55 h: ( $i * $i * $i ) > $i)).
% 0.19/0.55 tff(a_type, type, (
% 0.19/0.55 a: $i)).
% 0.19/0.55 tff(1,assumption,(~difference(aIb, cD_aIb, aIb)), introduced(assumption)).
% 0.19/0.55 tff(2,plain,
% 0.19/0.55 (^[Set1: $i, Set2: $i, Difference: $i] : refl((member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference)) <=> (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(3,plain,
% 0.19/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference)) <=> ![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.55 tff(4,plain,
% 0.19/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference)) <=> ![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(5,plain,
% 0.19/0.55 (^[Set1: $i, Set2: $i, Difference: $i] : trans(monotonicity(rewrite((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set1)) <=> (member(k(Set1, Set2, Difference), Set1) | difference(Set1, Set2, Difference))), (((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set1)) | member(k(Set1, Set2, Difference), Difference)) <=> ((member(k(Set1, Set2, Difference), Set1) | difference(Set1, Set2, Difference)) | member(k(Set1, Set2, Difference), Difference)))), rewrite(((member(k(Set1, Set2, Difference), Set1) | difference(Set1, Set2, Difference)) | member(k(Set1, Set2, Difference), Difference)) <=> (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))), (((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set1)) | member(k(Set1, Set2, Difference), Difference)) <=> (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(6,plain,
% 0.19/0.55 (![Set1: $i, Set2: $i, Difference: $i] : ((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set1)) | member(k(Set1, Set2, Difference), Difference)) <=> ![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.55 tff(7,axiom,(![Set1: $i, Set2: $i, Difference: $i] : ((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set1)) | member(k(Set1, Set2, Difference), Difference))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax','difference_axiom2')).
% 0.19/0.55 tff(8,plain,
% 0.19/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.55 tff(9,plain,
% 0.19/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.39/0.55 tff(10,plain,(
% 0.39/0.55 ![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.39/0.55 inference(skolemize,[status(sab)],[9])).
% 0.39/0.55 tff(11,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.39/0.55 tff(12,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | (member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(13,plain,
% 0.39/0.55 ((member(k(aIb, cD_aIb, aIb), aIb) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb)) <=> (member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(14,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | (member(k(aIb, cD_aIb, aIb), aIb) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | (member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb)))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[13])).
% 0.39/0.55 tff(15,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | (member(k(aIb, cD_aIb, aIb), aIb) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))),
% 0.39/0.55 inference(transitivity,[status(thm)],[14, 12])).
% 0.39/0.55 tff(16,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | (member(k(aIb, cD_aIb, aIb), aIb) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(17,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Difference: $i] : (member(k(Set1, Set2, Difference), Set1) | member(k(Set1, Set2, Difference), Difference) | difference(Set1, Set2, Difference))) | member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.39/0.55 tff(18,plain,
% 0.39/0.55 (member(k(aIb, cD_aIb, aIb), aIb) | difference(aIb, cD_aIb, aIb)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.39/0.55 tff(19,plain,
% 0.39/0.55 (member(k(aIb, cD_aIb, aIb), aIb)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[18, 1])).
% 0.39/0.55 tff(20,plain,
% 0.39/0.55 (difference(c, aIb, cD_aIb) <=> difference(c, aIb, cD_aIb)),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(21,axiom,(difference(c, aIb, cD_aIb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_minus_aIb')).
% 0.39/0.55 tff(22,plain,
% 0.39/0.55 (difference(c, aIb, cD_aIb)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.39/0.55 tff(23,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, A_set: $i, Element: $i] : refl(((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2))) <=> ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(24,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2))) <=> ![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[23])).
% 0.39/0.55 tff(25,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2))) <=> ![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(26,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, A_set: $i, Element: $i] : trans(monotonicity(rewrite(((~member(Element, Set1)) | (~member(Element, Set2))) <=> ((~member(Element, Set1)) | (~member(Element, Set2)))), ((((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2))) <=> (((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2))))), rewrite((((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2))) <=> ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))), ((((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2))) <=> ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(27,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : (((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2))) <=> ![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[26])).
% 0.39/0.55 tff(28,axiom,(![Set1: $i, Set2: $i, A_set: $i, Element: $i] : (((~member(Element, Set1)) | (~member(Element, Set2))) | (~difference(A_set, Set1, Set2)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax','not_member_of_difference')).
% 0.39/0.55 tff(29,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.39/0.55 tff(30,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.39/0.55 tff(31,plain,(
% 0.39/0.55 ![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[30])).
% 0.39/0.55 tff(32,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.39/0.55 tff(33,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(34,plain,
% 0.39/0.55 (((~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb))) <=> ((~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(35,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[34])).
% 0.39/0.55 tff(36,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[35, 33])).
% 0.39/0.55 tff(37,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(38,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~difference(c, aIb, cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), cD_aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.39/0.55 tff(39,plain,
% 0.39/0.55 (~member(k(aIb, cD_aIb, aIb), cD_aIb)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[38, 32, 22, 19])).
% 0.39/0.55 tff(40,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Difference: $i] : refl((difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))) <=> (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(41,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[40])).
% 0.39/0.55 tff(42,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(43,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Difference: $i] : trans(monotonicity(rewrite((((~member(k(Set1, Set2, Difference), Difference)) | (~member(k(Set1, Set2, Difference), Set1))) | member(k(Set1, Set2, Difference), Set2)) <=> (member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))), (((((~member(k(Set1, Set2, Difference), Difference)) | (~member(k(Set1, Set2, Difference), Set1))) | member(k(Set1, Set2, Difference), Set2)) | difference(Set1, Set2, Difference)) <=> ((member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))) | difference(Set1, Set2, Difference)))), rewrite(((member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference))) | difference(Set1, Set2, Difference)) <=> (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))), (((((~member(k(Set1, Set2, Difference), Difference)) | (~member(k(Set1, Set2, Difference), Set1))) | member(k(Set1, Set2, Difference), Set2)) | difference(Set1, Set2, Difference)) <=> (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(44,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : ((((~member(k(Set1, Set2, Difference), Difference)) | (~member(k(Set1, Set2, Difference), Set1))) | member(k(Set1, Set2, Difference), Set2)) | difference(Set1, Set2, Difference)) <=> ![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[43])).
% 0.39/0.55 tff(45,axiom,(![Set1: $i, Set2: $i, Difference: $i] : ((((~member(k(Set1, Set2, Difference), Difference)) | (~member(k(Set1, Set2, Difference), Set1))) | member(k(Set1, Set2, Difference), Set2)) | difference(Set1, Set2, Difference))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax','difference_axiom3')).
% 0.39/0.55 tff(46,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.39/0.55 tff(47,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.39/0.55 tff(48,plain,(
% 0.39/0.55 ![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[47])).
% 0.39/0.55 tff(49,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.39/0.55 tff(50,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(51,plain,
% 0.39/0.55 ((difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb))) <=> (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(52,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[51])).
% 0.39/0.55 tff(53,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(transitivity,[status(thm)],[52, 50])).
% 0.39/0.55 tff(54,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | (difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb)) | (~member(k(aIb, cD_aIb, aIb), aIb)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(55,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Difference: $i] : (difference(Set1, Set2, Difference) | member(k(Set1, Set2, Difference), Set2) | (~member(k(Set1, Set2, Difference), Set1)) | (~member(k(Set1, Set2, Difference), Difference)))) | difference(aIb, cD_aIb, aIb) | member(k(aIb, cD_aIb, aIb), cD_aIb) | (~member(k(aIb, cD_aIb, aIb), aIb))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.39/0.55 tff(56,plain,
% 0.39/0.55 ($false),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[55, 49, 19, 1, 39])).
% 0.39/0.55 tff(57,plain,(difference(aIb, cD_aIb, aIb)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.55 tff(58,assumption,(member(g(cDa, cDb, cD_aIb), cDb)), introduced(assumption)).
% 0.39/0.55 tff(59,plain,
% 0.39/0.55 ((~union(cDa, cDb, cD_aIb)) <=> (~union(cDa, cDb, cD_aIb))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(60,axiom,(~union(cDa, cDb, cD_aIb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_cDa_union_cDb_is_cD_aIb')).
% 0.39/0.55 tff(61,plain,
% 0.39/0.55 (~union(cDa, cDb, cD_aIb)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.39/0.55 tff(62,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Union: $i] : refl((union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(63,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[62])).
% 0.39/0.55 tff(64,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(65,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Union: $i] : trans(monotonicity(rewrite(((~member(g(Set1, Set2, Union), Set2)) | (~member(g(Set1, Set2, Union), Union))) <=> ((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))), ((((~member(g(Set1, Set2, Union), Set2)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> (((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))) | union(Set1, Set2, Union)))), rewrite((((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2))) | union(Set1, Set2, Union)) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))), ((((~member(g(Set1, Set2, Union), Set2)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(66,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (((~member(g(Set1, Set2, Union), Set2)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[65])).
% 0.39/0.55 tff(67,axiom,(![Set1: $i, Set2: $i, Union: $i] : (((~member(g(Set1, Set2, Union), Set2)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax','union_axiom3')).
% 0.39/0.55 tff(68,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.39/0.55 tff(69,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.39/0.55 tff(70,plain,(
% 0.39/0.55 ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(skolemize,[status(sab)],[69])).
% 0.39/0.55 tff(71,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.39/0.55 tff(72,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))) | (union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDb)))) <=> ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))) | union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDb)))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(73,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))) | (union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDb)))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(74,plain,
% 0.39/0.55 ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set2)))) | union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDb))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.39/0.55 tff(75,plain,
% 0.39/0.55 ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDb))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[74, 71, 61])).
% 0.39/0.55 tff(76,plain,
% 0.39/0.55 (~member(g(cDa, cDb, cD_aIb), cD_aIb)),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[75, 58])).
% 0.39/0.55 tff(77,assumption,(~intersection(cDb, c, cDb)), introduced(assumption)).
% 0.39/0.55 tff(78,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Intersection: $i] : refl((member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) <=> (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(79,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[78])).
% 0.39/0.55 tff(80,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(81,plain,
% 0.39/0.55 (^[Set1: $i, Set2: $i, Intersection: $i] : rewrite(((member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) | member(h(Set1, Set2, Intersection), Set1)) <=> (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(82,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : ((member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) | member(h(Set1, Set2, Intersection), Set1)) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[81])).
% 0.39/0.55 tff(83,axiom,(![Set1: $i, Set2: $i, Intersection: $i] : ((member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection)) | member(h(Set1, Set2, Intersection), Set1))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax','intersection_axiom1')).
% 0.39/0.55 tff(84,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.39/0.55 tff(85,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.39/0.55 tff(86,plain,(
% 0.39/0.55 ![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(skolemize,[status(sab)],[85])).
% 0.39/0.55 tff(87,plain,
% 0.39/0.55 (![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.39/0.55 tff(88,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | (member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(89,plain,
% 0.39/0.55 ((member(h(cDb, c, cDb), cDb) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb)) <=> (member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(90,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | (member(h(cDb, c, cDb), cDb) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | (member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb)))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[89])).
% 0.39/0.55 tff(91,plain,
% 0.39/0.55 (((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | (member(h(cDb, c, cDb), cDb) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))),
% 0.39/0.56 inference(transitivity,[status(thm)],[90, 88])).
% 0.39/0.56 tff(92,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | (member(h(cDb, c, cDb), cDb) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(93,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Intersection: $i] : (member(h(Set1, Set2, Intersection), Set1) | member(h(Set1, Set2, Intersection), Intersection) | intersection(Set1, Set2, Intersection))) | member(h(cDb, c, cDb), cDb) | intersection(cDb, c, cDb)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.39/0.56 tff(94,plain,
% 0.39/0.56 (member(h(cDb, c, cDb), cDb)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[93, 87, 77])).
% 0.39/0.56 tff(95,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Intersection: $i] : refl((intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))) <=> (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(96,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[95])).
% 0.39/0.56 tff(97,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(98,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Intersection: $i] : trans(monotonicity(rewrite((((~member(h(Set1, Set2, Intersection), Intersection)) | (~member(h(Set1, Set2, Intersection), Set2))) | (~member(h(Set1, Set2, Intersection), Set1))) <=> ((~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))), (((((~member(h(Set1, Set2, Intersection), Intersection)) | (~member(h(Set1, Set2, Intersection), Set2))) | (~member(h(Set1, Set2, Intersection), Set1))) | intersection(Set1, Set2, Intersection)) <=> (((~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))) | intersection(Set1, Set2, Intersection)))), rewrite((((~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection))) | intersection(Set1, Set2, Intersection)) <=> (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))), (((((~member(h(Set1, Set2, Intersection), Intersection)) | (~member(h(Set1, Set2, Intersection), Set2))) | (~member(h(Set1, Set2, Intersection), Set1))) | intersection(Set1, Set2, Intersection)) <=> (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(99,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : ((((~member(h(Set1, Set2, Intersection), Intersection)) | (~member(h(Set1, Set2, Intersection), Set2))) | (~member(h(Set1, Set2, Intersection), Set1))) | intersection(Set1, Set2, Intersection)) <=> ![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[98])).
% 0.39/0.56 tff(100,axiom,(![Set1: $i, Set2: $i, Intersection: $i] : ((((~member(h(Set1, Set2, Intersection), Intersection)) | (~member(h(Set1, Set2, Intersection), Set2))) | (~member(h(Set1, Set2, Intersection), Set1))) | intersection(Set1, Set2, Intersection))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax','intersection_axiom3')).
% 0.39/0.56 tff(101,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.39/0.56 tff(102,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.39/0.56 tff(103,plain,(
% 0.39/0.56 ![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(skolemize,[status(sab)],[102])).
% 0.39/0.56 tff(104,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.39/0.56 tff(105,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | ((~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(106,plain,
% 0.39/0.56 ((intersection(cDb, c, cDb) | (~member(h(cDb, c, cDb), cDb)) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb))) <=> ((~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(107,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (intersection(cDb, c, cDb) | (~member(h(cDb, c, cDb), cDb)) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | ((~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb)))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[106])).
% 0.39/0.56 tff(108,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (intersection(cDb, c, cDb) | (~member(h(cDb, c, cDb), cDb)) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)))) <=> ((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb))),
% 0.39/0.56 inference(transitivity,[status(thm)],[107, 105])).
% 0.39/0.56 tff(109,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (intersection(cDb, c, cDb) | (~member(h(cDb, c, cDb), cDb)) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(110,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Intersection: $i] : (intersection(Set1, Set2, Intersection) | (~member(h(Set1, Set2, Intersection), Set1)) | (~member(h(Set1, Set2, Intersection), Set2)) | (~member(h(Set1, Set2, Intersection), Intersection)))) | (~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb)) | intersection(cDb, c, cDb)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.39/0.56 tff(111,plain,
% 0.39/0.56 ((~member(h(cDb, c, cDb), c)) | (~member(h(cDb, c, cDb), cDb))),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[110, 104, 77])).
% 0.39/0.56 tff(112,plain,
% 0.39/0.56 (~member(h(cDb, c, cDb), c)),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[111, 94])).
% 0.39/0.56 tff(113,plain,
% 0.39/0.56 (difference(c, b, cDb) <=> difference(c, b, cDb)),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(114,axiom,(difference(c, b, cDb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_minus_b')).
% 0.39/0.56 tff(115,plain,
% 0.39/0.56 (difference(c, b, cDb)),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.39/0.56 tff(116,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Difference: $i, Element: $i] : refl((member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference))) <=> (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(117,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[116])).
% 0.39/0.56 tff(118,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(119,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Difference: $i, Element: $i] : trans(monotonicity(rewrite(((~difference(Set1, Set2, Difference)) | (~member(Element, Difference))) <=> ((~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))), ((((~difference(Set1, Set2, Difference)) | (~member(Element, Difference))) | member(Element, Set1)) <=> (((~member(Element, Difference)) | (~difference(Set1, Set2, Difference))) | member(Element, Set1)))), rewrite((((~member(Element, Difference)) | (~difference(Set1, Set2, Difference))) | member(Element, Set1)) <=> (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))), ((((~difference(Set1, Set2, Difference)) | (~member(Element, Difference))) | member(Element, Set1)) <=> (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(120,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (((~difference(Set1, Set2, Difference)) | (~member(Element, Difference))) | member(Element, Set1)) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[119])).
% 0.39/0.56 tff(121,axiom,(![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (((~difference(Set1, Set2, Difference)) | (~member(Element, Difference))) | member(Element, Set1))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax','member_of_difference')).
% 0.39/0.56 tff(122,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.39/0.56 tff(123,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.39/0.56 tff(124,plain,(
% 0.39/0.56 ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(skolemize,[status(sab)],[123])).
% 0.39/0.56 tff(125,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.39/0.56 tff(126,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(127,plain,
% 0.39/0.56 ((member(h(cDb, c, cDb), c) | (~member(h(cDb, c, cDb), cDb)) | (~difference(c, b, cDb))) <=> (member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(128,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(h(cDb, c, cDb), c) | (~member(h(cDb, c, cDb), cDb)) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb))))),
% 0.39/0.56 inference(monotonicity,[status(thm)],[127])).
% 0.39/0.56 tff(129,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(h(cDb, c, cDb), c) | (~member(h(cDb, c, cDb), cDb)) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb)))),
% 0.39/0.56 inference(transitivity,[status(thm)],[128, 126])).
% 0.39/0.56 tff(130,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(h(cDb, c, cDb), c) | (~member(h(cDb, c, cDb), cDb)) | (~difference(c, b, cDb)))),
% 0.39/0.56 inference(quant_inst,[status(thm)],[])).
% 0.39/0.56 tff(131,plain,
% 0.39/0.56 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | member(h(cDb, c, cDb), c) | (~difference(c, b, cDb)) | (~member(h(cDb, c, cDb), cDb))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.39/0.56 tff(132,plain,
% 0.39/0.56 ($false),
% 0.39/0.56 inference(unit_resolution,[status(thm)],[131, 125, 115, 112, 94])).
% 0.39/0.56 tff(133,plain,(intersection(cDb, c, cDb)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.56 tff(134,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : refl((member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(135,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[134])).
% 0.39/0.56 tff(136,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(rewrite,[status(thm)],[])).
% 0.39/0.56 tff(137,plain,
% 0.39/0.56 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : trans(monotonicity(rewrite(((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) <=> ((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set2)) <=> (((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) | member(Element, Set2)))), rewrite((((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) | member(Element, Set2)) <=> (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set2)) <=> (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(138,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set2)) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[137])).
% 0.39/0.56 tff(139,axiom,(![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set2))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax','member_of_intersection_is_member_of_set2')).
% 0.39/0.56 tff(140,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.39/0.56 tff(141,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.39/0.56 tff(142,plain,(
% 0.39/0.56 ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(skolemize,[status(sab)],[141])).
% 0.39/0.56 tff(143,plain,
% 0.39/0.56 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.39/0.56 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.39/0.56 tff(144,plain,
% 0.39/0.56 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(145,plain,
% 0.40/0.56 ((member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb))) <=> ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(146,plain,
% 0.40/0.56 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.56 inference(monotonicity,[status(thm)],[145])).
% 0.40/0.56 tff(147,plain,
% 0.40/0.56 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.56 inference(transitivity,[status(thm)],[146, 144])).
% 0.40/0.56 tff(148,plain,
% 0.40/0.56 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)))),
% 0.40/0.56 inference(quant_inst,[status(thm)],[])).
% 0.40/0.56 tff(149,plain,
% 0.40/0.56 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.40/0.56 tff(150,plain,
% 0.40/0.56 ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~intersection(cDb, c, cDb)) | member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[149, 143])).
% 0.40/0.56 tff(151,plain,
% 0.40/0.56 ((~member(g(cDa, cDb, cD_aIb), cDb)) | member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[150, 133])).
% 0.40/0.56 tff(152,plain,
% 0.40/0.56 (member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.56 inference(unit_resolution,[status(thm)],[151, 58])).
% 0.40/0.56 tff(153,assumption,(~member(g(cDa, cDb, cD_aIb), cD_aIb)), introduced(assumption)).
% 0.40/0.56 tff(154,plain,
% 0.40/0.56 (^[Set1: $i, Set2: $i, Difference: $i, Element: $i] : refl(((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference))) <=> ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(155,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[154])).
% 0.40/0.56 tff(156,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference))) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(157,plain,
% 0.40/0.56 (^[Set1: $i, Set2: $i, Difference: $i, Element: $i] : trans(monotonicity(rewrite((((~member(Element, Set1)) | (~difference(Set1, Set2, Difference))) | member(Element, Difference)) <=> ((~member(Element, Set1)) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))), (((((~member(Element, Set1)) | (~difference(Set1, Set2, Difference))) | member(Element, Difference)) | member(Element, Set2)) <=> (((~member(Element, Set1)) | member(Element, Difference) | (~difference(Set1, Set2, Difference))) | member(Element, Set2)))), rewrite((((~member(Element, Set1)) | member(Element, Difference) | (~difference(Set1, Set2, Difference))) | member(Element, Set2)) <=> ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))), (((((~member(Element, Set1)) | (~difference(Set1, Set2, Difference))) | member(Element, Difference)) | member(Element, Set2)) <=> ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))))),
% 0.40/0.56 inference(bind,[status(th)],[])).
% 0.40/0.56 tff(158,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((((~member(Element, Set1)) | (~difference(Set1, Set2, Difference))) | member(Element, Difference)) | member(Element, Set2)) <=> ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(quant_intro,[status(thm)],[157])).
% 0.40/0.56 tff(159,axiom,(![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((((~member(Element, Set1)) | (~difference(Set1, Set2, Difference))) | member(Element, Difference)) | member(Element, Set2))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-3.ax','member_of_difference_or_set2')).
% 0.40/0.56 tff(160,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.40/0.56 tff(161,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.40/0.56 tff(162,plain,(
% 0.40/0.56 ![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(skolemize,[status(sab)],[161])).
% 0.40/0.56 tff(163,plain,
% 0.40/0.56 (![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))),
% 0.40/0.56 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.40/0.56 tff(164,plain,
% 0.40/0.56 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb)))),
% 0.40/0.56 inference(rewrite,[status(thm)],[])).
% 0.40/0.56 tff(165,plain,
% 0.40/0.56 (((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~difference(c, aIb, cD_aIb))) <=> (member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(166,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[165])).
% 0.40/0.57 tff(167,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[166, 164])).
% 0.40/0.57 tff(168,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~difference(c, aIb, cD_aIb)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(169,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cD_aIb) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), aIb) | (~difference(c, aIb, cD_aIb))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.40/0.57 tff(170,plain,
% 0.40/0.57 (member(g(cDa, cDb, cD_aIb), aIb)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[169, 163, 22, 153, 152])).
% 0.40/0.57 tff(171,assumption,(member(g(cDa, cDb, cD_aIb), aIb)), introduced(assumption)).
% 0.40/0.57 tff(172,assumption,(~member(g(cDa, cDb, cD_aIb), b)), introduced(assumption)).
% 0.40/0.57 tff(173,plain,
% 0.40/0.57 (intersection(a, b, aIb) <=> intersection(a, b, aIb)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(174,axiom,(intersection(a, b, aIb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_intersection_b')).
% 0.40/0.57 tff(175,plain,
% 0.40/0.57 (intersection(a, b, aIb)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.40/0.57 tff(176,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(177,plain,
% 0.40/0.57 ((member(g(cDa, cDb, cD_aIb), b) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb))) <=> ((~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(178,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), b) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[177])).
% 0.40/0.57 tff(179,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), b) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.57 inference(transitivity,[status(thm)],[178, 176])).
% 0.40/0.57 tff(180,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), b) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(181,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set2) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)) | member(g(cDa, cDb, cD_aIb), b)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.40/0.57 tff(182,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[181, 143, 175, 172, 171])).
% 0.40/0.57 tff(183,plain,(member(g(cDa, cDb, cD_aIb), b) | (~member(g(cDa, cDb, cD_aIb), aIb))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(184,plain,
% 0.40/0.57 (member(g(cDa, cDb, cD_aIb), b)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[183, 170])).
% 0.40/0.57 tff(185,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(186,plain,
% 0.40/0.57 (((~member(g(cDa, cDb, cD_aIb), b)) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb))) <=> ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(187,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), b)) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b))))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[186])).
% 0.40/0.57 tff(188,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), b)) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.57 inference(transitivity,[status(thm)],[187, 185])).
% 0.40/0.57 tff(189,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), b)) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(190,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDb)) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.40/0.57 tff(191,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[190, 32, 115, 58, 184])).
% 0.40/0.57 tff(192,plain,((~member(g(cDa, cDb, cD_aIb), cDb)) | member(g(cDa, cDb, cD_aIb), cD_aIb)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(193,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[192, 76, 58])).
% 0.40/0.57 tff(194,plain,(~member(g(cDa, cDb, cD_aIb), cDb)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(195,assumption,(~member(g(cDa, cDb, cD_aIb), cDb)), introduced(assumption)).
% 0.40/0.57 tff(196,assumption,(~member(g(cDa, cDb, cD_aIb), c)), introduced(assumption)).
% 0.40/0.57 tff(197,assumption,(member(g(cDa, cDb, cD_aIb), cDa)), introduced(assumption)).
% 0.40/0.57 tff(198,plain,
% 0.40/0.57 (difference(c, a, cDa) <=> difference(c, a, cDa)),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(199,axiom,(difference(c, a, cDa)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c_minus_a')).
% 0.40/0.57 tff(200,plain,
% 0.40/0.57 (difference(c, a, cDa)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.40/0.57 tff(201,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(202,plain,
% 0.40/0.57 ((member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa))) <=> ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(203,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[202])).
% 0.40/0.57 tff(204,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.57 inference(transitivity,[status(thm)],[203, 201])).
% 0.40/0.57 tff(205,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(206,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.40/0.57 tff(207,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[206, 125, 200, 197, 196])).
% 0.40/0.57 tff(208,plain,(member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cDa))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.57 tff(209,plain,
% 0.40/0.57 (~member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[208, 196])).
% 0.40/0.57 tff(210,plain,
% 0.40/0.57 (^[Set1: $i, Set2: $i, Union: $i] : refl((member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) <=> (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(211,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) <=> ![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[210])).
% 0.40/0.57 tff(212,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) <=> ![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(213,plain,
% 0.40/0.57 (^[Set1: $i, Set2: $i, Union: $i] : trans(monotonicity(trans(monotonicity(rewrite((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) <=> (member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))), (((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) <=> ((member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) | member(g(Set1, Set2, Union), Set2)))), rewrite(((member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) | member(g(Set1, Set2, Union), Set2)) <=> (member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))), (((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) <=> (member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)))), ((((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) | member(g(Set1, Set2, Union), Union)) <=> ((member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) | member(g(Set1, Set2, Union), Union)))), rewrite(((member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union)) | member(g(Set1, Set2, Union), Union)) <=> (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))), ((((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) | member(g(Set1, Set2, Union), Union)) <=> (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))))),
% 0.40/0.57 inference(bind,[status(th)],[])).
% 0.40/0.57 tff(214,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) | member(g(Set1, Set2, Union), Union)) <=> ![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(quant_intro,[status(thm)],[213])).
% 0.40/0.57 tff(215,axiom,(![Set1: $i, Set2: $i, Union: $i] : (((union(Set1, Set2, Union) | member(g(Set1, Set2, Union), Set1)) | member(g(Set1, Set2, Union), Set2)) | member(g(Set1, Set2, Union), Union))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax','union_axiom1')).
% 0.40/0.57 tff(216,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.40/0.57 tff(217,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.40/0.57 tff(218,plain,(
% 0.40/0.57 ![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(skolemize,[status(sab)],[217])).
% 0.40/0.57 tff(219,plain,
% 0.40/0.57 (![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.40/0.57 tff(220,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | (union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa))) <=> ((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(221,plain,
% 0.40/0.57 ((member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa) | union(cDa, cDb, cD_aIb)) <=> (union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(222,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | (member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa) | union(cDa, cDb, cD_aIb))) <=> ((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | (union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa)))),
% 0.40/0.57 inference(monotonicity,[status(thm)],[221])).
% 0.40/0.57 tff(223,plain,
% 0.40/0.57 (((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | (member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa) | union(cDa, cDb, cD_aIb))) <=> ((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa))),
% 0.40/0.57 inference(transitivity,[status(thm)],[222, 220])).
% 0.40/0.57 tff(224,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | (member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa) | union(cDa, cDb, cD_aIb))),
% 0.40/0.57 inference(quant_inst,[status(thm)],[])).
% 0.40/0.57 tff(225,plain,
% 0.40/0.57 ((~![Set1: $i, Set2: $i, Union: $i] : (member(g(Set1, Set2, Union), Union) | member(g(Set1, Set2, Union), Set2) | member(g(Set1, Set2, Union), Set1) | union(Set1, Set2, Union))) | union(cDa, cDb, cD_aIb) | member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.40/0.58 tff(226,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[225, 219, 61])).
% 0.40/0.58 tff(227,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), cD_aIb)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[226, 209, 195])).
% 0.40/0.58 tff(228,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(229,plain,
% 0.40/0.58 ((member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb))) <=> ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(230,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[229])).
% 0.40/0.58 tff(231,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.58 inference(transitivity,[status(thm)],[230, 228])).
% 0.40/0.58 tff(232,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), c) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(233,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : (member(Element, Set1) | (~member(Element, Difference)) | (~difference(Set1, Set2, Difference)))) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~difference(c, aIb, cD_aIb)) | member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.40/0.58 tff(234,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[233, 125, 22, 227, 196])).
% 0.40/0.58 tff(235,plain,(member(g(cDa, cDb, cD_aIb), c) | member(g(cDa, cDb, cD_aIb), cDb)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(236,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), c)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[235, 195])).
% 0.40/0.58 tff(237,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(238,plain,
% 0.40/0.58 (((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb))) <=> (member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(239,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[238])).
% 0.40/0.58 tff(240,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.58 inference(transitivity,[status(thm)],[239, 237])).
% 0.40/0.58 tff(241,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(242,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDb) | (~difference(c, b, cDb)) | (~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), b)),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.40/0.58 tff(243,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), b)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[242, 163, 115, 195, 236])).
% 0.40/0.58 tff(244,assumption,(~member(g(cDa, cDb, cD_aIb), aIb)), introduced(assumption)).
% 0.40/0.58 tff(245,plain,
% 0.40/0.58 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : refl((member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))) <=> (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(246,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[245])).
% 0.40/0.58 tff(247,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(248,plain,
% 0.40/0.58 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) <=> ((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) <=> (((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection))) | (~member(Element, Set1))))), rewrite((((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection))) | (~member(Element, Set1))) <=> ((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) <=> ((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))))), (((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) | member(Element, Intersection)) <=> (((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))) | member(Element, Intersection)))), rewrite((((~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1))) | member(Element, Intersection)) <=> (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))), (((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) | member(Element, Intersection)) <=> (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(249,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) | member(Element, Intersection)) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[248])).
% 0.40/0.58 tff(250,axiom,(![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Set2))) | (~member(Element, Set1))) | member(Element, Intersection))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax','member_of_both_is_member_of_intersection')).
% 0.40/0.58 tff(251,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.40/0.58 tff(252,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.40/0.58 tff(253,plain,(
% 0.40/0.58 ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(skolemize,[status(sab)],[252])).
% 0.40/0.58 tff(254,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.40/0.58 tff(255,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | ((~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(256,plain,
% 0.40/0.58 ((member(g(cDa, cDb, cD_aIb), aIb) | (~member(g(cDa, cDb, cD_aIb), b)) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), a))) <=> ((~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(257,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (member(g(cDa, cDb, cD_aIb), aIb) | (~member(g(cDa, cDb, cD_aIb), b)) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), a)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | ((~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[256])).
% 0.40/0.58 tff(258,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (member(g(cDa, cDb, cD_aIb), aIb) | (~member(g(cDa, cDb, cD_aIb), b)) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), a)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[257, 255])).
% 0.40/0.58 tff(259,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (member(g(cDa, cDb, cD_aIb), aIb) | (~member(g(cDa, cDb, cD_aIb), b)) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), a)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(260,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Intersection) | (~member(Element, Set2)) | (~intersection(Set1, Set2, Intersection)) | (~member(Element, Set1)))) | (~member(g(cDa, cDb, cD_aIb), a)) | member(g(cDa, cDb, cD_aIb), aIb) | (~intersection(a, b, aIb)) | (~member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.40/0.58 tff(261,plain,
% 0.40/0.58 ((~member(g(cDa, cDb, cD_aIb), a)) | (~member(g(cDa, cDb, cD_aIb), b))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[260, 254, 175, 244])).
% 0.40/0.58 tff(262,plain,
% 0.40/0.58 (~member(g(cDa, cDb, cD_aIb), a)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[261, 243])).
% 0.40/0.58 tff(263,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), cD_aIb)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[169, 163, 22, 236, 244])).
% 0.40/0.58 tff(264,plain,
% 0.40/0.58 (^[Set1: $i, Set2: $i, Union: $i] : refl((union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(265,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[264])).
% 0.40/0.58 tff(266,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(267,plain,
% 0.40/0.58 (^[Set1: $i, Set2: $i, Union: $i] : trans(monotonicity(rewrite(((~member(g(Set1, Set2, Union), Set1)) | (~member(g(Set1, Set2, Union), Union))) <=> ((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))), ((((~member(g(Set1, Set2, Union), Set1)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> (((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))) | union(Set1, Set2, Union)))), rewrite((((~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1))) | union(Set1, Set2, Union)) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))), ((((~member(g(Set1, Set2, Union), Set1)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(268,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (((~member(g(Set1, Set2, Union), Set1)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union)) <=> ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(quant_intro,[status(thm)],[267])).
% 0.40/0.58 tff(269,axiom,(![Set1: $i, Set2: $i, Union: $i] : (((~member(g(Set1, Set2, Union), Set1)) | (~member(g(Set1, Set2, Union), Union))) | union(Set1, Set2, Union))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax','union_axiom2')).
% 0.40/0.58 tff(270,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.40/0.58 tff(271,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.40/0.58 tff(272,plain,(
% 0.40/0.58 ![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(skolemize,[status(sab)],[271])).
% 0.40/0.58 tff(273,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[272, 265])).
% 0.40/0.58 tff(274,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))) | (union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDa)))) <=> ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))) | union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDa)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(275,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))) | (union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDa)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(276,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Union: $i] : (union(Set1, Set2, Union) | (~member(g(Set1, Set2, Union), Union)) | (~member(g(Set1, Set2, Union), Set1)))) | union(cDa, cDb, cD_aIb) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDa))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.40/0.58 tff(277,plain,
% 0.40/0.58 ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), cDa))),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[276, 273, 61])).
% 0.40/0.58 tff(278,plain,
% 0.40/0.58 (~member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[277, 263])).
% 0.40/0.58 tff(279,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(280,plain,
% 0.40/0.58 (((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), a) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa))) <=> (member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.58 inference(rewrite,[status(thm)],[])).
% 0.40/0.58 tff(281,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), a) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | (member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c))))),
% 0.40/0.58 inference(monotonicity,[status(thm)],[280])).
% 0.40/0.58 tff(282,plain,
% 0.40/0.58 (((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), a) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c)))),
% 0.40/0.58 inference(transitivity,[status(thm)],[281, 279])).
% 0.40/0.58 tff(283,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | ((~member(g(cDa, cDb, cD_aIb), c)) | member(g(cDa, cDb, cD_aIb), a) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)))),
% 0.40/0.58 inference(quant_inst,[status(thm)],[])).
% 0.40/0.58 tff(284,plain,
% 0.40/0.58 ((~![Set1: $i, Set2: $i, Difference: $i, Element: $i] : ((~member(Element, Set1)) | member(Element, Set2) | member(Element, Difference) | (~difference(Set1, Set2, Difference)))) | member(g(cDa, cDb, cD_aIb), cDa) | (~difference(c, a, cDa)) | member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), c))),
% 0.40/0.58 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.40/0.58 tff(285,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), cDa) | member(g(cDa, cDb, cD_aIb), a)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[284, 163, 200, 236])).
% 0.40/0.58 tff(286,plain,
% 0.40/0.58 ($false),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[285, 278, 262])).
% 0.40/0.58 tff(287,plain,(member(g(cDa, cDb, cD_aIb), cDb) | member(g(cDa, cDb, cD_aIb), aIb)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.58 tff(288,plain,
% 0.40/0.58 (member(g(cDa, cDb, cD_aIb), aIb)),
% 0.40/0.58 inference(unit_resolution,[status(thm)],[287, 194])).
% 0.40/0.58 tff(289,assumption,(~member(g(cDa, cDb, cD_aIb), a)), introduced(assumption)).
% 0.40/0.58 tff(290,plain,
% 0.40/0.58 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : refl((member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))))),
% 0.40/0.58 inference(bind,[status(th)],[])).
% 0.40/0.58 tff(291,plain,
% 0.40/0.58 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[290])).
% 0.40/0.59 tff(292,plain,
% 0.40/0.59 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(293,plain,
% 0.40/0.59 (^[Set1: $i, Set2: $i, Element: $i, Intersection: $i] : trans(monotonicity(rewrite(((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) <=> ((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set1)) <=> (((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) | member(Element, Set1)))), rewrite((((~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection))) | member(Element, Set1)) <=> (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))), ((((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set1)) <=> (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))))),
% 0.40/0.59 inference(bind,[status(th)],[])).
% 0.40/0.59 tff(294,plain,
% 0.40/0.59 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set1)) <=> ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(quant_intro,[status(thm)],[293])).
% 0.40/0.59 tff(295,axiom,(![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (((~intersection(Set1, Set2, Intersection)) | (~member(Element, Intersection))) | member(Element, Set1))), file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax','member_of_intersection_is_member_of_set1')).
% 0.40/0.59 tff(296,plain,
% 0.40/0.59 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.40/0.59 tff(297,plain,
% 0.40/0.59 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[296, 292])).
% 0.40/0.59 tff(298,plain,(
% 0.40/0.59 ![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(skolemize,[status(sab)],[297])).
% 0.40/0.59 tff(299,plain,
% 0.40/0.59 (![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[298, 291])).
% 0.40/0.59 tff(300,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(301,plain,
% 0.40/0.59 ((member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb))) <=> ((~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(302,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | ((~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[301])).
% 0.40/0.59 tff(303,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))) <=> ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[302, 300])).
% 0.40/0.59 tff(304,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (member(g(cDa, cDb, cD_aIb), a) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~intersection(a, b, aIb)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(305,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, Element: $i, Intersection: $i] : (member(Element, Set1) | (~member(Element, Intersection)) | (~intersection(Set1, Set2, Intersection)))) | (~member(g(cDa, cDb, cD_aIb), aIb)) | member(g(cDa, cDb, cD_aIb), a) | (~intersection(a, b, aIb))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.40/0.59 tff(306,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[305, 299, 175, 289, 288])).
% 0.40/0.59 tff(307,plain,(member(g(cDa, cDb, cD_aIb), a)), inference(lemma,lemma(discharge,[]))).
% 0.40/0.59 tff(308,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(309,plain,
% 0.40/0.59 (((~member(g(cDa, cDb, cD_aIb), a)) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa))) <=> ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(310,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), a)) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa))))),
% 0.40/0.59 inference(monotonicity,[status(thm)],[309])).
% 0.40/0.59 tff(311,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), a)) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa)))),
% 0.40/0.59 inference(transitivity,[status(thm)],[310, 308])).
% 0.40/0.59 tff(312,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), a)) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~difference(c, a, cDa)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(313,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cDa)) | (~member(g(cDa, cDb, cD_aIb), a)) | (~difference(c, a, cDa))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.40/0.59 tff(314,plain,
% 0.40/0.59 (~member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[313, 32, 200, 307])).
% 0.40/0.59 tff(315,plain,
% 0.40/0.59 (member(g(cDa, cDb, cD_aIb), cD_aIb) | member(g(cDa, cDb, cD_aIb), cDa)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[226, 194])).
% 0.40/0.59 tff(316,plain,
% 0.40/0.59 (member(g(cDa, cDb, cD_aIb), cD_aIb)),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.40/0.59 tff(317,plain,
% 0.40/0.59 (((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~difference(aIb, cD_aIb, aIb)))) <=> ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~difference(aIb, cD_aIb, aIb)))),
% 0.40/0.59 inference(rewrite,[status(thm)],[])).
% 0.40/0.59 tff(318,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | ((~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~difference(aIb, cD_aIb, aIb)))),
% 0.40/0.59 inference(quant_inst,[status(thm)],[])).
% 0.40/0.59 tff(319,plain,
% 0.40/0.59 ((~![Set1: $i, Set2: $i, A_set: $i, Element: $i] : ((~member(Element, Set1)) | (~member(Element, Set2)) | (~difference(A_set, Set1, Set2)))) | (~member(g(cDa, cDb, cD_aIb), cD_aIb)) | (~member(g(cDa, cDb, cD_aIb), aIb)) | (~difference(aIb, cD_aIb, aIb))),
% 0.40/0.59 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.40/0.59 tff(320,plain,
% 0.40/0.59 ($false),
% 0.40/0.59 inference(unit_resolution,[status(thm)],[319, 32, 316, 288, 57])).
% 0.40/0.59 % SZS output end Proof
% 0.40/0.59 % E exiting
%------------------------------------------------------------------------------