%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET787-2 : TPTP v9.0.0. Released v2.7.0.
% 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 05:26:21 AM UTC 2025
% Result : Unsatisfiable 118.92s 119.08s
% Output : Proof 119.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET787-2 : TPTP v9.0.0. Released v2.7.0.
% 0.10/0.12 % 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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:42:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 118.92/119.08 % SZS status Unsatisfiable
% 118.92/119.08 % SZS output start Proof
% 118.92/119.08 tff(member_type, type, (
% 118.92/119.08 member: ( $i * $i ) > $o)).
% 118.92/119.08 tff(unionE_sk1_type, type, (
% 118.92/119.08 unionE_sk1: ( $i * $i ) > $i)).
% 118.92/119.08 tff(cons_type, type, (
% 118.92/119.08 cons: ( $i * $i ) > $i)).
% 118.92/119.08 tff(eptset_type, type, (
% 118.92/119.08 eptset: $i)).
% 118.92/119.08 tff(b_type, type, (
% 118.92/119.08 b: $i)).
% 118.92/119.08 tff(a_type, type, (
% 118.92/119.08 a: $i)).
% 118.92/119.08 tff(powI_sk1_type, type, (
% 118.92/119.08 powI_sk1: ( $i * $i ) > $i)).
% 118.92/119.08 tff(un_type, type, (
% 118.92/119.08 un: ( $i * $i ) > $i)).
% 118.92/119.08 tff(subsetI_sk1_type, type, (
% 118.92/119.08 subsetI_sk1: ( $i * $i ) > $i)).
% 118.92/119.08 tff(pow_type, type, (
% 118.92/119.08 pow: $i > $i)).
% 118.92/119.08 tff(subset_type, type, (
% 118.92/119.08 subset: ( $i * $i ) > $o)).
% 118.92/119.08 tff(sk2_type, type, (
% 118.92/119.08 sk2: $i)).
% 118.92/119.08 tff(union_type, type, (
% 118.92/119.08 union: $i > $i)).
% 118.92/119.08 tff(1,assumption,(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b), introduced(assumption)).
% 118.92/119.08 tff(2,plain,
% 118.92/119.08 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))) <=> member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)),
% 118.92/119.08 inference(monotonicity,[status(thm)],[1])).
% 118.92/119.08 tff(3,plain,
% 118.92/119.08 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b) <=> member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(symmetry,[status(thm)],[2])).
% 118.92/119.08 tff(4,plain,
% 118.92/119.08 ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)) <=> (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))))),
% 118.92/119.08 inference(monotonicity,[status(thm)],[3])).
% 118.92/119.08 tff(5,plain,
% 118.92/119.08 (member(sk2, union(cons(a, cons(b, eptset)))) <=> member(sk2, union(cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(6,axiom,(member(sk2, union(cons(a, cons(b, eptset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','un_eq_Union_2_c1')).
% 118.92/119.08 tff(7,plain,
% 118.92/119.08 (member(sk2, union(cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[6, 5])).
% 118.92/119.08 tff(8,plain,
% 118.92/119.08 (^[V: $i, U: $i] : refl(((~member(U, union(V))) | member(U, unionE_sk1(U, V))) <=> ((~member(U, union(V))) | member(U, unionE_sk1(U, V))))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(9,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V))) <=> ![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[8])).
% 118.92/119.08 tff(10,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V))) <=> ![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(11,axiom,(![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 118.92/119.08 tff(12,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[11, 10])).
% 118.92/119.08 tff(13,plain,(
% 118.92/119.08 ![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 118.92/119.08 inference(skolemize,[status(sab)],[12])).
% 118.92/119.08 tff(14,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[13, 9])).
% 118.92/119.08 tff(15,plain,
% 118.92/119.08 (((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | ((~member(sk2, union(cons(a, cons(b, eptset))))) | member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))))) <=> ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | (~member(sk2, union(cons(a, cons(b, eptset))))) | member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(16,plain,
% 118.92/119.08 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | ((~member(sk2, union(cons(a, cons(b, eptset))))) | member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))))),
% 118.92/119.08 inference(quant_inst,[status(thm)],[])).
% 118.92/119.08 tff(17,plain,
% 118.92/119.08 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | (~member(sk2, union(cons(a, cons(b, eptset))))) | member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[16, 15])).
% 118.92/119.08 tff(18,plain,
% 118.92/119.08 (member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(unit_resolution,[status(thm)],[17, 14, 7])).
% 118.92/119.08 tff(19,plain,
% 118.92/119.08 ((~member(sk2, un(a, b))) <=> (~member(sk2, un(a, b)))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(20,axiom,(~member(sk2, un(a, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','un_eq_Union_2_c2')).
% 118.92/119.08 tff(21,plain,
% 118.92/119.08 (~member(sk2, un(a, b))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[20, 19])).
% 118.92/119.08 tff(22,plain,
% 118.92/119.08 (^[W: $i, V: $i, U: $i] : refl((member(W, V) | (~member(W, U)) | (~member(U, pow(V)))) <=> (member(W, V) | (~member(W, U)) | (~member(U, pow(V)))))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(23,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V)))) <=> ![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[22])).
% 118.92/119.08 tff(24,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V)))) <=> ![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(25,plain,
% 118.92/119.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(rewrite(((~member(U, pow(V))) | (~member(W, U))) <=> ((~member(W, U)) | (~member(U, pow(V))))), ((((~member(U, pow(V))) | (~member(W, U))) | member(W, V)) <=> (((~member(W, U)) | (~member(U, pow(V)))) | member(W, V)))), rewrite((((~member(W, U)) | (~member(U, pow(V)))) | member(W, V)) <=> (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))), ((((~member(U, pow(V))) | (~member(W, U))) | member(W, V)) <=> (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(26,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (((~member(U, pow(V))) | (~member(W, U))) | member(W, V)) <=> ![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[25])).
% 118.92/119.08 tff(27,axiom,(![W: $i, V: $i, U: $i] : (((~member(U, pow(V))) | (~member(W, U))) | member(W, V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 118.92/119.08 tff(28,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[27, 26])).
% 118.92/119.08 tff(29,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[28, 24])).
% 118.92/119.08 tff(30,plain,(
% 118.92/119.08 ![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(skolemize,[status(sab)],[29])).
% 118.92/119.08 tff(31,plain,
% 118.92/119.08 (![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[30, 23])).
% 118.92/119.08 tff(32,plain,
% 118.92/119.08 (((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | (member(sk2, un(a, b)) | (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b)))))) <=> ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | member(sk2, un(a, b)) | (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b)))))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(33,plain,
% 118.92/119.08 ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | (member(sk2, un(a, b)) | (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b)))))),
% 118.92/119.08 inference(quant_inst,[status(thm)],[])).
% 118.92/119.08 tff(34,plain,
% 118.92/119.08 ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | member(sk2, un(a, b)) | (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[33, 32])).
% 118.92/119.08 tff(35,plain,
% 118.92/119.08 (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b)))),
% 118.92/119.08 inference(unit_resolution,[status(thm)],[34, 31, 21, 18])).
% 118.92/119.08 tff(36,plain,
% 118.92/119.08 (^[V: $i, U: $i] : refl(((~member(U, union(V))) | member(unionE_sk1(U, V), V)) <=> ((~member(U, union(V))) | member(unionE_sk1(U, V), V)))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(37,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V)) <=> ![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[36])).
% 118.92/119.08 tff(38,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V)) <=> ![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(39,axiom,(![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 118.92/119.08 tff(40,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[39, 38])).
% 118.92/119.08 tff(41,plain,(
% 118.92/119.08 ![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 118.92/119.08 inference(skolemize,[status(sab)],[40])).
% 118.92/119.08 tff(42,plain,
% 118.92/119.08 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[41, 37])).
% 118.92/119.08 tff(43,plain,
% 118.92/119.08 (((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | ((~member(sk2, union(cons(a, cons(b, eptset))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))) <=> ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | (~member(sk2, union(cons(a, cons(b, eptset))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(44,plain,
% 118.92/119.08 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | ((~member(sk2, union(cons(a, cons(b, eptset))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 118.92/119.08 inference(quant_inst,[status(thm)],[])).
% 118.92/119.08 tff(45,plain,
% 118.92/119.08 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | (~member(sk2, union(cons(a, cons(b, eptset))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))),
% 118.92/119.08 inference(modus_ponens,[status(thm)],[44, 43])).
% 118.92/119.08 tff(46,plain,
% 118.92/119.08 (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))),
% 118.92/119.08 inference(unit_resolution,[status(thm)],[45, 42, 7])).
% 118.92/119.08 tff(47,plain,
% 118.92/119.08 (^[B: $i, A: $i, C: $i] : refl(((~member(C, A)) | member(C, B) | (~subset(A, B))) <=> ((~member(C, A)) | member(C, B) | (~subset(A, B))))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(48,plain,
% 118.92/119.08 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[47])).
% 118.92/119.08 tff(49,plain,
% 118.92/119.08 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.08 inference(rewrite,[status(thm)],[])).
% 118.92/119.08 tff(50,plain,
% 118.92/119.08 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | (~member(C, A))) <=> ((~member(C, A)) | (~subset(A, B)))), ((((~subset(A, B)) | (~member(C, A))) | member(C, B)) <=> (((~member(C, A)) | (~subset(A, B))) | member(C, B)))), rewrite((((~member(C, A)) | (~subset(A, B))) | member(C, B)) <=> ((~member(C, A)) | member(C, B) | (~subset(A, B)))), ((((~subset(A, B)) | (~member(C, A))) | member(C, B)) <=> ((~member(C, A)) | member(C, B) | (~subset(A, B)))))),
% 118.92/119.08 inference(bind,[status(th)],[])).
% 118.92/119.08 tff(51,plain,
% 118.92/119.08 (![B: $i, A: $i, C: $i] : (((~subset(A, B)) | (~member(C, A))) | member(C, B)) <=> ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.08 inference(quant_intro,[status(thm)],[50])).
% 118.92/119.09 tff(52,axiom,(![B: $i, A: $i, C: $i] : (((~subset(A, B)) | (~member(C, A))) | member(C, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subsetD')).
% 118.92/119.09 tff(53,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[52, 51])).
% 118.92/119.09 tff(54,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[53, 49])).
% 118.92/119.09 tff(55,plain,(
% 118.92/119.09 ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.09 inference(skolemize,[status(sab)],[54])).
% 118.92/119.09 tff(56,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[55, 48])).
% 118.92/119.09 tff(57,plain,
% 118.92/119.09 (((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(58,plain,
% 118.92/119.09 (((~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b))))) <=> (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(59,plain,
% 118.92/119.09 (((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | ((~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b))))))),
% 118.92/119.09 inference(monotonicity,[status(thm)],[58])).
% 118.92/119.09 tff(60,plain,
% 118.92/119.09 (((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | ((~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(transitivity,[status(thm)],[59, 57])).
% 118.92/119.09 tff(61,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | ((~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(62,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, B) | (~subset(A, B)))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), pow(un(a, b))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))) | (~subset(cons(a, cons(b, eptset)), pow(un(a, b))))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[61, 60])).
% 118.92/119.09 tff(63,plain,
% 118.92/119.09 (~subset(cons(a, cons(b, eptset)), pow(un(a, b)))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[62, 56, 46, 35])).
% 118.92/119.09 tff(64,plain,
% 118.92/119.09 (^[B: $i, A: $i] : refl(((~member(subsetI_sk1(A, B), B)) | subset(A, B)) <=> ((~member(subsetI_sk1(A, B), B)) | subset(A, B)))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(65,plain,
% 118.92/119.09 (![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B)) <=> ![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[64])).
% 118.92/119.09 tff(66,plain,
% 118.92/119.09 (![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B)) <=> ![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(67,axiom,(![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 118.92/119.09 tff(68,plain,
% 118.92/119.09 (![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[67, 66])).
% 118.92/119.09 tff(69,plain,(
% 118.92/119.09 ![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))),
% 118.92/119.09 inference(skolemize,[status(sab)],[68])).
% 118.92/119.09 tff(70,plain,
% 118.92/119.09 (![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[69, 65])).
% 118.92/119.09 tff(71,plain,
% 118.92/119.09 (((~![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))) | ((~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))) | subset(cons(a, cons(b, eptset)), pow(un(a, b))))) <=> ((~![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))) | (~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))) | subset(cons(a, cons(b, eptset)), pow(un(a, b))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(72,plain,
% 118.92/119.09 ((~![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))) | ((~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))) | subset(cons(a, cons(b, eptset)), pow(un(a, b))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(73,plain,
% 118.92/119.09 ((~![B: $i, A: $i] : ((~member(subsetI_sk1(A, B), B)) | subset(A, B))) | (~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))) | subset(cons(a, cons(b, eptset)), pow(un(a, b)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[72, 71])).
% 118.92/119.09 tff(74,plain,
% 118.92/119.09 (~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[73, 70, 63])).
% 118.92/119.09 tff(75,plain,
% 118.92/119.09 (^[V: $i, U: $i] : refl(((~member(powI_sk1(U, V), V)) | member(U, pow(V))) <=> ((~member(powI_sk1(U, V), V)) | member(U, pow(V))))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(76,plain,
% 118.92/119.09 (![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V))) <=> ![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[75])).
% 118.92/119.09 tff(77,plain,
% 118.92/119.09 (![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V))) <=> ![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(78,axiom,(![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 118.92/119.09 tff(79,plain,
% 118.92/119.09 (![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[78, 77])).
% 118.92/119.09 tff(80,plain,(
% 118.92/119.09 ![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))),
% 118.92/119.09 inference(skolemize,[status(sab)],[79])).
% 118.92/119.09 tff(81,plain,
% 118.92/119.09 (![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[80, 76])).
% 118.92/119.09 tff(82,plain,
% 118.92/119.09 (((~![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))) <=> ((~![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(83,plain,
% 118.92/119.09 ((~![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(84,plain,
% 118.92/119.09 ((~![V: $i, U: $i] : ((~member(powI_sk1(U, V), V)) | member(U, pow(V)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[83, 82])).
% 118.92/119.09 tff(85,plain,
% 118.92/119.09 (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[84, 81, 74])).
% 118.92/119.09 tff(86,plain,
% 118.92/119.09 (^[B: $i, A: $i, C: $i] : refl(((~member(C, B)) | member(C, un(A, B))) <=> ((~member(C, B)) | member(C, un(A, B))))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(87,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[86])).
% 118.92/119.09 tff(88,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(89,axiom,(![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unI2')).
% 118.92/119.09 tff(90,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[89, 88])).
% 118.92/119.09 tff(91,plain,(
% 118.92/119.09 ![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 118.92/119.09 inference(skolemize,[status(sab)],[90])).
% 118.92/119.09 tff(92,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[91, 87])).
% 118.92/119.09 tff(93,plain,
% 118.92/119.09 (((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(94,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(95,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[94, 93])).
% 118.92/119.09 tff(96,plain,
% 118.92/119.09 (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), b)),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[95, 92, 85])).
% 118.92/119.09 tff(97,plain,
% 118.92/119.09 (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[96, 4])).
% 118.92/119.09 tff(98,plain,
% 118.92/119.09 (^[V: $i, U: $i] : refl((member(powI_sk1(U, V), U) | member(U, pow(V))) <=> (member(powI_sk1(U, V), U) | member(U, pow(V))))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(99,plain,
% 118.92/119.09 (![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V))) <=> ![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[98])).
% 118.92/119.09 tff(100,plain,
% 118.92/119.09 (![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V))) <=> ![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(101,axiom,(![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause21')).
% 118.92/119.09 tff(102,plain,
% 118.92/119.09 (![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[101, 100])).
% 118.92/119.09 tff(103,plain,(
% 118.92/119.09 ![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))),
% 118.92/119.09 inference(skolemize,[status(sab)],[102])).
% 118.92/119.09 tff(104,plain,
% 118.92/119.09 (![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[103, 99])).
% 118.92/119.09 tff(105,plain,
% 118.92/119.09 (((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | (member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))))) <=> ((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(106,plain,
% 118.92/119.09 ((member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b)))) <=> (member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(107,plain,
% 118.92/119.09 (((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))) <=> ((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | (member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))))),
% 118.92/119.09 inference(monotonicity,[status(thm)],[106])).
% 118.92/119.09 tff(108,plain,
% 118.92/119.09 (((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))) <=> ((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(transitivity,[status(thm)],[107, 105])).
% 118.92/119.09 tff(109,plain,
% 118.92/119.09 ((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(110,plain,
% 118.92/119.09 ((~![V: $i, U: $i] : (member(powI_sk1(U, V), U) | member(U, pow(V)))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), pow(un(a, b))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[109, 108])).
% 118.92/119.09 tff(111,plain,
% 118.92/119.09 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[110, 104, 74])).
% 118.92/119.09 tff(112,plain,
% 118.92/119.09 (^[B: $i, A: $i] : refl((subset(A, B) | member(subsetI_sk1(A, B), A)) <=> (subset(A, B) | member(subsetI_sk1(A, B), A)))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(113,plain,
% 118.92/119.09 (![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A)) <=> ![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[112])).
% 118.92/119.09 tff(114,plain,
% 118.92/119.09 (![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A)) <=> ![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(115,plain,
% 118.92/119.09 (^[B: $i, A: $i] : rewrite((member(subsetI_sk1(A, B), A) | subset(A, B)) <=> (subset(A, B) | member(subsetI_sk1(A, B), A)))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(116,plain,
% 118.92/119.09 (![B: $i, A: $i] : (member(subsetI_sk1(A, B), A) | subset(A, B)) <=> ![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[115])).
% 118.92/119.09 tff(117,axiom,(![B: $i, A: $i] : (member(subsetI_sk1(A, B), A) | subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 118.92/119.09 tff(118,plain,
% 118.92/119.09 (![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[117, 116])).
% 118.92/119.09 tff(119,plain,
% 118.92/119.09 (![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[118, 114])).
% 118.92/119.09 tff(120,plain,(
% 118.92/119.09 ![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(skolemize,[status(sab)],[119])).
% 118.92/119.09 tff(121,plain,
% 118.92/119.09 (![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[120, 113])).
% 118.92/119.09 tff(122,plain,
% 118.92/119.09 (((~![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))) | (subset(cons(a, cons(b, eptset)), pow(un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset))))) <=> ((~![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))) | subset(cons(a, cons(b, eptset)), pow(un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(123,plain,
% 118.92/119.09 ((~![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))) | (subset(cons(a, cons(b, eptset)), pow(un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(124,plain,
% 118.92/119.09 ((~![B: $i, A: $i] : (subset(A, B) | member(subsetI_sk1(A, B), A))) | subset(cons(a, cons(b, eptset)), pow(un(a, b))) | member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[123, 122])).
% 118.92/119.09 tff(125,plain,
% 118.92/119.09 (member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[124, 121, 63])).
% 118.92/119.09 tff(126,plain,
% 118.92/119.09 (^[B: $i, A: $i, C: $i] : refl(((~member(B, C)) | member(A, union(C)) | (~member(A, B))) <=> ((~member(B, C)) | member(A, union(C)) | (~member(A, B))))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(127,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[126])).
% 118.92/119.09 tff(128,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(129,plain,
% 118.92/119.09 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~member(B, C)) | (~member(A, B))) <=> ((~member(B, C)) | (~member(A, B)))), ((((~member(B, C)) | (~member(A, B))) | member(A, union(C))) <=> (((~member(B, C)) | (~member(A, B))) | member(A, union(C))))), rewrite((((~member(B, C)) | (~member(A, B))) | member(A, union(C))) <=> ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))), ((((~member(B, C)) | (~member(A, B))) | member(A, union(C))) <=> ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))))),
% 118.92/119.09 inference(bind,[status(th)],[])).
% 118.92/119.09 tff(130,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : (((~member(B, C)) | (~member(A, B))) | member(A, union(C))) <=> ![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(quant_intro,[status(thm)],[129])).
% 118.92/119.09 tff(131,axiom,(![B: $i, A: $i, C: $i] : (((~member(B, C)) | (~member(A, B))) | member(A, union(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 118.92/119.09 tff(132,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[131, 130])).
% 118.92/119.09 tff(133,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[132, 128])).
% 118.92/119.09 tff(134,plain,(
% 118.92/119.09 ![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(skolemize,[status(sab)],[133])).
% 118.92/119.09 tff(135,plain,
% 118.92/119.09 (![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[134, 127])).
% 118.92/119.09 tff(136,plain,
% 118.92/119.09 (((~![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))) | ((~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))) | (~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(137,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))) | ((~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))))))),
% 118.92/119.09 inference(quant_inst,[status(thm)],[])).
% 118.92/119.09 tff(138,plain,
% 118.92/119.09 ((~![B: $i, A: $i, C: $i] : ((~member(B, C)) | member(A, union(C)) | (~member(A, B)))) | (~member(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), cons(a, cons(b, eptset)))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b)))))),
% 118.92/119.09 inference(modus_ponens,[status(thm)],[137, 136])).
% 118.92/119.09 tff(139,plain,
% 118.92/119.09 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))),
% 118.92/119.09 inference(unit_resolution,[status(thm)],[138, 135, 125, 111])).
% 118.92/119.09 tff(140,plain,
% 118.92/119.09 (((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))))) <=> ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))))),
% 118.92/119.09 inference(rewrite,[status(thm)],[])).
% 118.92/119.09 tff(141,plain,
% 118.92/119.09 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(142,plain,
% 118.92/119.10 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[141, 140])).
% 118.92/119.10 tff(143,plain,
% 118.92/119.10 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[142, 14, 139])).
% 118.92/119.10 tff(144,plain,
% 118.92/119.10 ($false),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[143, 97])).
% 118.92/119.10 tff(145,plain,(~(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b)), inference(lemma,lemma(discharge,[]))).
% 118.92/119.10 tff(146,plain,
% 118.92/119.10 (((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b)))))) <=> ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b)))))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(147,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b)))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(148,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : (member(W, V) | (~member(W, U)) | (~member(U, pow(V))))) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[147, 146])).
% 118.92/119.10 tff(149,plain,
% 118.92/119.10 (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b)))),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[148, 31, 85, 143])).
% 118.92/119.10 tff(150,plain,
% 118.92/119.10 (^[A: $i, X: $i] : refl(((~member(X, eptset)) | member(X, A)) <=> ((~member(X, eptset)) | member(X, A)))),
% 118.92/119.10 inference(bind,[status(th)],[])).
% 118.92/119.10 tff(151,plain,
% 118.92/119.10 (![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A)) <=> ![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))),
% 118.92/119.10 inference(quant_intro,[status(thm)],[150])).
% 118.92/119.10 tff(152,plain,
% 118.92/119.10 (![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A)) <=> ![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(153,axiom,(![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 118.92/119.10 tff(154,plain,
% 118.92/119.10 (![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[153, 152])).
% 118.92/119.10 tff(155,plain,(
% 118.92/119.10 ![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))),
% 118.92/119.10 inference(skolemize,[status(sab)],[154])).
% 118.92/119.10 tff(156,plain,
% 118.92/119.10 (![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[155, 151])).
% 118.92/119.10 tff(157,plain,
% 118.92/119.10 (((~![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))) | ((~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset)) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b))))) <=> ((~![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset)) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b))))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(158,plain,
% 118.92/119.10 ((~![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))) | ((~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset)) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(159,plain,
% 118.92/119.10 ((~![A: $i, X: $i] : ((~member(X, eptset)) | member(X, A))) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset)) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), pow(un(a, b)))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[158, 157])).
% 118.92/119.10 tff(160,plain,
% 118.92/119.10 (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset)),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[159, 156, 149])).
% 118.92/119.10 tff(161,assumption,(member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))), introduced(assumption)).
% 118.92/119.10 tff(162,plain,
% 118.92/119.10 (^[W: $i, V: $i, U: $i] : refl(((U = V) | member(U, W) | (~member(U, cons(V, W)))) <=> ((U = V) | member(U, W) | (~member(U, cons(V, W)))))),
% 118.92/119.10 inference(bind,[status(th)],[])).
% 118.92/119.10 tff(163,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W)))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(quant_intro,[status(thm)],[162])).
% 118.92/119.10 tff(164,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W)))) <=> ![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(165,plain,
% 118.92/119.10 (^[W: $i, V: $i, U: $i] : rewrite((((~member(U, cons(V, W))) | (U = V)) | member(U, W)) <=> ((U = V) | member(U, W) | (~member(U, cons(V, W)))))),
% 118.92/119.10 inference(bind,[status(th)],[])).
% 118.92/119.10 tff(166,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : (((~member(U, cons(V, W))) | (U = V)) | member(U, W)) <=> ![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(quant_intro,[status(thm)],[165])).
% 118.92/119.10 tff(167,axiom,(![W: $i, V: $i, U: $i] : (((~member(U, cons(V, W))) | (U = V)) | member(U, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 118.92/119.10 tff(168,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[167, 166])).
% 118.92/119.10 tff(169,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[168, 164])).
% 118.92/119.10 tff(170,plain,(
% 118.92/119.10 ![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(skolemize,[status(sab)],[169])).
% 118.92/119.10 tff(171,plain,
% 118.92/119.10 (![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[170, 163])).
% 118.92/119.10 tff(172,plain,
% 118.92/119.10 (((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | (member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(173,plain,
% 118.92/119.10 (((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset)))) <=> (member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(174,plain,
% 118.92/119.10 (((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | (member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b)))),
% 118.92/119.10 inference(monotonicity,[status(thm)],[173])).
% 118.92/119.10 tff(175,plain,
% 118.92/119.10 (((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b))),
% 118.92/119.10 inference(transitivity,[status(thm)],[174, 172])).
% 118.92/119.10 tff(176,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(177,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), eptset) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = b)),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[176, 175])).
% 118.92/119.10 tff(178,plain,
% 118.92/119.10 ($false),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[177, 171, 161, 160, 145])).
% 118.92/119.10 tff(179,plain,(~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))), inference(lemma,lemma(discharge,[]))).
% 118.92/119.10 tff(180,plain,
% 118.92/119.10 (((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))) <=> ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(181,plain,
% 118.92/119.10 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(182,plain,
% 118.92/119.10 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), union(cons(a, cons(b, eptset))))) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[181, 180])).
% 118.92/119.10 tff(183,plain,
% 118.92/119.10 (member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[182, 42, 139])).
% 118.92/119.10 tff(184,plain,
% 118.92/119.10 (((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset)) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))) <=> ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset)) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(185,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset)) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))),
% 118.92/119.10 inference(quant_inst,[status(thm)],[])).
% 118.92/119.10 tff(186,plain,
% 118.92/119.10 ((~![W: $i, V: $i, U: $i] : ((U = V) | member(U, W) | (~member(U, cons(V, W))))) | (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset)) | (~member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[185, 184])).
% 118.92/119.10 tff(187,plain,
% 118.92/119.10 ((unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a) | member(unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))), cons(b, eptset))),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[186, 171, 183])).
% 118.92/119.10 tff(188,plain,
% 118.92/119.10 (unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))) = a),
% 118.92/119.10 inference(unit_resolution,[status(thm)],[187, 179])).
% 118.92/119.10 tff(189,plain,
% 118.92/119.10 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))) <=> member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)),
% 118.92/119.10 inference(monotonicity,[status(thm)],[188])).
% 118.92/119.10 tff(190,plain,
% 118.92/119.10 (member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a) <=> member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 118.92/119.10 inference(symmetry,[status(thm)],[189])).
% 118.92/119.10 tff(191,plain,
% 118.92/119.10 ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)) <=> (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset)))))),
% 118.92/119.10 inference(monotonicity,[status(thm)],[190])).
% 118.92/119.10 tff(192,plain,
% 118.92/119.10 (^[B: $i, A: $i, C: $i] : refl(((~member(C, A)) | member(C, un(A, B))) <=> ((~member(C, A)) | member(C, un(A, B))))),
% 118.92/119.10 inference(bind,[status(th)],[])).
% 118.92/119.10 tff(193,plain,
% 118.92/119.10 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 118.92/119.10 inference(quant_intro,[status(thm)],[192])).
% 118.92/119.10 tff(194,plain,
% 118.92/119.10 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 118.92/119.10 inference(rewrite,[status(thm)],[])).
% 118.92/119.10 tff(195,axiom,(![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unI1')).
% 118.92/119.10 tff(196,plain,
% 118.92/119.10 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 118.92/119.10 inference(modus_ponens,[status(thm)],[195, 194])).
% 118.92/119.10 tff(197,plain,(
% 118.92/119.10 ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 119.16/119.32 inference(skolemize,[status(sab)],[196])).
% 119.16/119.32 tff(198,plain,
% 119.16/119.32 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 119.16/119.32 inference(modus_ponens,[status(thm)],[197, 193])).
% 119.16/119.32 tff(199,plain,
% 119.16/119.32 (((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))),
% 119.16/119.32 inference(rewrite,[status(thm)],[])).
% 119.16/119.32 tff(200,plain,
% 119.16/119.32 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | ((~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b)))),
% 119.16/119.32 inference(quant_inst,[status(thm)],[])).
% 119.16/119.32 tff(201,plain,
% 119.16/119.32 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)) | member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), un(a, b))),
% 119.16/119.32 inference(modus_ponens,[status(thm)],[200, 199])).
% 119.16/119.32 tff(202,plain,
% 119.16/119.32 (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), a)),
% 119.16/119.32 inference(unit_resolution,[status(thm)],[201, 198, 85])).
% 119.16/119.32 tff(203,plain,
% 119.16/119.32 (~member(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), unionE_sk1(powI_sk1(subsetI_sk1(cons(a, cons(b, eptset)), pow(un(a, b))), un(a, b)), cons(a, cons(b, eptset))))),
% 119.16/119.32 inference(modus_ponens,[status(thm)],[202, 191])).
% 119.16/119.32 tff(204,plain,
% 119.16/119.32 ($false),
% 119.16/119.32 inference(unit_resolution,[status(thm)],[143, 203])).
% 119.16/119.32 % SZS output end Proof
% 119.16/119.33 % E exiting
%------------------------------------------------------------------------------