%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET787-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SET787-1 : TPTP v9.0.0. Released v2.7.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n016.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 05:43:17 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.24/0.41 % SZS status Unsatisfiable
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(member_type, type, (
% 0.24/0.41 member: ( $i * $i ) > $o)).
% 0.24/0.41 tff(unionE_sk1_type, type, (
% 0.24/0.41 unionE_sk1: ( $i * $i ) > $i)).
% 0.24/0.41 tff(cons_type, type, (
% 0.24/0.41 cons: ( $i * $i ) > $i)).
% 0.24/0.41 tff(eptset_type, type, (
% 0.24/0.41 eptset: $i)).
% 0.24/0.41 tff(b_type, type, (
% 0.24/0.41 b: $i)).
% 0.24/0.41 tff(a_type, type, (
% 0.24/0.41 a: $i)).
% 0.24/0.41 tff(sk2_type, type, (
% 0.24/0.41 sk2: $i)).
% 0.24/0.41 tff(un_type, type, (
% 0.24/0.41 un: ( $i * $i ) > $i)).
% 0.24/0.41 tff(union_type, type, (
% 0.24/0.41 union: $i > $i)).
% 0.24/0.41 tff(1,assumption,(member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset)), introduced(assumption)).
% 0.24/0.41 tff(2,plain,
% 0.24/0.41 (^[X: $i] : refl((~member(X, eptset)) <=> (~member(X, eptset)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 (![X: $i] : (~member(X, eptset)) <=> ![X: $i] : (~member(X, eptset))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.24/0.41 tff(4,plain,
% 0.24/0.41 (![X: $i] : (~member(X, eptset)) <=> ![X: $i] : (~member(X, eptset))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(5,axiom,(![X: $i] : (~member(X, eptset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.24/0.41 tff(6,plain,
% 0.24/0.41 (![X: $i] : (~member(X, eptset))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.24/0.41 tff(7,plain,(
% 0.24/0.41 ![X: $i] : (~member(X, eptset))),
% 0.24/0.41 inference(skolemize,[status(sab)],[6])).
% 0.24/0.41 tff(8,plain,
% 0.24/0.41 (![X: $i] : (~member(X, eptset))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.24/0.41 tff(9,plain,
% 0.24/0.41 ((~![X: $i] : (~member(X, eptset))) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(10,plain,
% 0.24/0.41 ($false),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.24/0.41 tff(11,plain,(~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.41 tff(12,assumption,(unionE_sk1(sk2, cons(a, cons(b, eptset))) = b), introduced(assumption)).
% 0.24/0.41 tff(13,plain,
% 0.24/0.41 (member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))) <=> member(sk2, b)),
% 0.24/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.24/0.41 tff(14,plain,
% 0.24/0.41 (member(sk2, b) <=> member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(symmetry,[status(thm)],[13])).
% 0.24/0.41 tff(15,plain,
% 0.24/0.41 ((~member(sk2, b)) <=> (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))))),
% 0.24/0.41 inference(monotonicity,[status(thm)],[14])).
% 0.24/0.41 tff(16,plain,
% 0.24/0.41 ((~member(sk2, un(a, b))) <=> (~member(sk2, un(a, b)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(17,axiom,(~member(sk2, un(a, b))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','un_eq_Union_2_c2')).
% 0.24/0.41 tff(18,plain,
% 0.24/0.41 (~member(sk2, un(a, b))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.24/0.41 tff(19,plain,
% 0.24/0.41 (^[B: $i, A: $i, C: $i] : refl(((~member(C, B)) | member(C, un(A, B))) <=> ((~member(C, B)) | member(C, un(A, B))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(20,plain,
% 0.24/0.41 (![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)))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.24/0.41 tff(21,plain,
% 0.24/0.41 (![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)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(22,axiom,(![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unI2')).
% 0.24/0.41 tff(23,plain,
% 0.24/0.41 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.24/0.41 tff(24,plain,(
% 0.24/0.41 ![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 0.24/0.41 inference(skolemize,[status(sab)],[23])).
% 0.24/0.41 tff(25,plain,
% 0.24/0.41 (![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.24/0.41 tff(26,plain,
% 0.24/0.41 (((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | ((~member(sk2, b)) | member(sk2, un(a, b)))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | (~member(sk2, b)) | member(sk2, un(a, b)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(27,plain,
% 0.24/0.41 ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | ((~member(sk2, b)) | member(sk2, un(a, b)))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(28,plain,
% 0.24/0.41 ((~![B: $i, A: $i, C: $i] : ((~member(C, B)) | member(C, un(A, B)))) | (~member(sk2, b)) | member(sk2, un(a, b))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.24/0.41 tff(29,plain,
% 0.24/0.41 (~member(sk2, b)),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 0.24/0.41 tff(30,plain,
% 0.24/0.41 (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[29, 15])).
% 0.24/0.41 tff(31,plain,
% 0.24/0.41 (member(sk2, union(cons(a, cons(b, eptset)))) <=> member(sk2, union(cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(32,axiom,(member(sk2, union(cons(a, cons(b, eptset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','un_eq_Union_2_c1')).
% 0.24/0.41 tff(33,plain,
% 0.24/0.41 (member(sk2, union(cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.24/0.41 tff(34,plain,
% 0.24/0.41 (^[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))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(35,plain,
% 0.24/0.41 (![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)))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.24/0.41 tff(36,plain,
% 0.24/0.41 (![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)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(37,axiom,(![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.24/0.41 tff(38,plain,
% 0.24/0.41 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.24/0.41 tff(39,plain,(
% 0.24/0.41 ![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 0.24/0.41 inference(skolemize,[status(sab)],[38])).
% 0.24/0.41 tff(40,plain,
% 0.24/0.41 (![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.24/0.41 tff(41,plain,
% 0.24/0.41 (((~![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)))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(42,plain,
% 0.24/0.41 ((~![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)))))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(43,plain,
% 0.24/0.41 ((~![V: $i, U: $i] : ((~member(U, union(V))) | member(U, unionE_sk1(U, V)))) | (~member(sk2, union(cons(a, cons(b, eptset))))) | member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.24/0.41 tff(44,plain,
% 0.24/0.41 (member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.24/0.41 tff(45,plain,
% 0.24/0.41 ($false),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[44, 30])).
% 0.24/0.41 tff(46,plain,(~(unionE_sk1(sk2, cons(a, cons(b, eptset))) = b)), inference(lemma,lemma(discharge,[]))).
% 0.24/0.41 tff(47,assumption,(member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset))), introduced(assumption)).
% 0.24/0.41 tff(48,plain,
% 0.24/0.41 (^[W: $i, V: $i, U: $i] : refl((member(U, W) | (U = V) | (~member(U, cons(V, W)))) <=> (member(U, W) | (U = V) | (~member(U, cons(V, W)))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(49,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W)))) <=> ![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.24/0.41 tff(50,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W)))) <=> ![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(51,plain,
% 0.24/0.41 (^[W: $i, V: $i, U: $i] : rewrite((((~member(U, cons(V, W))) | (U = V)) | member(U, W)) <=> (member(U, W) | (U = V) | (~member(U, cons(V, W)))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(52,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (((~member(U, cons(V, W))) | (U = V)) | member(U, W)) <=> ![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.24/0.41 tff(53,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')).
% 0.24/0.41 tff(54,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.24/0.41 tff(55,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.24/0.41 tff(56,plain,(
% 0.24/0.41 ![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(skolemize,[status(sab)],[55])).
% 0.24/0.41 tff(57,plain,
% 0.24/0.41 (![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.24/0.41 tff(58,plain,
% 0.24/0.41 (((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = b) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset))))) <=> ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = b) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(59,plain,
% 0.24/0.41 ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = b) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset))))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(60,plain,
% 0.24/0.41 ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), eptset) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = b) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.24/0.41 tff(61,plain,
% 0.24/0.41 ($false),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[60, 57, 47, 46, 11])).
% 0.24/0.41 tff(62,plain,(~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.41 tff(63,plain,
% 0.24/0.41 (^[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)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(64,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.24/0.41 tff(65,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(66,axiom,(![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.24/0.41 tff(67,plain,
% 0.24/0.41 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.24/0.41 tff(68,plain,(
% 0.24/0.41 ![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 0.24/0.41 inference(skolemize,[status(sab)],[67])).
% 0.24/0.41 tff(69,plain,
% 0.24/0.41 (![V: $i, U: $i] : ((~member(U, union(V))) | member(unionE_sk1(U, V), V))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.24/0.41 tff(70,plain,
% 0.24/0.41 (((~![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))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(71,plain,
% 0.24/0.42 ((~![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))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(72,plain,
% 0.24/0.42 ((~![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)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.24/0.42 tff(73,plain,
% 0.24/0.42 (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[72, 69, 33])).
% 0.24/0.42 tff(74,plain,
% 0.24/0.42 (((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))) <=> ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(75,plain,
% 0.24/0.42 ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset)))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(76,plain,
% 0.24/0.42 ((~![W: $i, V: $i, U: $i] : (member(U, W) | (U = V) | (~member(U, cons(V, W))))) | member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a) | (~member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(a, cons(b, eptset))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.24/0.42 tff(77,plain,
% 0.24/0.42 (member(unionE_sk1(sk2, cons(a, cons(b, eptset))), cons(b, eptset)) | (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a)),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[76, 57, 73])).
% 0.24/0.42 tff(78,plain,
% 0.24/0.42 (unionE_sk1(sk2, cons(a, cons(b, eptset))) = a),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[77, 62])).
% 0.24/0.42 tff(79,plain,
% 0.24/0.42 (member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))) <=> member(sk2, a)),
% 0.24/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.24/0.42 tff(80,plain,
% 0.24/0.42 (member(sk2, a) <=> member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.42 inference(symmetry,[status(thm)],[79])).
% 0.24/0.42 tff(81,plain,
% 0.24/0.42 ((~member(sk2, a)) <=> (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset)))))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[80])).
% 0.24/0.42 tff(82,plain,
% 0.24/0.42 (^[B: $i, A: $i, C: $i] : refl(((~member(C, A)) | member(C, un(A, B))) <=> ((~member(C, A)) | member(C, un(A, B))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(83,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.24/0.42 tff(84,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(85,axiom,(![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unI1')).
% 0.24/0.42 tff(86,plain,
% 0.24/0.42 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.24/0.42 tff(87,plain,(
% 0.24/0.42 ![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 0.24/0.42 inference(skolemize,[status(sab)],[86])).
% 0.24/0.42 tff(88,plain,
% 0.24/0.42 (![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.24/0.42 tff(89,plain,
% 0.24/0.42 (((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | ((~member(sk2, a)) | member(sk2, un(a, b)))) <=> ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | (~member(sk2, a)) | member(sk2, un(a, b)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(90,plain,
% 0.24/0.42 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | ((~member(sk2, a)) | member(sk2, un(a, b)))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(91,plain,
% 0.24/0.42 ((~![B: $i, A: $i, C: $i] : ((~member(C, A)) | member(C, un(A, B)))) | (~member(sk2, a)) | member(sk2, un(a, b))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.24/0.42 tff(92,plain,
% 0.24/0.42 (~member(sk2, a)),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[91, 88, 18])).
% 0.24/0.42 tff(93,plain,
% 0.24/0.42 (~member(sk2, unionE_sk1(sk2, cons(a, cons(b, eptset))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[92, 81])).
% 0.24/0.42 tff(94,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[44, 93])).
% 0.24/0.42 % SZS output end Proof
% 0.24/0.42 % E exiting
%------------------------------------------------------------------------------