%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT276-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:14:08 AM UTC 2025
% Result : Unsatisfiable 0.23s 0.41s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LAT276-2 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 19:58:26 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.23/0.41 % SZS status Unsatisfiable
% 0.23/0.41 % SZS output start Proof
% 0.23/0.41 tff(c_in_type, type, (
% 0.23/0.41 c_in: ( $i * $i * $i ) > $o)).
% 0.23/0.41 tff(tc_prod_type, type, (
% 0.23/0.41 tc_prod: ( $i * $i ) > $i)).
% 0.23/0.41 tff(t_a_type, type, (
% 0.23/0.41 t_a: $i)).
% 0.23/0.41 tff(c_Tarski_Opotype_Oorder_type, type, (
% 0.23/0.41 c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i)).
% 0.23/0.41 tff(tc_Product__Type_Ounit_type, type, (
% 0.23/0.41 tc_Product__Type_Ounit: $i)).
% 0.23/0.41 tff(v_cl_type, type, (
% 0.23/0.41 v_cl: $i)).
% 0.23/0.41 tff(c_Pair_type, type, (
% 0.23/0.41 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.23/0.41 tff(v_xa_type, type, (
% 0.23/0.41 v_xa: $i)).
% 0.23/0.41 tff(v_sko__4mP_type, type, (
% 0.23/0.41 v_sko__4mP: ( $i * $i * $i ) > $i)).
% 0.23/0.41 tff(v_r_type, type, (
% 0.23/0.41 v_r: $i)).
% 0.23/0.41 tff(v_S_type, type, (
% 0.23/0.41 v_S: $i)).
% 0.23/0.41 tff(v_A_type, type, (
% 0.23/0.41 v_A: $i)).
% 0.23/0.41 tff(c_Tarski_Opotype_Opset_type, type, (
% 0.23/0.41 c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i)).
% 0.23/0.41 tff(c_lessequals_type, type, (
% 0.23/0.41 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.23/0.41 tff(tc_set_type, type, (
% 0.23/0.41 tc_set: $i > $i)).
% 0.23/0.41 tff(c_Tarski_Olub_type, type, (
% 0.23/0.41 c_Tarski_Olub: ( $i * $i * $i ) > $i)).
% 0.23/0.41 tff(1,plain,
% 0.23/0.41 ((v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)) <=> (v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(2,axiom,(v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_Or_A_61_61_Aorder_Acl_0')).
% 0.23/0.41 tff(3,plain,
% 0.23/0.41 (v_r = c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.23/0.41 tff(4,plain,
% 0.23/0.41 (c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit) = v_r),
% 0.23/0.41 inference(symmetry,[status(thm)],[3])).
% 0.23/0.41 tff(5,plain,
% 0.23/0.41 (c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) <=> c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.23/0.41 tff(6,plain,
% 0.23/0.41 (c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.41 inference(symmetry,[status(thm)],[5])).
% 0.23/0.41 tff(7,plain,
% 0.23/0.41 ((~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[6])).
% 0.23/0.41 tff(8,plain,
% 0.23/0.41 ((v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)) <=> (v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(9,axiom,(v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_OA_A_61_61_Apset_Acl_0')).
% 0.23/0.41 tff(10,plain,
% 0.23/0.41 (v_A = c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.23/0.41 tff(11,plain,
% 0.23/0.41 (c_in(v_xa, v_A, t_a) <=> c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)),
% 0.23/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.23/0.41 tff(12,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) <=> c_in(v_xa, v_A, t_a)),
% 0.23/0.41 inference(symmetry,[status(thm)],[11])).
% 0.23/0.41 tff(13,plain,
% 0.23/0.41 (c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit) = v_A),
% 0.23/0.41 inference(symmetry,[status(thm)],[10])).
% 0.23/0.41 tff(14,plain,
% 0.23/0.41 (c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)) <=> c_lessequals(v_S, v_A, tc_set(t_a))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.23/0.41 tff(15,plain,
% 0.23/0.41 (c_lessequals(v_S, v_A, tc_set(t_a)) <=> c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))),
% 0.23/0.41 inference(symmetry,[status(thm)],[14])).
% 0.23/0.41 tff(16,plain,
% 0.23/0.41 (c_lessequals(v_S, v_A, tc_set(t_a)) <=> c_lessequals(v_S, v_A, tc_set(t_a))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(17,axiom,(c_lessequals(v_S, v_A, tc_set(t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.23/0.41 tff(18,plain,
% 0.23/0.41 (c_lessequals(v_S, v_A, tc_set(t_a))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.23/0.41 tff(19,plain,
% 0.23/0.41 (c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.23/0.41 tff(20,assumption,(~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), introduced(assumption)).
% 0.23/0.41 tff(21,plain,
% 0.23/0.41 ($false),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.23/0.41 tff(22,plain,(c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.41 tff(23,plain,
% 0.23/0.41 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(24,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.23/0.41 tff(25,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(26,plain,
% 0.23/0.41 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a))))),
% 0.23/0.41 inference(bind,[status(th)],[])).
% 0.23/0.41 tff(27,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.41 tff(28,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OsubsetD_0')).
% 0.23/0.41 tff(29,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.23/0.41 tff(30,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.23/0.41 tff(31,plain,(
% 0.23/0.41 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(skolemize,[status(sab)],[30])).
% 0.23/0.41 tff(32,plain,
% 0.23/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.23/0.41 tff(33,assumption,(~c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)), introduced(assumption)).
% 0.23/0.41 tff(34,plain,
% 0.23/0.41 ((c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(35,axiom,(c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_3')).
% 0.23/0.41 tff(36,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.23/0.41 tff(37,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.23/0.41 tff(38,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.23/0.41 tff(39,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.23/0.41 tff(40,plain,
% 0.23/0.41 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.23/0.41 tff(41,plain,
% 0.23/0.41 (c_in(v_xa, v_S, t_a)),
% 0.23/0.41 inference(unit_resolution,[status(thm)],[40, 33])).
% 0.23/0.41 tff(42,plain,
% 0.23/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(43,plain,
% 0.23/0.41 ((c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a))) <=> (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.23/0.41 inference(rewrite,[status(thm)],[])).
% 0.23/0.41 tff(44,plain,
% 0.23/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))))),
% 0.23/0.41 inference(monotonicity,[status(thm)],[43])).
% 0.23/0.41 tff(45,plain,
% 0.23/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))))),
% 0.23/0.41 inference(transitivity,[status(thm)],[44, 42])).
% 0.23/0.41 tff(46,plain,
% 0.23/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))),
% 0.23/0.41 inference(quant_inst,[status(thm)],[])).
% 0.23/0.41 tff(47,plain,
% 0.23/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | (~c_lessequals(V_A, V_B, tc_set(T_a))) | (~c_in(V_c, V_A, T_a)))) | c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a) | (~c_in(v_xa, v_S, t_a)) | (~c_lessequals(v_S, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), tc_set(t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[47, 33, 41, 32, 22])).
% 0.23/0.42 tff(49,plain,(c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(50,plain,
% 0.23/0.42 (c_in(v_xa, v_A, t_a)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[49, 12])).
% 0.23/0.42 tff(51,plain,
% 0.23/0.42 (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.23/0.42 tff(52,plain,
% 0.23/0.42 (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) <=> c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.42 inference(symmetry,[status(thm)],[51])).
% 0.23/0.42 tff(53,plain,
% 0.23/0.42 ((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) <=> c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.23/0.42 tff(55,plain,
% 0.23/0.42 (^[V_x: $i, V_S: $i] : refl((c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a))) <=> (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a))) <=> ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[55])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a))) <=> ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(58,plain,
% 0.23/0.42 (^[V_x: $i, V_S: $i] : rewrite((((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(59,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.23/0.42 tff(60,axiom,(![V_x: $i, V_S: $i] : (((~c_in(V_x, V_S, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0')).
% 0.23/0.42 tff(61,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.23/0.42 tff(62,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.23/0.42 tff(63,plain,(
% 0.23/0.42 ![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[62])).
% 0.23/0.42 tff(64,plain,
% 0.23/0.42 (![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.23/0.42 tff(65,assumption,(~c_in(v_xa, v_S, t_a)), introduced(assumption)).
% 0.23/0.42 tff(66,plain,
% 0.23/0.42 (((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)) <=> ((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(67,axiom,((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_4')).
% 0.23/0.42 tff(68,plain,
% 0.23/0.42 ((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.23/0.42 tff(69,plain,
% 0.23/0.42 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.23/0.42 tff(70,plain,
% 0.23/0.42 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[69, 53])).
% 0.23/0.42 tff(71,assumption,(~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))), introduced(assumption)).
% 0.23/0.42 tff(72,plain,
% 0.23/0.42 (c_in(v_xa, c_Tarski_Opotype_Opset(v_cl, t_a, tc_Product__Type_Ounit), t_a)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[40, 65])).
% 0.23/0.42 tff(73,plain,
% 0.23/0.42 (c_in(v_xa, v_A, t_a)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[72, 12])).
% 0.23/0.42 tff(74,plain,
% 0.23/0.42 (^[V_S: $i, V_L: $i] : refl((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(75,plain,
% 0.23/0.42 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.42 tff(76,plain,
% 0.23/0.42 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) <=> ((~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (((~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), rewrite((((~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))), (((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 (![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.23/0.43 tff(79,axiom,(![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1')).
% 0.23/0.43 tff(80,plain,
% 0.23/0.43 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.23/0.43 tff(82,plain,(
% 0.23/0.43 ![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[81])).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 (![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 (((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))))) <=> ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(85,plain,
% 0.23/0.43 ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 ((~![V_S: $i, V_L: $i] : (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(V_L, V_S, v_r), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))))) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.43 tff(87,plain,
% 0.23/0.43 (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[86, 18, 83])).
% 0.23/0.43 tff(88,plain,
% 0.23/0.43 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[87, 73, 71])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[88, 7])).
% 0.23/0.43 tff(90,plain,
% 0.23/0.43 (^[V_S: $i, V_L: $i] : refl((c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))) <=> (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[90])).
% 0.23/0.44 tff(92,plain,
% 0.23/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(93,plain,
% 0.23/0.44 (^[V_S: $i, V_L: $i] : trans(monotonicity(rewrite((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) <=> (c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))), (((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> ((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)))), rewrite(((c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))), (((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(94,plain,
% 0.23/0.44 (![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a)) <=> ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.23/0.44 tff(95,axiom,(![V_S: $i, V_L: $i] : ((((~c_in(V_L, v_A, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a)))) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a))) | c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0')).
% 0.23/0.44 tff(96,plain,
% 0.23/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.23/0.44 tff(97,plain,
% 0.23/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.23/0.44 tff(98,plain,(
% 0.23/0.44 ![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[97])).
% 0.23/0.44 tff(99,plain,
% 0.23/0.44 (![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.23/0.44 tff(100,plain,
% 0.23/0.44 (((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))) | (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)))) <=> ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))) | c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(101,plain,
% 0.23/0.44 ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))) | (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(102,plain,
% 0.23/0.44 ((~![V_S: $i, V_L: $i] : (c_in(v_sko__4mP(V_L, V_S, v_r), V_S, t_a) | c_in(c_Pair(c_Tarski_Olub(V_S, v_cl, t_a), V_L, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_L, v_A, t_a)))) | c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_A, t_a))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.23/0.44 tff(103,plain,
% 0.23/0.44 (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_A, t_a))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[102, 18, 99])).
% 0.23/0.44 tff(104,plain,
% 0.23/0.44 (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[103, 73, 71])).
% 0.23/0.44 tff(105,plain,
% 0.23/0.44 (^[V_U: $i] : refl((c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(106,plain,
% 0.23/0.44 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[105])).
% 0.23/0.44 tff(107,plain,
% 0.23/0.44 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(108,plain,
% 0.23/0.44 (^[V_U: $i] : trans(monotonicity(rewrite((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) <=> ((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> (((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)))), rewrite((((~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(109,plain,
% 0.23/0.45 (![V_U: $i] : ((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a)) <=> ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[108])).
% 0.23/0.45 tff(110,axiom,(![V_U: $i] : ((c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_U, v_S, t_a))) | c_in(v_xa, v_S, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_9')).
% 0.23/0.45 tff(111,plain,
% 0.23/0.45 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.23/0.45 tff(112,plain,
% 0.23/0.45 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.23/0.45 tff(113,plain,(
% 0.23/0.45 ![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[112])).
% 0.23/0.45 tff(114,plain,
% 0.23/0.45 (![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.23/0.45 tff(115,plain,
% 0.23/0.45 (((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(116,plain,
% 0.23/0.45 ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(117,plain,
% 0.23/0.45 ((~![V_U: $i] : (c_in(v_xa, v_S, t_a) | (~c_in(V_U, v_S, t_a)) | c_in(c_Pair(V_U, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | c_in(v_xa, v_S, t_a) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.23/0.45 tff(118,plain,
% 0.23/0.45 (c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[117, 65, 114, 104])).
% 0.23/0.45 tff(119,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[118, 89])).
% 0.23/0.45 tff(120,plain,(c_in(v_xa, v_S, t_a) | c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(121,plain,
% 0.23/0.45 (c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[120, 65])).
% 0.23/0.45 tff(122,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[121, 70])).
% 0.23/0.45 tff(123,plain,(c_in(v_xa, v_S, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(124,plain,
% 0.23/0.45 (((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | ((~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(125,plain,
% 0.23/0.45 ((c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_S, t_a))) <=> ((~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(126,plain,
% 0.23/0.45 (((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | ((~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[125])).
% 0.23/0.45 tff(127,plain,
% 0.23/0.45 (((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))) <=> ((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[126, 124])).
% 0.23/0.45 tff(128,plain,
% 0.23/0.45 ((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | (~c_in(v_xa, v_S, t_a)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(129,plain,
% 0.23/0.45 ((~![V_x: $i, V_S: $i] : (c_in(c_Pair(V_x, c_Tarski_Olub(V_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_lessequals(V_S, v_A, tc_set(t_a))) | (~c_in(V_x, V_S, t_a)))) | (~c_lessequals(v_S, v_A, tc_set(t_a))) | c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a)) | (~c_in(v_xa, v_S, t_a))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.23/0.45 tff(130,plain,
% 0.23/0.45 (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[129, 18, 123, 64])).
% 0.23/0.45 tff(131,plain,
% 0.23/0.45 (c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[130, 54])).
% 0.23/0.45 tff(132,plain,
% 0.23/0.45 (((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(133,plain,
% 0.23/0.45 (((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(134,axiom,((~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_6')).
% 0.23/0.45 tff(135,plain,
% 0.23/0.45 ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.23/0.45 tff(136,plain,
% 0.23/0.45 ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[135, 132])).
% 0.23/0.45 tff(137,plain,
% 0.23/0.45 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[136, 131])).
% 0.23/0.45 tff(138,plain,
% 0.23/0.45 (~c_in(c_Pair(c_Tarski_Olub(v_S, v_cl, t_a), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[137, 53])).
% 0.23/0.45 tff(139,plain,
% 0.23/0.45 ((~c_in(v_xa, v_A, t_a)) | (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[86, 18, 83, 138])).
% 0.23/0.45 tff(140,plain,
% 0.23/0.45 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), v_r, tc_prod(t_a, t_a))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[139, 50])).
% 0.23/0.46 tff(141,plain,
% 0.23/0.46 (~c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[140, 7])).
% 0.23/0.46 tff(142,plain,
% 0.23/0.46 (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a) | (~c_in(v_xa, v_A, t_a))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[102, 18, 99, 138])).
% 0.23/0.46 tff(143,plain,
% 0.23/0.46 (c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[142, 50])).
% 0.23/0.46 tff(144,plain,
% 0.23/0.46 (^[V_V: $i] : refl(((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(145,plain,
% 0.23/0.46 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[144])).
% 0.23/0.46 tff(146,plain,
% 0.23/0.46 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(147,plain,
% 0.23/0.46 (^[V_V: $i] : trans(monotonicity(rewrite((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) <=> ((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> (((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))), rewrite((((~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))), (((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(148,plain,
% 0.23/0.46 (![V_V: $i] : ((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[147])).
% 0.23/0.46 tff(149,axiom,(![V_V: $i] : ((c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)) | (~c_in(V_V, v_S, t_a))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_10')).
% 0.23/0.46 tff(150,plain,
% 0.23/0.46 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.23/0.46 tff(151,plain,
% 0.23/0.46 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.23/0.46 tff(152,plain,(
% 0.23/0.46 ![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[151])).
% 0.23/0.46 tff(153,plain,
% 0.23/0.46 (![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.23/0.46 tff(154,plain,
% 0.23/0.46 (((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) <=> ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(155,plain,
% 0.23/0.47 ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(156,plain,
% 0.23/0.47 ((~![V_V: $i] : ((~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(V_V, v_S, t_a)) | c_in(c_Pair(V_V, v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a)))) | (~c_in(c_Pair(v_xa, c_Tarski_Olub(v_S, v_cl, t_a), t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))) | (~c_in(v_sko__4mP(v_xa, v_S, v_r), v_S, t_a)) | c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.23/0.47 tff(157,plain,
% 0.23/0.47 (c_in(c_Pair(v_sko__4mP(v_xa, v_S, v_r), v_xa, t_a, t_a), c_Tarski_Opotype_Oorder(v_cl, t_a, tc_Product__Type_Ounit), tc_prod(t_a, t_a))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[156, 153, 131, 143])).
% 0.23/0.47 tff(158,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[157, 141])).
% 0.23/0.47 % SZS output end Proof
% 0.23/0.47 % E exiting
%------------------------------------------------------------------------------