%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET822-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:26:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET822-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 05:44:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(c_in_type, type, (
% 0.20/0.43 c_in: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(tc_IntDef_Oint_type, type, (
% 0.20/0.43 tc_IntDef_Oint: $i)).
% 0.20/0.43 tff(c_emptyset_type, type, (
% 0.20/0.43 c_emptyset: $i)).
% 0.20/0.43 tff(v_x_type, type, (
% 0.20/0.43 v_x: ( $i * $i ) > $i)).
% 0.20/0.43 tff(c_insert_type, type, (
% 0.20/0.43 c_insert: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(v_f_type, type, (
% 0.20/0.43 v_f: $i > $i)).
% 0.20/0.43 tff(v_b_type, type, (
% 0.20/0.43 v_b: $i)).
% 0.20/0.43 tff(v_P_type, type, (
% 0.20/0.43 v_P: $i > $o)).
% 0.20/0.43 tff(1,assumption,(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)), introduced(assumption)).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint))) <=> v_P(v_f(v_b))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (v_P(v_f(v_b)) <=> v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (v_P(v_f(v_b)) <=> v_P(v_f(v_b))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(5,axiom,(v_P(v_f(v_b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (v_P(v_f(v_b))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[6, 3])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(11,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OinsertCI_1')).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.43 tff(13,plain,(
% 0.20/0.43 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.43 inference(skolemize,[status(sab)],[12])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (^[V_V: $i, V_U: $i] : refl(((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V)))) <=> ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V)))) <=> ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V)))) <=> ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(20,axiom,(![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.43 tff(22,plain,(
% 0.20/0.43 ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[21])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))) | ((~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | (~v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))) | (~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | (~v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))) | ((~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | (~v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | (~v_P(v_x(V_U, V_V))))) | (~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | (~v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (~v_P(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[26, 23, 16])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[27, 7])).
% 0.20/0.43 tff(29,plain,(~(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (^[V_V: $i, V_U: $i] : refl(((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint)) <=> ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint)) <=> ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint)) <=> ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(33,axiom,(![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,(
% 0.20/0.43 ![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))),
% 0.20/0.43 inference(skolemize,[status(sab)],[34])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))) | ((~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint))) <=> ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))) | (~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))) | ((~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~![V_V: $i, V_U: $i] : ((~c_in(v_f(V_U), V_V, tc_IntDef_Oint)) | c_in(v_x(V_U, V_V), V_V, tc_IntDef_Oint))) | (~c_in(v_f(v_b), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[39, 36, 16])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : refl(((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : rewrite((((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.44 tff(46,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OinsertE_0')).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.44 tff(49,plain,(
% 0.20/0.44 ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[48])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | ((v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint) | (~c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint) | (~c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | ((v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint) | (~c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : ((V_a = V_b) | c_in(V_a, V_A, T_a) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint) | (~c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint), tc_IntDef_Oint))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 ((v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)) = v_f(v_b)) | c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[53, 50, 40])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[54, 29])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (^[V_a: $i, T_a: $i] : refl((~c_in(V_a, c_emptyset, T_a)) <=> (~c_in(V_a, c_emptyset, T_a)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a)) <=> ![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a)) <=> ![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(59,axiom,(![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OemptyE_0')).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.44 tff(61,plain,(
% 0.20/0.44 ![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))),
% 0.20/0.44 inference(skolemize,[status(sab)],[60])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![V_a: $i, T_a: $i] : (~c_in(V_a, c_emptyset, T_a))) | (~c_in(v_x(v_b, c_insert(v_f(v_b), c_emptyset, tc_IntDef_Oint)), c_emptyset, tc_IntDef_Oint))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[63, 62, 55])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------