%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET824-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET824-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:44:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(c_in_type, type, (
% 0.19/0.36 c_in: ( $i * $i * $i ) > $o)).
% 0.19/0.36 tff(tc_IntDef_Oint_type, type, (
% 0.19/0.36 tc_IntDef_Oint: $i)).
% 0.19/0.36 tff(c_uminus_type, type, (
% 0.19/0.36 c_uminus: ( $i * $i ) > $i)).
% 0.19/0.36 tff(tc_set_type, type, (
% 0.19/0.36 tc_set: $i > $i)).
% 0.19/0.36 tff(elem_0_type, type, (
% 0.19/0.36 elem_0: $i)).
% 0.19/0.36 tff(v_a_type, type, (
% 0.19/0.36 v_a: $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[V_U: $i] : refl(c_in(v_a, V_U, tc_IntDef_Oint) <=> c_in(v_a, V_U, tc_IntDef_Oint))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint) <=> ![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint) <=> ![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(4,axiom,(![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.36 tff(6,plain,(
% 0.19/0.36 ![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)),
% 0.19/0.36 inference(skolemize,[status(sab)],[5])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 ((~![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)) | c_in(v_a, elem!0, tc_IntDef_Oint)),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (c_in(v_a, elem!0, tc_IntDef_Oint)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (^[V_c: $i, T_a: $i, V_A: $i] : refl(((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a))) <=> ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a))) <=> ![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a))) <=> ![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(13,axiom,(![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Set_OComplD__dest_0')).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.36 tff(15,plain,(
% 0.19/0.36 ![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))),
% 0.19/0.36 inference(skolemize,[status(sab)],[14])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 (![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (((~![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))) | ((~c_in(v_a, elem!0, tc_IntDef_Oint)) | (~c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint)))) <=> ((~![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))) | (~c_in(v_a, elem!0, tc_IntDef_Oint)) | (~c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 ((~![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))) | ((~c_in(v_a, elem!0, tc_IntDef_Oint)) | (~c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint)))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 ((~![V_c: $i, T_a: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | (~c_in(V_c, c_uminus(V_A, tc_set(T_a)), T_a)))) | (~c_in(v_a, elem!0, tc_IntDef_Oint)) | (~c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 (~c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint)),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 ((~![V_U: $i] : c_in(v_a, V_U, tc_IntDef_Oint)) | c_in(v_a, c_uminus(elem!0, tc_set(tc_IntDef_Oint)), tc_IntDef_Oint)),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[21, 7, 20])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------