%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM009-2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:57 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.38s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COM009-2 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 12:20:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.38 % SZS status Unsatisfiable
% 0.22/0.38 % SZS output start Proof
% 0.22/0.38 tff(c_UNITY_Ototalize_type, type, (
% 0.22/0.38 c_UNITY_Ototalize: ( $i * $i ) > $i)).
% 0.22/0.38 tff(c_UNITY_Oall__total_type, type, (
% 0.22/0.38 c_UNITY_Oall__total: ( $i * $i ) > $o)).
% 0.22/0.38 tff(t_a_type, type, (
% 0.22/0.38 t_a: $i)).
% 0.22/0.38 tff(v_F_type, type, (
% 0.22/0.38 v_F: $i)).
% 0.22/0.38 tff(1,plain,
% 0.22/0.38 (^[V_F: $i, T_a: $i] : refl(((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F)) <=> ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F)))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(2,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F)) <=> ![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.38 tff(3,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F)) <=> ![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(4,axiom,(![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_UNITY_Oall__total__imp__totalize_0')).
% 0.22/0.38 tff(5,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.38 tff(6,plain,(
% 0.22/0.38 ![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))),
% 0.22/0.38 inference(skolemize,[status(sab)],[5])).
% 0.22/0.38 tff(7,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.38 tff(8,assumption,(~c_UNITY_Oall__total(v_F, t_a)), introduced(assumption)).
% 0.22/0.38 tff(9,plain,
% 0.22/0.38 ((c_UNITY_Oall__total(v_F, t_a) | (c_UNITY_Ototalize(v_F, t_a) = v_F)) <=> (c_UNITY_Oall__total(v_F, t_a) | (c_UNITY_Ototalize(v_F, t_a) = v_F))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(10,axiom,(c_UNITY_Oall__total(v_F, t_a) | (c_UNITY_Ototalize(v_F, t_a) = v_F)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.22/0.38 tff(11,plain,
% 0.22/0.38 (c_UNITY_Oall__total(v_F, t_a) | (c_UNITY_Ototalize(v_F, t_a) = v_F)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.22/0.38 tff(12,plain,
% 0.22/0.38 (c_UNITY_Ototalize(v_F, t_a) = v_F),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.22/0.38 tff(13,plain,
% 0.22/0.38 (c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a) <=> c_UNITY_Oall__total(v_F, t_a)),
% 0.22/0.38 inference(monotonicity,[status(thm)],[12])).
% 0.22/0.38 tff(14,plain,
% 0.22/0.38 (c_UNITY_Oall__total(v_F, t_a) <=> c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a)),
% 0.22/0.38 inference(symmetry,[status(thm)],[13])).
% 0.22/0.38 tff(15,plain,
% 0.22/0.38 ((~c_UNITY_Oall__total(v_F, t_a)) <=> (~c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a))),
% 0.22/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.22/0.38 tff(16,plain,
% 0.22/0.38 (~c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[8, 15])).
% 0.22/0.38 tff(17,plain,
% 0.22/0.38 (^[V_F: $i, T_a: $i] : refl(c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a) <=> c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(18,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a) <=> ![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)),
% 0.22/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.22/0.38 tff(19,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a) <=> ![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(20,axiom,(![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_UNITY_Oall__total__totalize_0')).
% 0.22/0.38 tff(21,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.38 tff(22,plain,(
% 0.22/0.38 ![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)),
% 0.22/0.38 inference(skolemize,[status(sab)],[21])).
% 0.22/0.38 tff(23,plain,
% 0.22/0.38 (![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.22/0.38 tff(24,plain,
% 0.22/0.38 ((~![V_F: $i, T_a: $i] : c_UNITY_Oall__total(c_UNITY_Ototalize(V_F, T_a), T_a)) | c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a)),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(25,plain,
% 0.22/0.38 (c_UNITY_Oall__total(c_UNITY_Ototalize(v_F, t_a), t_a)),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.22/0.38 tff(26,plain,
% 0.22/0.38 ($false),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[25, 16])).
% 0.22/0.38 tff(27,plain,(c_UNITY_Oall__total(v_F, t_a)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.38 tff(28,plain,
% 0.22/0.38 (((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))) <=> ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(29,axiom,((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.22/0.38 tff(30,plain,
% 0.22/0.38 ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.22/0.38 tff(31,plain,
% 0.22/0.38 ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.22/0.38 tff(32,plain,
% 0.22/0.38 ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.22/0.38 tff(33,plain,
% 0.22/0.38 ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.22/0.38 tff(34,plain,
% 0.22/0.38 ((~(c_UNITY_Ototalize(v_F, t_a) = v_F)) | (~c_UNITY_Oall__total(v_F, t_a))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.22/0.38 tff(35,plain,
% 0.22/0.38 (~(c_UNITY_Ototalize(v_F, t_a) = v_F)),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[34, 27])).
% 0.22/0.38 tff(36,plain,
% 0.22/0.38 (((~![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))) | ((~c_UNITY_Oall__total(v_F, t_a)) | (c_UNITY_Ototalize(v_F, t_a) = v_F))) <=> ((~![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))) | (~c_UNITY_Oall__total(v_F, t_a)) | (c_UNITY_Ototalize(v_F, t_a) = v_F))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(37,plain,
% 0.22/0.38 ((~![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))) | ((~c_UNITY_Oall__total(v_F, t_a)) | (c_UNITY_Ototalize(v_F, t_a) = v_F))),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(38,plain,
% 0.22/0.38 ((~![V_F: $i, T_a: $i] : ((~c_UNITY_Oall__total(V_F, T_a)) | (c_UNITY_Ototalize(V_F, T_a) = V_F))) | (~c_UNITY_Oall__total(v_F, t_a)) | (c_UNITY_Ototalize(v_F, t_a) = v_F)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.38 tff(39,plain,
% 0.22/0.38 ($false),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[38, 35, 27, 7])).
% 0.22/0.38 % SZS output end Proof
% 0.22/0.38 % E exiting
%------------------------------------------------------------------------------