%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW209+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:36:37 AM UTC 2025
% Result : Theorem 18.62s 18.82s
% Output : Proof 18.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW209+1 : TPTP v9.0.0. Released v5.2.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 11:15:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 18.62/18.82 % SZS status Theorem
% 18.62/18.82 % SZS output start Proof
% 18.62/18.82 tff(c_Orderings_Oord__class_Oless_type, type, (
% 18.62/18.82 c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o)).
% 18.62/18.82 tff(hAPP_type, type, (
% 18.62/18.82 hAPP: ( $i * $i ) > $i)).
% 18.62/18.82 tff(tptp_fun_B_n_49_type, type, (
% 18.62/18.82 tptp_fun_B_n_49: $i)).
% 18.62/18.82 tff(v_ga_____type, type, (
% 18.62/18.82 v_ga____: $i)).
% 18.62/18.82 tff(tptp_fun_B_m_50_type, type, (
% 18.62/18.82 tptp_fun_B_m_50: $i)).
% 18.62/18.82 tff(tc_Nat_Onat_type, type, (
% 18.62/18.82 tc_Nat_Onat: $i)).
% 18.62/18.82 tff(c_Nat_OSuc_type, type, (
% 18.62/18.82 c_Nat_OSuc: $i > $i)).
% 18.62/18.82 tff(c_Groups_Oplus__class_Oplus_type, type, (
% 18.62/18.82 c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 18.62/18.82 tff(tptp_fun_B_k_11_type, type, (
% 18.62/18.82 tptp_fun_B_k_11: ( $i * $i ) > $i)).
% 18.62/18.82 tff(c_Fun_Ocomp_type, type, (
% 18.62/18.82 c_Fun_Ocomp: ( $i * $i * $i * $i ) > $i)).
% 18.62/18.82 tff(v_f_____type, type, (
% 18.62/18.82 v_f____: $i)).
% 18.62/18.82 tff(1,plain,
% 18.62/18.82 (^[V_n_2: $i, V_m_2: $i] : refl((~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))) <=> (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(2,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))) <=> ![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[1])).
% 18.62/18.82 tff(3,plain,
% 18.62/18.82 (^[V_n_2: $i, V_m_2: $i] : rewrite((~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))) <=> (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(4,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))) <=> ![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[3])).
% 18.62/18.82 tff(5,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))) <=> ![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(transitivity,[status(thm)],[4, 2])).
% 18.62/18.82 tff(6,plain,
% 18.62/18.82 (^[V_n_2: $i, V_m_2: $i] : trans(monotonicity(rewrite((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))) <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))), ((((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))) <=> (((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))))), rewrite((((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))) <=> (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))), ((((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))) <=> (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(7,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))))) <=> ![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[6])).
% 18.62/18.82 tff(8,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) <=> ?[B_k: $i] : (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k)))) <=> ![V_n_2: $i, V_m_2: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) <=> ?[B_k: $i] : (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(9,axiom,(![V_n_2: $i, V_m_2: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) <=> ?[B_k: $i] : (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_less__iff__Suc__add')).
% 18.62/18.82 tff(10,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) <=> ?[B_k: $i] : (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[9, 8])).
% 18.62/18.82 tff(11,plain,(
% 18.62/18.82 ![V_n_2: $i, V_m_2: $i] : (((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2))))) & (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))),
% 18.62/18.82 inference(skolemize,[status(sab)],[10])).
% 18.62/18.82 tff(12,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[11, 7])).
% 18.62/18.82 tff(13,plain,
% 18.62/18.82 (![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[12, 5])).
% 18.62/18.82 tff(14,plain,
% 18.62/18.82 ((~![V_n_2: $i, V_m_2: $i] : (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2)) | (V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, tptp_fun_B_k_11(V_m_2, V_n_2)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) | ![B_k: $i] : (~(V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_m_2, B_k))))))))) | (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49) | ![B_k: $i] : (~(B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, B_k))))))))),
% 18.62/18.82 inference(quant_inst,[status(thm)],[])).
% 18.62/18.82 tff(15,plain,
% 18.62/18.82 (~((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49) | ![B_k: $i] : (~(B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, B_k)))))))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[14, 13])).
% 18.62/18.82 tff(16,plain,
% 18.62/18.82 (((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))) | (~(c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49) | ![B_k: $i] : (~(B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, B_k))))))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))),
% 18.62/18.82 inference(tautology,[status(thm)],[])).
% 18.62/18.82 tff(17,plain,
% 18.62/18.82 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[16, 15])).
% 18.62/18.82 tff(18,plain,
% 18.62/18.82 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))) <=> (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n))))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(19,plain,
% 18.62/18.82 ((~![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))) <=> (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n))))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(20,axiom,(~![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_0')).
% 18.62/18.82 tff(21,plain,
% 18.62/18.82 (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[20, 19])).
% 18.62/18.82 tff(22,plain,
% 18.62/18.82 (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[21, 18])).
% 18.62/18.82 tff(23,plain,
% 18.62/18.82 (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[22, 18])).
% 18.62/18.82 tff(24,plain,
% 18.62/18.82 (~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[23, 18])).
% 18.62/18.82 tff(25,plain,(
% 18.62/18.82 ~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49)))),
% 18.62/18.82 inference(skolemize,[status(sab)],[24])).
% 18.62/18.82 tff(26,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)),
% 18.62/18.82 inference(or_elim,[status(thm)],[25])).
% 18.62/18.82 tff(27,plain,
% 18.62/18.82 ((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))),
% 18.62/18.82 inference(tautology,[status(thm)],[])).
% 18.62/18.82 tff(28,plain,
% 18.62/18.82 ((~((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))) | (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[27, 26])).
% 18.62/18.82 tff(29,plain,
% 18.62/18.82 (B_n!49 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[28, 17])).
% 18.62/18.82 tff(30,plain,
% 18.62/18.82 (c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))) = B_n!49),
% 18.62/18.82 inference(symmetry,[status(thm)],[29])).
% 18.62/18.82 tff(31,plain,
% 18.62/18.82 (hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))) = hAPP(v_ga____, B_n!49)),
% 18.62/18.82 inference(monotonicity,[status(thm)],[30])).
% 18.62/18.82 tff(32,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))),
% 18.62/18.82 inference(monotonicity,[status(thm)],[31])).
% 18.62/18.82 tff(33,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)),
% 18.62/18.82 inference(monotonicity,[status(thm)],[30])).
% 18.62/18.82 tff(34,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))),
% 18.62/18.82 inference(symmetry,[status(thm)],[33])).
% 18.62/18.82 tff(35,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[26, 34])).
% 18.62/18.82 tff(36,plain,
% 18.62/18.82 (^[B_m: $i, B_n: $i] : refl(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(37,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[36])).
% 18.62/18.82 tff(38,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(39,plain,
% 18.62/18.82 (^[B_m: $i, B_n: $i] : rewrite((c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(40,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[39])).
% 18.62/18.82 tff(41,axiom,(![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096')).
% 18.62/18.82 tff(42,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[41, 40])).
% 18.62/18.82 tff(43,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[42, 38])).
% 18.62/18.82 tff(44,plain,(
% 18.62/18.82 ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(skolemize,[status(sab)],[43])).
% 18.62/18.82 tff(45,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[44, 37])).
% 18.62/18.82 tff(46,plain,
% 18.62/18.82 (((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))))) <=> ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(47,plain,
% 18.62/18.82 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))))),
% 18.62/18.82 inference(quant_inst,[status(thm)],[])).
% 18.62/18.82 tff(48,plain,
% 18.62/18.82 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m), hAPP(v_ga____, B_n)))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[47, 46])).
% 18.62/18.82 tff(49,plain,
% 18.62/18.82 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[48, 45])).
% 18.62/18.82 tff(50,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, B_m!50, tptp_fun_B_k_11(B_m!50, B_n!49)))))),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[49, 35])).
% 18.62/18.82 tff(51,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[50, 32])).
% 18.62/18.82 tff(52,plain,
% 18.62/18.82 (^[V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : refl((hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2)) <=> (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2)))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(53,plain,
% 18.62/18.82 (![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2)) <=> ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[52])).
% 18.62/18.82 tff(54,plain,
% 18.62/18.82 (![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2)) <=> ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(rewrite,[status(thm)],[])).
% 18.62/18.82 tff(55,plain,
% 18.62/18.82 (![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2)) <=> ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(elim_unused_vars,[status(thm)],[])).
% 18.62/18.82 tff(56,plain,
% 18.62/18.82 (![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((~(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2)) | (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))) <=> ![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(destructive_equality_resolution,[status(thm)],[])).
% 18.62/18.82 tff(57,plain,
% 18.62/18.82 (![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((~(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2)) | (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))) <=> ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(transitivity,[status(thm)],[56, 55])).
% 18.62/18.82 tff(58,plain,
% 18.62/18.82 (^[V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : rewrite(((hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2) => (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))) <=> ((~(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2)) | (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(59,plain,
% 18.62/18.82 (![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2) => (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))) <=> ![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((~(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2)) | (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2)))),
% 18.62/18.82 inference(quant_intro,[status(thm)],[58])).
% 18.62/18.82 tff(60,plain,
% 18.62/18.82 (![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2) => (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2))) <=> ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(transitivity,[status(thm)],[59, 57])).
% 18.62/18.82 tff(61,axiom,(![V_v_2: $i, V_c_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : ((hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2) = V_c_2) => (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(V_c_2, V_v_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_o__eq__dest__lhs')).
% 18.62/18.82 tff(62,plain,
% 18.62/18.82 (![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[61, 60])).
% 18.62/18.82 tff(63,plain,
% 18.62/18.82 (![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[62, 54])).
% 18.62/18.82 tff(64,plain,(
% 18.62/18.82 ![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(skolemize,[status(sab)],[63])).
% 18.62/18.82 tff(65,plain,
% 18.62/18.82 (![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[64, 53])).
% 18.62/18.82 tff(66,plain,
% 18.62/18.82 ((~![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))) | (hAPP(v_f____, hAPP(v_ga____, B_n!49)) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49))),
% 18.62/18.82 inference(quant_inst,[status(thm)],[])).
% 18.62/18.82 tff(67,plain,
% 18.62/18.82 (hAPP(v_f____, hAPP(v_ga____, B_n!49)) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49)),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[66, 65])).
% 18.62/18.82 tff(68,plain,
% 18.62/18.82 ((~![V_v_2: $i, V_b_2: $i, V_a_2: $i, T_a: $i, T_b: $i, T_c: $i] : (hAPP(V_a_2, hAPP(V_b_2, V_v_2)) = hAPP(hAPP(c_Fun_Ocomp(T_c, T_b, T_a, V_a_2), V_b_2), V_v_2))) | (hAPP(v_f____, hAPP(v_ga____, B_m!50)) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50))),
% 18.62/18.82 inference(quant_inst,[status(thm)],[])).
% 18.62/18.82 tff(69,plain,
% 18.62/18.82 (hAPP(v_f____, hAPP(v_ga____, B_m!50)) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50)),
% 18.62/18.82 inference(unit_resolution,[status(thm)],[68, 65])).
% 18.62/18.82 tff(70,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49))),
% 18.62/18.82 inference(monotonicity,[status(thm)],[69, 67])).
% 18.62/18.82 tff(71,plain,
% 18.62/18.82 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49)))),
% 18.62/18.82 inference(symmetry,[status(thm)],[70])).
% 18.62/18.82 tff(72,plain,
% 18.62/18.82 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49))) <=> (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49))))),
% 18.62/18.82 inference(monotonicity,[status(thm)],[71])).
% 18.62/18.82 tff(73,plain,
% 18.62/18.82 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_m!50), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), B_n!49))),
% 18.62/18.82 inference(or_elim,[status(thm)],[25])).
% 18.62/18.82 tff(74,plain,
% 18.62/18.82 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49)))),
% 18.62/18.82 inference(modus_ponens,[status(thm)],[73, 72])).
% 18.62/18.82 tff(75,plain,
% 18.62/18.82 (^[B_m: $i, B_n: $i] : refl(((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))))),
% 18.62/18.82 inference(bind,[status(th)],[])).
% 18.62/18.82 tff(76,plain,
% 18.62/18.82 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(quant_intro,[status(thm)],[75])).
% 18.62/18.83 tff(77,plain,
% 18.62/18.83 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(rewrite,[status(thm)],[])).
% 18.62/18.83 tff(78,plain,
% 18.62/18.83 (^[B_m: $i, B_n: $i] : rewrite((c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))) <=> ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))))),
% 18.62/18.83 inference(bind,[status(th)],[])).
% 18.62/18.83 tff(79,plain,
% 18.62/18.83 (![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n))) <=> ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(quant_intro,[status(thm)],[78])).
% 18.62/18.83 tff(80,axiom,(![B_m: $i, B_n: $i] : (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n) => c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096')).
% 18.62/18.83 tff(81,plain,
% 18.62/18.83 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(modus_ponens,[status(thm)],[80, 79])).
% 18.62/18.83 tff(82,plain,
% 18.62/18.83 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(modus_ponens,[status(thm)],[81, 77])).
% 18.62/18.83 tff(83,plain,(
% 18.62/18.83 ![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(skolemize,[status(sab)],[82])).
% 18.62/18.83 tff(84,plain,
% 18.62/18.83 (![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))),
% 18.62/18.83 inference(modus_ponens,[status(thm)],[83, 76])).
% 18.62/18.83 tff(85,plain,
% 18.62/18.83 (((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49))))) <=> ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49))))),
% 18.62/18.83 inference(rewrite,[status(thm)],[])).
% 18.62/18.83 tff(86,plain,
% 18.62/18.83 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))) | ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49))))),
% 18.62/18.83 inference(quant_inst,[status(thm)],[])).
% 18.62/18.83 tff(87,plain,
% 18.62/18.83 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49)))),
% 18.74/18.92 inference(modus_ponens,[status(thm)],[86, 85])).
% 18.74/18.92 tff(88,plain,
% 18.74/18.92 ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, B_m!50)), hAPP(v_f____, hAPP(v_ga____, B_n!49)))),
% 18.74/18.92 inference(unit_resolution,[status(thm)],[87, 84])).
% 18.74/18.92 tff(89,plain,
% 18.74/18.92 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_m!50), hAPP(v_ga____, B_n!49))),
% 18.74/18.92 inference(unit_resolution,[status(thm)],[88, 74])).
% 18.74/18.92 tff(90,plain,
% 18.74/18.92 ($false),
% 18.74/18.92 inference(unit_resolution,[status(thm)],[89, 51])).
% 18.74/18.92 % SZS output end Proof
% 18.76/18.94 % E exiting
%------------------------------------------------------------------------------