TSTP Solution File: SWW209+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Thu Sep 29 20:57:54 EDT 2022
% Result : Theorem 82.68s 52.09s
% Output : Proof 82.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.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 : Sun Sep 4 12:45:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 82.68/52.09 % SZS status Theorem
% 82.68/52.09 % SZS output start Proof
% 82.68/52.09 tff(c_Orderings_Oord__class_Oless_type, type, (
% 82.68/52.09 c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o)).
% 82.68/52.09 tff(hAPP_type, type, (
% 82.68/52.09 hAPP: ( $i * $i ) > $i)).
% 82.68/52.09 tff(c_Nat_OSuc_type, type, (
% 82.68/52.09 c_Nat_OSuc: $i > $i)).
% 82.68/52.09 tff(tptp_fun_B_n_4_type, type, (
% 82.68/52.09 tptp_fun_B_n_4: ( $i * $i ) > $i)).
% 82.68/52.09 tff(v_ga_____type, type, (
% 82.68/52.09 v_ga____: $i)).
% 82.68/52.09 tff(c_Fun_Ocomp_type, type, (
% 82.68/52.09 c_Fun_Ocomp: ( $i * $i * $i * $i ) > $i)).
% 82.68/52.09 tff(v_f_____type, type, (
% 82.68/52.09 v_f____: $i)).
% 82.68/52.09 tff(tc_Nat_Onat_type, type, (
% 82.68/52.09 tc_Nat_Onat: $i)).
% 82.68/52.09 tff(tptp_fun_B_n_49_type, type, (
% 82.68/52.09 tptp_fun_B_n_49: $i)).
% 82.68/52.09 tff(tptp_fun_B_m_50_type, type, (
% 82.68/52.09 tptp_fun_B_m_50: $i)).
% 82.68/52.09 tff(class_Orderings_Oorder_type, type, (
% 82.68/52.09 class_Orderings_Oorder: $i > $o)).
% 82.68/52.09 tff(c_SEQ_Osubseq_type, type, (
% 82.68/52.09 c_SEQ_Osubseq: $i > $o)).
% 82.68/52.09 tff(tptp_fun_B_n_3_type, type, (
% 82.68/52.09 tptp_fun_B_n_3: $i > $i)).
% 82.68/52.09 tff(1,plain,
% 82.68/52.09 (^[V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : refl((hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2))) <=> (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2))))),
% 82.68/52.09 inference(bind,[status(th)],[])).
% 82.68/52.09 tff(2,plain,
% 82.68/52.09 (![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2))) <=> ![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))),
% 82.68/52.09 inference(quant_intro,[status(thm)],[1])).
% 82.68/52.09 tff(3,plain,
% 82.68/52.09 (![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2))) <=> ![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(4,axiom,(![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_o__apply')).
% 82.68/52.09 tff(5,plain,
% 82.68/52.09 (![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[4, 3])).
% 82.68/52.09 tff(6,plain,(
% 82.68/52.09 ![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))),
% 82.68/52.09 inference(skolemize,[status(sab)],[5])).
% 82.68/52.09 tff(7,plain,
% 82.68/52.09 (![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[6, 2])).
% 82.68/52.09 tff(8,plain,
% 82.68/52.09 ((~![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))) | (hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))) = hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.68/52.09 inference(quant_inst,[status(thm)],[])).
% 82.68/52.09 tff(9,plain,
% 82.68/52.09 (hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))) = hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.09 inference(unit_resolution,[status(thm)],[8, 7])).
% 82.68/52.09 tff(10,plain,
% 82.68/52.09 (hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))),
% 82.68/52.09 inference(symmetry,[status(thm)],[9])).
% 82.68/52.09 tff(11,plain,
% 82.68/52.09 ((~![V_xa_2: $i, V_gb_2: $i, V_fa_2: $i, T_c: $i, T_a: $i, T_b: $i] : (hAPP(hAPP(c_Fun_Ocomp(T_b, T_a, T_c, V_fa_2), V_gb_2), V_xa_2) = hAPP(V_fa_2, hAPP(V_gb_2, V_xa_2)))) | (hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))) = hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.09 inference(quant_inst,[status(thm)],[])).
% 82.68/52.09 tff(12,plain,
% 82.68/52.09 (hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))) = hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))),
% 82.68/52.09 inference(unit_resolution,[status(thm)],[11, 7])).
% 82.68/52.09 tff(13,plain,
% 82.68/52.09 (hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))) = hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))),
% 82.68/52.09 inference(symmetry,[status(thm)],[12])).
% 82.68/52.09 tff(14,plain,
% 82.68/52.09 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) <=> 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.09 inference(monotonicity,[status(thm)],[13, 10])).
% 82.68/52.09 tff(15,plain,
% 82.68/52.09 (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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.68/52.09 inference(symmetry,[status(thm)],[14])).
% 82.68/52.09 tff(16,plain,
% 82.68/52.09 ((~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) <=> (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.09 inference(monotonicity,[status(thm)],[15])).
% 82.68/52.09 tff(17,plain,
% 82.68/52.09 ((~![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))))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(18,plain,
% 82.68/52.09 ((~![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))))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(19,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')).
% 82.68/52.09 tff(20,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[19, 18])).
% 82.68/52.09 tff(21,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[20, 17])).
% 82.68/52.09 tff(22,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[21, 17])).
% 82.68/52.09 tff(23,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[22, 17])).
% 82.68/52.09 tff(24,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[23, 17])).
% 82.68/52.09 tff(25,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[24, 17])).
% 82.68/52.09 tff(26,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[25, 17])).
% 82.68/52.09 tff(27,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[26, 17])).
% 82.68/52.09 tff(28,plain,
% 82.68/52.09 (~![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)))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[27, 17])).
% 82.68/52.09 tff(29,plain,(
% 82.68/52.09 ~((~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)))),
% 82.68/52.09 inference(skolemize,[status(sab)],[28])).
% 82.68/52.09 tff(30,plain,
% 82.68/52.09 (~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))),
% 82.68/52.09 inference(or_elim,[status(thm)],[29])).
% 82.68/52.09 tff(31,plain,
% 82.68/52.09 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49)),
% 82.68/52.09 inference(or_elim,[status(thm)],[29])).
% 82.68/52.09 tff(32,plain,
% 82.68/52.09 ((~(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, 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)) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m!50, B_n!49))),
% 82.68/52.09 inference(tautology,[status(thm)],[])).
% 82.68/52.09 tff(33,plain,
% 82.68/52.09 (~(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, B_m!50, B_n!49))),
% 82.68/52.09 inference(unit_resolution,[status(thm)],[32, 31, 30])).
% 82.68/52.09 tff(34,plain,
% 82.68/52.09 (class_Orderings_Oorder(tc_Nat_Onat) <=> class_Orderings_Oorder(tc_Nat_Onat)),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(35,axiom,(class_Orderings_Oorder(tc_Nat_Onat)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arity_Nat__Onat__Orderings_Oorder')).
% 82.68/52.09 tff(36,plain,
% 82.68/52.09 (class_Orderings_Oorder(tc_Nat_Onat)),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[35, 34])).
% 82.68/52.09 tff(37,plain,
% 82.68/52.09 (^[V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : refl(((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2)))))) <=> ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2)))))))),
% 82.68/52.09 inference(bind,[status(th)],[])).
% 82.68/52.09 tff(38,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2)))))) <=> ![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))),
% 82.68/52.09 inference(quant_intro,[status(thm)],[37])).
% 82.68/52.09 tff(39,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) <=> ![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(40,plain,
% 82.68/52.09 (^[V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : trans(monotonicity(rewrite((![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))) => (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2))) <=> ((~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) | (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))), ((class_Orderings_Oorder(T_a) => (![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))) => (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))) <=> (class_Orderings_Oorder(T_a) => ((~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) | (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))))), rewrite((class_Orderings_Oorder(T_a) => ((~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) | (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))) <=> ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))), ((class_Orderings_Oorder(T_a) => (![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))) => (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))) <=> ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))))),
% 82.68/52.09 inference(bind,[status(th)],[])).
% 82.68/52.09 tff(41,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : (class_Orderings_Oorder(T_a) => (![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))) => (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)))) <=> ![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))),
% 82.68/52.09 inference(quant_intro,[status(thm)],[40])).
% 82.68/52.09 tff(42,axiom,(![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : (class_Orderings_Oorder(T_a) => (![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))) => (c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_lift__Suc__mono__less__iff')).
% 82.68/52.09 tff(43,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[42, 41])).
% 82.68/52.09 tff(44,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~![B_n: $i] : c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[43, 39])).
% 82.68/52.09 tff(45,plain,(
% 82.68/52.09 ![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))),
% 82.68/52.09 inference(skolemize,[status(sab)],[44])).
% 82.68/52.09 tff(46,plain,
% 82.68/52.09 (![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))),
% 82.68/52.09 inference(modus_ponens,[status(thm)],[45, 38])).
% 82.68/52.09 tff(47,plain,
% 82.68/52.09 (((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | ((~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))) <=> ((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(48,plain,
% 82.68/52.09 (((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, B_m!50, B_n!49)) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))) <=> ((~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.09 inference(rewrite,[status(thm)],[])).
% 82.68/52.09 tff(49,plain,
% 82.68/52.09 (((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | ((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, B_m!50, B_n!49)) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))) <=> ((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | ((~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))))),
% 82.68/52.10 inference(monotonicity,[status(thm)],[48])).
% 82.68/52.10 tff(50,plain,
% 82.68/52.10 (((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | ((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, B_m!50, B_n!49)) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))) <=> ((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.10 inference(transitivity,[status(thm)],[49, 47])).
% 82.68/52.10 tff(51,plain,
% 82.68/52.10 ((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | ((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, B_m!50, B_n!49)) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.10 inference(quant_inst,[status(thm)],[])).
% 82.68/52.10 tff(52,plain,
% 82.68/52.10 ((~![V_m_2: $i, V_n_2: $i, V_fa_2: $i, T_a: $i] : ((c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, V_n_2), hAPP(V_fa_2, V_m_2)) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2)) | (~class_Orderings_Oorder(T_a)) | (~c_Orderings_Oord__class_Oless(T_a, hAPP(V_fa_2, tptp_fun_B_n_4(T_a, V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_4(T_a, V_fa_2))))))) | (~class_Orderings_Oorder(tc_Nat_Onat)) | (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, 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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[51, 50])).
% 82.68/52.10 tff(53,plain,
% 82.68/52.10 (~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____), tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____), c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[52, 46, 36, 33])).
% 82.68/52.10 tff(54,plain,
% 82.68/52.10 (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[53, 16])).
% 82.68/52.10 tff(55,plain,
% 82.68/52.10 (^[V_fa_2: $i] : refl((~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))) <=> (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))))),
% 82.68/52.10 inference(bind,[status(th)],[])).
% 82.68/52.10 tff(56,plain,
% 82.68/52.10 (![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))) <=> ![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(quant_intro,[status(thm)],[55])).
% 82.68/52.10 tff(57,plain,
% 82.68/52.10 (^[V_fa_2: $i] : rewrite((~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))) <=> (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))))),
% 82.68/52.10 inference(bind,[status(th)],[])).
% 82.68/52.10 tff(58,plain,
% 82.68/52.10 (![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))) <=> ![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(quant_intro,[status(thm)],[57])).
% 82.68/52.10 tff(59,plain,
% 82.68/52.10 (![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))) <=> ![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(transitivity,[status(thm)],[58, 56])).
% 82.68/52.10 tff(60,plain,
% 82.68/52.10 (^[V_fa_2: $i] : trans(monotonicity(rewrite(((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) <=> ((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))), ((((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))) <=> (((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))))), rewrite((((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))) <=> (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))), ((((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))) <=> (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))))),
% 82.68/52.10 inference(bind,[status(th)],[])).
% 82.68/52.10 tff(61,plain,
% 82.68/52.10 (![V_fa_2: $i] : (((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2))))))) <=> ![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(quant_intro,[status(thm)],[60])).
% 82.68/52.10 tff(62,plain,
% 82.68/52.10 (![V_fa_2: $i] : (c_SEQ_Osubseq(V_fa_2) <=> ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) <=> ![V_fa_2: $i] : (c_SEQ_Osubseq(V_fa_2) <=> ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))),
% 82.68/52.10 inference(rewrite,[status(thm)],[])).
% 82.68/52.10 tff(63,axiom,(![V_fa_2: $i] : (c_SEQ_Osubseq(V_fa_2) <=> ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_subseq__Suc__iff')).
% 82.68/52.10 tff(64,plain,
% 82.68/52.10 (![V_fa_2: $i] : (c_SEQ_Osubseq(V_fa_2) <=> ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[63, 62])).
% 82.68/52.10 tff(65,plain,(
% 82.68/52.10 ![V_fa_2: $i] : (((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n)))) & (c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))),
% 82.68/52.10 inference(skolemize,[status(sab)],[64])).
% 82.68/52.10 tff(66,plain,
% 82.68/52.10 (![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[65, 61])).
% 82.68/52.10 tff(67,plain,
% 82.68/52.10 (![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[66, 59])).
% 82.68/52.10 tff(68,plain,
% 82.68/52.10 ((~![V_fa_2: $i] : (~((~((~c_SEQ_Osubseq(V_fa_2)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, B_n), hAPP(V_fa_2, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(V_fa_2) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(V_fa_2, tptp_fun_B_n_3(V_fa_2)), hAPP(V_fa_2, c_Nat_OSuc(tptp_fun_B_n_3(V_fa_2)))))))))) | (~((~((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(v_ga____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_3(v_ga____)), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_3(v_ga____)))))))))),
% 82.68/52.10 inference(quant_inst,[status(thm)],[])).
% 82.68/52.10 tff(69,plain,
% 82.68/52.10 (~((~((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(v_ga____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_3(v_ga____)), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_3(v_ga____))))))))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[68, 67])).
% 82.68/52.10 tff(70,plain,
% 82.68/52.10 (((~((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))) | (~(c_SEQ_Osubseq(v_ga____) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_3(v_ga____)), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_3(v_ga____)))))))) | ((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))),
% 82.68/52.10 inference(tautology,[status(thm)],[])).
% 82.68/52.10 tff(71,plain,
% 82.68/52.10 ((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n)))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[70, 69])).
% 82.68/52.10 tff(72,plain,
% 82.68/52.10 (c_SEQ_Osubseq(v_ga____) <=> c_SEQ_Osubseq(v_ga____)),
% 82.68/52.10 inference(rewrite,[status(thm)],[])).
% 82.68/52.10 tff(73,axiom,(c_SEQ_Osubseq(v_ga____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_g_I1_J')).
% 82.68/52.10 tff(74,plain,
% 82.68/52.10 (c_SEQ_Osubseq(v_ga____)),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[73, 72])).
% 82.68/52.10 tff(75,plain,
% 82.68/52.10 ((~((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))) | (~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n)))),
% 82.68/52.10 inference(tautology,[status(thm)],[])).
% 82.68/52.10 tff(76,plain,
% 82.68/52.10 ((~((~c_SEQ_Osubseq(v_ga____)) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n))))) | ![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n)))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[75, 74])).
% 82.68/52.10 tff(77,plain,
% 82.68/52.10 (![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n)))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[76, 71])).
% 82.68/52.10 tff(78,plain,
% 82.68/52.10 ((~![B_n: $i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, B_n), hAPP(v_ga____, c_Nat_OSuc(B_n)))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.10 inference(quant_inst,[status(thm)],[])).
% 82.68/52.10 tff(79,plain,
% 82.68/52.10 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))),
% 82.68/52.10 inference(unit_resolution,[status(thm)],[78, 77])).
% 82.68/52.10 tff(80,plain,
% 82.68/52.10 (^[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))))),
% 82.68/52.10 inference(bind,[status(th)],[])).
% 82.68/52.10 tff(81,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(quant_intro,[status(thm)],[80])).
% 82.68/52.10 tff(82,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(rewrite,[status(thm)],[])).
% 82.68/52.10 tff(83,plain,
% 82.68/52.10 (^[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))))),
% 82.68/52.10 inference(bind,[status(th)],[])).
% 82.68/52.10 tff(84,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(quant_intro,[status(thm)],[83])).
% 82.68/52.10 tff(85,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')).
% 82.68/52.10 tff(86,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[85, 84])).
% 82.68/52.10 tff(87,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[86, 82])).
% 82.68/52.10 tff(88,plain,(
% 82.68/52.10 ![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)))),
% 82.68/52.10 inference(skolemize,[status(sab)],[87])).
% 82.68/52.10 tff(89,plain,
% 82.68/52.10 (![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)))),
% 82.68/52.10 inference(modus_ponens,[status(thm)],[88, 81])).
% 82.68/52.10 tff(90,plain,
% 82.68/52.10 (((~![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____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))) <=> ((~![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____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.10 inference(rewrite,[status(thm)],[])).
% 82.68/52.10 tff(91,plain,
% 82.68/52.10 ((~![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____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))))),
% 82.68/52.10 inference(quant_inst,[status(thm)],[])).
% 82.68/52.10 tff(92,plain,
% 82.68/52.10 ((~![B_m: $i, B_n: $i] : ((~c_Orderings_Oord__class_Oless(tc_Nat_Onat, B_m, B_n)) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, B_m), hAPP(v_f____, B_n)))) | (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))), hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))))) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.78/52.18 inference(modus_ponens,[status(thm)],[91, 90])).
% 82.78/52.18 tff(93,plain,
% 82.78/52.18 (c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(v_f____, hAPP(v_ga____, tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____)))), hAPP(v_f____, hAPP(v_ga____, c_Nat_OSuc(tptp_fun_B_n_4(tc_Nat_Onat, hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____), v_ga____))))))),
% 82.78/52.18 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 82.78/52.18 tff(94,plain,
% 82.78/52.18 ($false),
% 82.78/52.18 inference(unit_resolution,[status(thm)],[93, 54])).
% 82.78/52.18 % SZS output end Proof
%------------------------------------------------------------------------------