TSTP Solution File: SWW257+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW257+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 20:58:05 EDT 2022
% Result : Theorem 2.67s 2.00s
% Output : Proof 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW257+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 13:32:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 2.67/2.00 % SZS status Theorem
% 2.67/2.00 % SZS output start Proof
% 2.67/2.00 tff(c_Groups_Ouminus__class_Ouminus_type, type, (
% 2.67/2.00 c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i)).
% 2.67/2.00 tff(c_Groups_Oone__class_Oone_type, type, (
% 2.67/2.00 c_Groups_Oone__class_Oone: $i > $i)).
% 2.67/2.00 tff(tc_Complex_Ocomplex_type, type, (
% 2.67/2.00 tc_Complex_Ocomplex: $i)).
% 2.67/2.00 tff(hAPP_type, type, (
% 2.67/2.00 hAPP: ( $i * $i ) > $i)).
% 2.67/2.00 tff(v_a_____type, type, (
% 2.67/2.00 v_a____: $i)).
% 2.67/2.00 tff(v_k_____type, type, (
% 2.67/2.00 v_k____: $i)).
% 2.67/2.00 tff(tptp_fun_B_z_1_type, type, (
% 2.67/2.00 tptp_fun_B_z_1: $i)).
% 2.67/2.00 tff(c_Power_Opower__class_Opower_type, type, (
% 2.67/2.00 c_Power_Opower__class_Opower: $i > $i)).
% 2.67/2.00 tff(c_Groups_Otimes__class_Otimes_type, type, (
% 2.67/2.00 c_Groups_Otimes__class_Otimes: $i > $i)).
% 2.67/2.00 tff(c_Groups_Ominus__class_Ominus_type, type, (
% 2.67/2.00 c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i)).
% 2.67/2.00 tff(tc_Nat_Onat_type, type, (
% 2.67/2.00 tc_Nat_Onat: $i)).
% 2.67/2.00 tff(class_Groups_Ogroup__add_type, type, (
% 2.67/2.00 class_Groups_Ogroup__add: $i > $o)).
% 2.67/2.00 tff(c_Groups_Ozero__class_Ozero_type, type, (
% 2.67/2.00 c_Groups_Ozero__class_Ozero: $i > $i)).
% 2.67/2.00 tff(c_Groups_Oplus__class_Oplus_type, type, (
% 2.67/2.00 c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i)).
% 2.67/2.00 tff(class_Rings_Ocomm__semiring__1_type, type, (
% 2.67/2.00 class_Rings_Ocomm__semiring__1: $i > $o)).
% 2.67/2.00 tff(class_Power_Opower_type, type, (
% 2.67/2.00 class_Power_Opower: $i > $o)).
% 2.67/2.00 tff(v_thesis_____type, type, (
% 2.67/2.00 v_thesis____: $o)).
% 2.67/2.00 tff(1,plain,
% 2.67/2.00 (class_Groups_Ogroup__add(tc_Complex_Ocomplex) <=> class_Groups_Ogroup__add(tc_Complex_Ocomplex)),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(2,axiom,(class_Groups_Ogroup__add(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Groups_Ogroup__add')).
% 2.67/2.00 tff(3,plain,
% 2.67/2.00 (class_Groups_Ogroup__add(tc_Complex_Ocomplex)),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[2, 1])).
% 2.67/2.00 tff(4,plain,
% 2.67/2.00 (^[V_b: $i, V_a: $i, T_a: $i] : refl(((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)))))),
% 2.67/2.00 inference(bind,[status(th)],[])).
% 2.67/2.00 tff(5,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(quant_intro,[status(thm)],[4])).
% 2.67/2.00 tff(6,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(7,plain,
% 2.67/2.00 (^[V_b: $i, V_a: $i, T_a: $i] : trans(monotonicity(rewrite(((c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)) => (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b)) <=> ((~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))) | (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))), ((class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)) => (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))) <=> (class_Groups_Ogroup__add(T_a) => ((~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))) | (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))))), rewrite((class_Groups_Ogroup__add(T_a) => ((~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))) | (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))) <=> ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))), ((class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)) => (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))) <=> ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))))),
% 2.67/2.00 inference(bind,[status(th)],[])).
% 2.67/2.00 tff(8,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : (class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)) => (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(quant_intro,[status(thm)],[7])).
% 2.67/2.00 tff(9,axiom,(![V_b: $i, V_a: $i, T_a: $i] : (class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a)) => (c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_minus__unique')).
% 2.67/2.00 tff(10,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[9, 8])).
% 2.67/2.00 tff(11,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[10, 6])).
% 2.67/2.00 tff(12,plain,(
% 2.67/2.00 ![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(skolemize,[status(sab)],[11])).
% 2.67/2.00 tff(13,plain,
% 2.67/2.00 (![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[12, 5])).
% 2.67/2.00 tff(14,plain,
% 2.67/2.00 (?[B_z: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> ?[B_z: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(15,axiom,(?[B_z: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact__096EX_Az_O_A1_A_L_Az_A_K_A_Ia_A_K_Az_A_094_A_Ik_A_N_A1_J_J_A_061_A0_096')).
% 2.67/2.00 tff(16,plain,
% 2.67/2.00 (?[B_z: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.67/2.00 tff(17,plain,(
% 2.67/2.00 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
% 2.67/2.00 inference(skolemize,[status(sab)],[16])).
% 2.67/2.00 tff(18,plain,
% 2.67/2.00 (((~![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))) | ((c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))) | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(19,plain,
% 2.67/2.00 ((~![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))) | ((c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.00 inference(quant_inst,[status(thm)],[])).
% 2.67/2.00 tff(20,plain,
% 2.67/2.00 ((~![V_b: $i, V_a: $i, T_a: $i] : ((c_Groups_Ouminus__class_Ouminus(T_a, V_a) = V_b) | (~class_Groups_Ogroup__add(T_a)) | (~(c_Groups_Oplus__class_Oplus(T_a, V_a, V_b) = c_Groups_Ozero__class_Ozero(T_a))))) | (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.67/2.00 tff(21,plain,
% 2.67/2.00 (c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.00 inference(unit_resolution,[status(thm)],[20, 17, 13, 3])).
% 2.67/2.00 tff(22,plain,
% 2.67/2.00 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 2.67/2.00 inference(symmetry,[status(thm)],[21])).
% 2.67/2.00 tff(23,plain,
% 2.67/2.00 (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) <=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(24,axiom,(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Rings_Ocomm__semiring__1')).
% 2.67/2.00 tff(25,plain,
% 2.67/2.00 (class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.67/2.00 tff(26,plain,
% 2.67/2.00 (^[V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : refl(((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))))),
% 2.67/2.00 inference(bind,[status(th)],[])).
% 2.67/2.00 tff(27,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))) <=> ![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(quant_intro,[status(thm)],[26])).
% 2.67/2.00 tff(28,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))) <=> ![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(rewrite,[status(thm)],[])).
% 2.67/2.00 tff(29,plain,
% 2.67/2.00 (^[V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : rewrite((class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))))),
% 2.67/2.00 inference(bind,[status(th)],[])).
% 2.67/2.00 tff(30,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry)))) <=> ![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(quant_intro,[status(thm)],[29])).
% 2.67/2.00 tff(31,axiom,(![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J')).
% 2.67/2.00 tff(32,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[31, 30])).
% 2.67/2.00 tff(33,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.67/2.00 tff(34,plain,(
% 2.67/2.00 ![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.00 inference(skolemize,[status(sab)],[33])).
% 2.67/2.00 tff(35,plain,
% 2.67/2.00 (![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[34, 27])).
% 2.67/2.01 tff(36,plain,
% 2.67/2.01 (((~![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(37,plain,
% 2.67/2.01 ((~![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))),
% 2.67/2.01 inference(quant_inst,[status(thm)],[])).
% 2.67/2.01 tff(38,plain,
% 2.67/2.01 ((~![V_ry: $i, V_rx: $i, V_lx: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_rx), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_lx), V_ry))))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.67/2.01 tff(39,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 2.67/2.01 tff(40,plain,
% 2.67/2.01 (^[V_b: $i, V_a: $i, T_a: $i] : refl(((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(41,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[40])).
% 2.67/2.01 tff(42,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(43,plain,
% 2.67/2.01 (^[V_b: $i, V_a: $i, T_a: $i] : rewrite((class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))) <=> ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(44,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a))) <=> ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[43])).
% 2.67/2.01 tff(45,axiom,(![V_b: $i, V_a: $i, T_a: $i] : (class_Rings_Ocomm__semiring__1(T_a) => (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J')).
% 2.67/2.01 tff(46,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[45, 44])).
% 2.67/2.01 tff(47,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[46, 42])).
% 2.67/2.01 tff(48,plain,(
% 2.67/2.01 ![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(skolemize,[status(sab)],[47])).
% 2.67/2.01 tff(49,plain,
% 2.67/2.01 (![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[48, 41])).
% 2.67/2.01 tff(50,plain,
% 2.67/2.01 (((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____)))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(51,plain,
% 2.67/2.01 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))) | ((~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____)))),
% 2.67/2.01 inference(quant_inst,[status(thm)],[])).
% 2.67/2.01 tff(52,plain,
% 2.67/2.01 ((~![V_b: $i, V_a: $i, T_a: $i] : ((~class_Rings_Ocomm__semiring__1(T_a)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_b), V_a)))) | (~class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)) | (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.67/2.01 tff(53,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____)),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[52, 49, 25])).
% 2.67/2.01 tff(54,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(symmetry,[status(thm)],[53])).
% 2.67/2.01 tff(55,plain,
% 2.67/2.01 (class_Power_Opower(tc_Complex_Ocomplex) <=> class_Power_Opower(tc_Complex_Ocomplex)),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(56,axiom,(class_Power_Opower(tc_Complex_Ocomplex)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','arity_Complex__Ocomplex__Power_Opower')).
% 2.67/2.01 tff(57,plain,
% 2.67/2.01 (class_Power_Opower(tc_Complex_Ocomplex)),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.67/2.01 tff(58,plain,
% 2.67/2.01 (^[V_m: $i, V_n: $i, T_a: $i] : refl(((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))) <=> ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(59,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[58])).
% 2.67/2.01 tff(60,plain,
% 2.67/2.01 (^[V_m: $i, V_n: $i, T_a: $i] : rewrite(((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(61,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[60])).
% 2.67/2.01 tff(62,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(63,plain,
% 2.67/2.01 (^[V_m: $i, V_n: $i, T_a: $i] : trans(monotonicity(rewrite((((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) <=> (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))), ((class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> (class_Power_Opower(T_a) => (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))), rewrite((class_Power_Opower(T_a) => (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))), ((class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(64,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : (class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) <=> ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[63])).
% 2.67/2.01 tff(65,axiom,(![V_m: $i, V_n: $i, T_a: $i] : (class_Power_Opower(T_a) => (((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_realpow__num__eq__if')).
% 2.67/2.01 tff(66,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.67/2.01 tff(67,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.67/2.01 tff(68,plain,(
% 2.67/2.01 ![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a))) & ((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(skolemize,[status(sab)],[67])).
% 2.67/2.01 tff(69,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[68, 61])).
% 2.67/2.01 tff(70,plain,
% 2.67/2.01 (![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[69, 59])).
% 2.67/2.01 tff(71,plain,
% 2.67/2.01 (((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) <=> ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(72,plain,
% 2.67/2.01 ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | ((~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))),
% 2.67/2.01 inference(quant_inst,[status(thm)],[])).
% 2.67/2.01 tff(73,plain,
% 2.67/2.01 ((~![V_m: $i, V_n: $i, T_a: $i] : ((~class_Power_Opower(T_a)) | (~((~((~(V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = c_Groups_Oone__class_Oone(T_a)))) | (~((V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_m), hAPP(hAPP(c_Power_Opower__class_Opower(T_a), V_m), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, V_n, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))))) | (~class_Power_Opower(tc_Complex_Ocomplex)) | (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[72, 71])).
% 2.67/2.01 tff(74,plain,
% 2.67/2.01 (~((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[73, 70, 57])).
% 2.67/2.01 tff(75,plain,
% 2.67/2.01 (((~((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) | (~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))) | ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))),
% 2.67/2.01 inference(tautology,[status(thm)],[])).
% 2.67/2.01 tff(76,plain,
% 2.67/2.01 ((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[75, 74])).
% 2.67/2.01 tff(77,plain,
% 2.67/2.01 ((~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) <=> (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(78,axiom,(~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_kas_I2_J')).
% 2.67/2.01 tff(79,plain,
% 2.67/2.01 (~(v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.67/2.01 tff(80,plain,
% 2.67/2.01 ((~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) | (v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(tautology,[status(thm)],[])).
% 2.67/2.01 tff(81,plain,
% 2.67/2.01 ((~((v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))) | (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[80, 79])).
% 2.67/2.01 tff(82,plain,
% 2.67/2.01 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[81, 76])).
% 2.67/2.01 tff(83,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)),
% 2.67/2.01 inference(symmetry,[status(thm)],[82])).
% 2.67/2.01 tff(84,plain,
% 2.67/2.01 (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____))),
% 2.67/2.01 inference(monotonicity,[status(thm)],[83])).
% 2.67/2.01 tff(85,plain,
% 2.67/2.01 (hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
% 2.67/2.01 inference(symmetry,[status(thm)],[84])).
% 2.67/2.01 tff(86,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), B_z!1), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_a____)),
% 2.67/2.01 inference(monotonicity,[status(thm)],[85])).
% 2.67/2.01 tff(87,plain,
% 2.67/2.01 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),
% 2.67/2.01 inference(transitivity,[status(thm)],[86, 54, 39, 22])).
% 2.67/2.01 tff(88,plain,
% 2.67/2.01 (^[V_y_2: $i, V_x_2: $i, T_a: $i] : refl(((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))) <=> ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(89,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))) <=> ![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[88])).
% 2.67/2.01 tff(90,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))) <=> ![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(91,plain,
% 2.67/2.01 (^[V_y_2: $i, V_x_2: $i, T_a: $i] : rewrite((class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))) <=> ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(92,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : (class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2)))) <=> ![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(quant_intro,[status(thm)],[91])).
% 2.67/2.01 tff(93,axiom,(![V_y_2: $i, V_x_2: $i, T_a: $i] : (class_Groups_Ogroup__add(T_a) => ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fact_add__eq__0__iff')).
% 2.67/2.01 tff(94,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[93, 92])).
% 2.67/2.01 tff(95,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[94, 90])).
% 2.67/2.01 tff(96,plain,(
% 2.67/2.01 ![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(skolemize,[status(sab)],[95])).
% 2.67/2.01 tff(97,plain,
% 2.67/2.01 (![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[96, 89])).
% 2.67/2.01 tff(98,plain,
% 2.67/2.01 (((~![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))) | ((~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | ((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))))) <=> ((~![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | ((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))))),
% 2.67/2.01 inference(rewrite,[status(thm)],[])).
% 2.67/2.01 tff(99,plain,
% 2.67/2.01 ((~![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))) | ((~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | ((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))))),
% 2.67/2.01 inference(quant_inst,[status(thm)],[])).
% 2.67/2.01 tff(100,plain,
% 2.67/2.01 ((~![V_y_2: $i, V_x_2: $i, T_a: $i] : ((~class_Groups_Ogroup__add(T_a)) | ((c_Groups_Oplus__class_Oplus(T_a, V_x_2, V_y_2) = c_Groups_Ozero__class_Ozero(T_a)) <=> (V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a, V_x_2))))) | (~class_Groups_Ogroup__add(tc_Complex_Ocomplex)) | ((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))),
% 2.67/2.01 inference(modus_ponens,[status(thm)],[99, 98])).
% 2.67/2.01 tff(101,plain,
% 2.67/2.01 ((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 2.67/2.01 inference(unit_resolution,[status(thm)],[100, 97, 3])).
% 2.67/2.01 tff(102,plain,
% 2.67/2.01 (^[B_w: $i] : refl((~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.01 inference(bind,[status(th)],[])).
% 2.67/2.01 tff(103,plain,
% 2.67/2.01 (![B_w: $i] : (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> ![B_w: $i] : (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(quant_intro,[status(thm)],[102])).
% 2.67/2.02 tff(104,plain,
% 2.67/2.02 ((~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) <=> (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(rewrite,[status(thm)],[])).
% 2.67/2.02 tff(105,plain,
% 2.67/2.02 (($false | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(rewrite,[status(thm)],[])).
% 2.67/2.02 tff(106,axiom,(~v_thesis____), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 2.67/2.02 tff(107,plain,
% 2.67/2.02 (v_thesis____ <=> $false),
% 2.67/2.02 inference(iff_false,[status(thm)],[106])).
% 2.67/2.02 tff(108,plain,
% 2.67/2.02 ((v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> ($false | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.02 inference(monotonicity,[status(thm)],[107, 104])).
% 2.67/2.02 tff(109,plain,
% 2.67/2.02 ((v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(transitivity,[status(thm)],[108, 105])).
% 2.67/2.02 tff(110,plain,
% 2.67/2.02 ((v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) <=> (v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.02 inference(monotonicity,[status(thm)],[104])).
% 2.67/2.02 tff(111,plain,
% 2.67/2.02 ((?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) => v_thesis____) <=> (v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))),
% 2.67/2.02 inference(rewrite,[status(thm)],[])).
% 2.67/2.02 tff(112,axiom,(?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) => v_thesis____), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 2.67/2.02 tff(113,plain,
% 2.67/2.02 (v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[112, 111])).
% 2.67/2.02 tff(114,plain,
% 2.67/2.02 (v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[113, 110])).
% 2.67/2.02 tff(115,plain,
% 2.67/2.02 (v_thesis____ | (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[114, 110])).
% 2.67/2.02 tff(116,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[115, 109])).
% 2.67/2.02 tff(117,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[116, 104])).
% 2.67/2.02 tff(118,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[117, 104])).
% 2.67/2.02 tff(119,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[118, 104])).
% 2.67/2.02 tff(120,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[119, 104])).
% 2.67/2.02 tff(121,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[120, 104])).
% 2.67/2.02 tff(122,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[121, 104])).
% 2.67/2.02 tff(123,plain,
% 2.67/2.02 (~?[B_w: $i] : (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[122, 104])).
% 2.67/2.02 tff(124,plain,
% 2.67/2.02 (^[B_w: $i] : refl($oeq((~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))),
% 2.67/2.02 inference(bind,[status(th)],[])).
% 2.67/2.02 tff(125,plain,(
% 2.67/2.02 ![B_w: $i] : (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(nnf-neg,[status(sab)],[123, 124])).
% 2.67/2.02 tff(126,plain,
% 2.67/2.02 (![B_w: $i] : (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(modus_ponens,[status(thm)],[125, 103])).
% 2.67/2.02 tff(127,plain,
% 2.67/2.02 ((~![B_w: $i] : (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_w), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) | (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
% 2.67/2.02 inference(quant_inst,[status(thm)],[])).
% 2.67/2.02 tff(128,plain,
% 2.67/2.02 (~(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
% 2.67/2.02 inference(unit_resolution,[status(thm)],[127, 126])).
% 2.67/2.07 tff(129,plain,
% 2.67/2.07 ((~((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))) | (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))),
% 2.67/2.07 inference(tautology,[status(thm)],[])).
% 2.67/2.07 tff(130,plain,
% 2.67/2.07 ((~((c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) <=> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))) | (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))))),
% 2.67/2.07 inference(unit_resolution,[status(thm)],[129, 128])).
% 2.67/2.07 tff(131,plain,
% 2.67/2.07 (~(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), B_z!1), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
% 2.67/2.07 inference(unit_resolution,[status(thm)],[130, 101])).
% 2.67/2.07 tff(132,plain,
% 2.67/2.07 ($false),
% 2.67/2.07 inference(unit_resolution,[status(thm)],[131, 87])).
% 2.67/2.07 % SZS output end Proof
%------------------------------------------------------------------------------