TSTP Solution File: SWV633-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV633-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 : 600s
% DateTime : Wed Jul 20 21:44:38 EDT 2022
% Result : Unsatisfiable 4.10s 4.32s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 15 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(822,axiom,
equal(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
file('SWV633-1.p',unknown),
[] ).
cnf(1261,axiom,
equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),
file('SWV633-1.p',unknown),
[] ).
cnf(1306,axiom,
equal(c_HOL_Otimes__class_Otimes(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(u,u,tc_nat)),
file('SWV633-1.p',unknown),
[] ).
cnf(1307,axiom,
equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),u,tc_nat),c_HOL_Oplus__class_Oplus(u,u,tc_nat)),
file('SWV633-1.p',unknown),
[] ).
cnf(1326,axiom,
equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(u,v,tc_nat),w,tc_nat),c_HOL_Otimes__class_Otimes(u,c_HOL_Otimes__class_Otimes(v,w,tc_nat),tc_nat)),
file('SWV633-1.p',unknown),
[] ).
cnf(1346,axiom,
equal(c_HOL_Otimes__class_Otimes(u,v,tc_nat),c_HOL_Otimes__class_Otimes(v,u,tc_nat)),
file('SWV633-1.p',unknown),
[] ).
cnf(1484,axiom,
~ equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)),
file('SWV633-1.p',unknown),
[] ).
cnf(1493,plain,
equal(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat))),
inference(rew,[status(thm),theory(equality)],[822,1261]),
[iquote('0:Rew:822.0,1261.0')] ).
cnf(1518,plain,
equal(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),u,tc_nat),c_HOL_Oplus__class_Oplus(u,u,tc_nat)),
inference(rew,[status(thm),theory(equality)],[1493,1307]),
[iquote('0:Rew:1493.0,1307.0')] ).
cnf(1519,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),c_HOL_Oplus__class_Oplus(u,u,tc_nat)),
inference(rew,[status(thm),theory(equality)],[1493,1306]),
[iquote('0:Rew:1493.0,1306.0')] ).
cnf(1673,plain,
~ equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[1518,1484,1493]),
[iquote('0:Rew:1518.0,1484.0,1518.0,1484.0,1493.0,1484.0')] ).
cnf(24275,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Otimes__class_Otimes(v,w,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v,c_HOL_Otimes__class_Otimes(w,u,tc_nat),tc_nat)),
inference(spr,[status(thm),theory(equality)],[1326,1346]),
[iquote('0:SpR:1326.0,1346.0')] ).
cnf(24392,plain,
~ equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[24275,1673]),
[iquote('0:Rew:24275.0,1673.0')] ).
cnf(24424,plain,
~ equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[1519,24392]),
[iquote('0:Rew:1519.0,24392.0')] ).
cnf(24425,plain,
$false,
inference(obv,[status(thm),theory(equality)],[24424]),
[iquote('0:Obv:24424.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV633-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 10:32:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.10/4.32
% 4.10/4.32 SPASS V 3.9
% 4.10/4.32 SPASS beiseite: Proof found.
% 4.10/4.32 % SZS status Theorem
% 4.10/4.32 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/4.32 SPASS derived 19087 clauses, backtracked 0 clauses, performed 0 splits and kept 3597 clauses.
% 4.10/4.32 SPASS allocated 90723 KBytes.
% 4.10/4.32 SPASS spent 0:00:03.86 on the problem.
% 4.10/4.32 0:00:00.11 for the input.
% 4.10/4.32 0:00:00.00 for the FLOTTER CNF translation.
% 4.10/4.32 0:00:00.19 for inferences.
% 4.10/4.32 0:00:00.00 for the backtracking.
% 4.10/4.32 0:00:03.37 for the reduction.
% 4.10/4.32
% 4.10/4.32
% 4.10/4.32 Here is a proof with depth 1, length 15 :
% 4.10/4.32 % SZS output start Refutation
% See solution above
% 4.10/4.32 Formulae used in the proof : cls_One__nat__def_0 cls_comp__arith_I115_J_0 cls_nat__mult__2__right_0 cls_nat__mult__2_0 cls_nat__mult__assoc_0 cls_nat__mult__commute_0 cls_conjecture_0
% 4.10/4.32
%------------------------------------------------------------------------------