%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM844+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 : 600s
% DateTime : Mon Jul 18 14:30:59 EDT 2022
% Result : Theorem 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 6 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(25,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM844+1.p',unknown),
[] ).
cnf(33,axiom,
equal(vplus(vsucc(u),v),vsucc(vplus(u,v))),
file('NUM844+1.p',unknown),
[] ).
cnf(34,axiom,
equal(vplus(u,vsucc(v)),vsucc(vplus(u,v))),
file('NUM844+1.p',unknown),
[] ).
cnf(64,axiom,
~ equal(vplus(vmul(vd411,vd413),vplus(vsucc(vd411),vd413)),vplus(vmul(vd411,vd413),vplus(vd413,vsucc(vd411)))),
file('NUM844+1.p',unknown),
[] ).
cnf(71,plain,
~ equal(vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413))),vsucc(vplus(vmul(vd411,vd413),vplus(vd411,vd413)))),
inference(rew,[status(thm),theory(equality)],[34,64,33,25]),
[iquote('0:Rew:34.0,64.0,33.0,64.0,34.0,64.0,25.0,64.0,34.0,64.0')] ).
cnf(72,plain,
$false,
inference(obv,[status(thm),theory(equality)],[71]),
[iquote('0:Obv:71.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM844+1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 18:37:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 48 clauses.
% 0.18/0.44 SPASS allocated 85283 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.44 0:00:00.04 for the input.
% 0.18/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.00 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 0, length 6 :
% 0.18/0.44 % SZS output start Refutation
% See solution above
% 0.18/0.44 Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_52_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_3_a41__a44__a32_and_a40_holds_a40_definiens_a40_29_a41__a44__a32_45_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_29_a41__a44__a32_44_a44__a32_0_a41__a41__a41_ holds_a40_266_a44__a32_415_a44__a32_3_a41_
% 0.18/0.44
%------------------------------------------------------------------------------