%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 14:31:02 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM848+2.p',unknown),
[] ).
cnf(10,axiom,
equal(vplus(vmul(u,v),u),vmul(u,vsucc(v))),
file('NUM848+2.p',unknown),
[] ).
cnf(17,axiom,
~ equal(vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))),
file('NUM848+2.p',unknown),
[] ).
cnf(20,plain,
equal(vplus(u,vmul(u,v)),vmul(u,vsucc(v))),
inference(rew,[status(thm),theory(equality)],[4,10]),
[iquote('0:Rew:4.0,10.0')] ).
cnf(26,plain,
~ equal(vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))),
inference(rew,[status(thm),theory(equality)],[20,17,4]),
[iquote('0:Rew:20.0,17.0,4.0,17.0')] ).
cnf(27,plain,
$false,
inference(obv,[status(thm),theory(equality)],[26]),
[iquote('0:Obv:26.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM848+2 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n006.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 14:49:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.18/0.43 SPASS allocated 85108 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.00 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 0, length 6 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_32_a41__a44__a32_and_a40_holds_a40_definiens_a40_249_a41__a44__a32_399_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_249_a41__a44__a32_398_a44__a32_0_a41__a41__a41_ holds_a40_286_a44__a32_441_a44__a32_4_a41_
% 0.18/0.43
%------------------------------------------------------------------------------