TSTP Solution File: NUM849+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 14:31:03 EDT 2022
% Result : Theorem 0.21s 0.45s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
equal(vmul(u,v),vmul(v,u)),
file('NUM849+2.p',unknown),
[] ).
cnf(4,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM849+2.p',unknown),
[] ).
cnf(7,axiom,
equal(vmul(vsucc(u),v),vplus(vmul(u,v),v)),
file('NUM849+2.p',unknown),
[] ).
cnf(8,axiom,
equal(vmul(u,vsucc(v)),vplus(vmul(u,v),u)),
file('NUM849+2.p',unknown),
[] ).
cnf(9,axiom,
equal(vmul(vmul(vd448,vd449),skc1),vmul(vd448,vmul(vd449,skc1))),
file('NUM849+2.p',unknown),
[] ).
cnf(10,axiom,
equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
file('NUM849+2.p',unknown),
[] ).
cnf(11,axiom,
~ equal(vmul(vmul(vd448,vd449),vsucc(skc1)),vmul(vd448,vmul(vd449,vsucc(skc1)))),
file('NUM849+2.p',unknown),
[] ).
cnf(17,plain,
equal(vmul(u,vsucc(v)),vplus(u,vmul(u,v))),
inference(rew,[status(thm),theory(equality)],[4,8]),
[iquote('0:Rew:4.0,8.0')] ).
cnf(18,plain,
equal(vmul(vsucc(u),v),vplus(v,vmul(u,v))),
inference(rew,[status(thm),theory(equality)],[4,7]),
[iquote('0:Rew:4.0,7.0')] ).
cnf(19,plain,
equal(vmul(skc1,vmul(vd448,vd449)),vmul(vd448,vmul(vd449,skc1))),
inference(rew,[status(thm),theory(equality)],[3,9]),
[iquote('0:Rew:3.0,9.0')] ).
cnf(20,plain,
~ equal(vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,skc1))),vplus(vmul(vd448,vd449),vmul(vd448,vmul(vd449,skc1)))),
inference(rew,[status(thm),theory(equality)],[19,11,18,3,10,17]),
[iquote('0:Rew:19.0,11.0,18.0,11.0,3.0,11.0,10.0,11.0,17.0,11.0')] ).
cnf(21,plain,
$false,
inference(obv,[status(thm),theory(equality)],[20]),
[iquote('0:Obv:20.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM849+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jul 7 22:34:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.45
% 0.21/0.45 SPASS V 3.9
% 0.21/0.45 SPASS beiseite: Proof found.
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.45 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.21/0.45 SPASS allocated 85111 KBytes.
% 0.21/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.21/0.45 0:00:00.04 for the input.
% 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.45 0:00:00.00 for inferences.
% 0.21/0.45 0:00:00.00 for the backtracking.
% 0.21/0.45 0:00:00.00 for the reduction.
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 Here is a proof with depth 0, length 12 :
% 0.21/0.45 % SZS output start Refutation
% See solution above
% 0.21/0.45 Formulae used in the proof : ass_a40_cond_a40_270_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_261_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_ qu_a40_ind_a40_296_a41__a44__a32_imp_a40_296_a41__a41_ ass_a40_cond_a40_281_a44__a32_0_a41__a44__a32_0_a41_
% 0.21/0.45
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