TSTP Solution File: NUM849+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.17s 0.43s
% Output : Refutation 0.17s
% 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(14,axiom,
equal(vmul(u,v),vmul(v,u)),
file('NUM849+1.p',unknown),
[] ).
cnf(24,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM849+1.p',unknown),
[] ).
cnf(38,axiom,
equal(vmul(vsucc(u),v),vplus(vmul(u,v),v)),
file('NUM849+1.p',unknown),
[] ).
cnf(39,axiom,
equal(vmul(u,vsucc(v)),vplus(vmul(u,v),u)),
file('NUM849+1.p',unknown),
[] ).
cnf(42,axiom,
equal(vmul(vmul(vd448,vd449),skc1),vmul(vd448,vmul(vd449,skc1))),
file('NUM849+1.p',unknown),
[] ).
cnf(57,axiom,
equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
file('NUM849+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(vmul(vmul(vd448,vd449),vsucc(skc1)),vmul(vd448,vmul(vd449,vsucc(skc1)))),
file('NUM849+1.p',unknown),
[] ).
cnf(70,plain,
equal(vmul(u,vsucc(v)),vplus(u,vmul(u,v))),
inference(rew,[status(thm),theory(equality)],[24,39]),
[iquote('0:Rew:24.0,39.0')] ).
cnf(71,plain,
equal(vmul(vsucc(u),v),vplus(v,vmul(u,v))),
inference(rew,[status(thm),theory(equality)],[24,38]),
[iquote('0:Rew:24.0,38.0')] ).
cnf(72,plain,
equal(vmul(skc1,vmul(vd448,vd449)),vmul(vd448,vmul(vd449,skc1))),
inference(rew,[status(thm),theory(equality)],[14,42]),
[iquote('0:Rew:14.0,42.0')] ).
cnf(73,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)],[72,58,71,14,57,70]),
[iquote('0:Rew:72.0,58.0,71.0,58.0,14.0,58.0,57.0,58.0,70.0,58.0')] ).
cnf(74,plain,
$false,
inference(obv,[status(thm),theory(equality)],[73]),
[iquote('0:Obv:73.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM849+1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 23:39:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.17/0.43
% 0.17/0.43 SPASS V 3.9
% 0.17/0.43 SPASS beiseite: Proof found.
% 0.17/0.43 % SZS status Theorem
% 0.17/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 41 clauses.
% 0.17/0.43 SPASS allocated 85306 KBytes.
% 0.17/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.17/0.43 0:00:00.04 for the input.
% 0.17/0.43 0:00:00.03 for the FLOTTER CNF translation.
% 0.17/0.43 0:00:00.00 for inferences.
% 0.17/0.43 0:00:00.00 for the backtracking.
% 0.17/0.43 0:00:00.00 for the reduction.
% 0.17/0.43
% 0.17/0.43
% 0.17/0.43 Here is a proof with depth 0, length 12 :
% 0.17/0.43 % SZS output start Refutation
% See solution above
% 0.17/0.43 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_
% 0.17/0.43
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