TSTP Solution File: NUM851+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:31:05 EDT 2022
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 0 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(vplus(vd471,vd473),vd470),
file('NUM851+2.p',unknown),
[] ).
cnf(11,axiom,
equal(vmul(u,v),vmul(v,u)),
file('NUM851+2.p',unknown),
[] ).
cnf(28,axiom,
equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
file('NUM851+2.p',unknown),
[] ).
cnf(29,axiom,
~ equal(vmul(vplus(vd471,vd473),vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
file('NUM851+2.p',unknown),
[] ).
cnf(36,plain,
~ equal(vmul(vd469,vd470),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[11,29,2]),
[iquote('0:Rew:11.0,29.0,2.0,29.0')] ).
cnf(465,plain,
equal(vmul(u,vd470),vplus(vmul(u,vd471),vmul(u,vd473))),
inference(spr,[status(thm),theory(equality)],[2,28]),
[iquote('0:SpR:2.0,28.0')] ).
cnf(475,plain,
~ equal(vplus(vmul(vd469,vd471),vmul(vd469,vd473)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[465,36]),
[iquote('0:Rew:465.0,36.0')] ).
cnf(482,plain,
~ equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[11,475]),
[iquote('0:Rew:11.0,475.0,11.0,475.0')] ).
cnf(483,plain,
$false,
inference(obv,[status(thm),theory(equality)],[482]),
[iquote('0:Obv:482.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM851+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 5 14:14:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 348 clauses, backtracked 0 clauses, performed 0 splits and kept 188 clauses.
% 0.21/0.48 SPASS allocated 85485 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.21/0.48 0:00:00.04 for the input.
% 0.21/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.03 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 1, length 9 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : holds_a40_conseq_conjunct1_a40_conseq_a40_302_a41__a41__a44__a32_474_a44__a32_0_a41_ ass_a40_cond_a40_270_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_281_a44__a32_0_a41__a44__a32_0_a41_ holds_a40_conseq_conjunct2_a40_conseq_a40_302_a41__a41__a44__a32_475_a44__a32_1_a41_
% 0.21/0.48
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