TSTP Solution File: NUM851+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM851+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 14:31:04 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% 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(5,axiom,
equal(vplus(vd471,vd473),vd470),
file('NUM851+1.p',unknown),
[] ).
cnf(16,axiom,
equal(vmul(u,v),vmul(v,u)),
file('NUM851+1.p',unknown),
[] ).
cnf(58,axiom,
equal(vmul(u,vplus(v,w)),vplus(vmul(u,v),vmul(u,w))),
file('NUM851+1.p',unknown),
[] ).
cnf(59,axiom,
~ equal(vmul(vplus(vd471,vd473),vd469),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
file('NUM851+1.p',unknown),
[] ).
cnf(69,plain,
~ equal(vmul(vd469,vd470),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[16,59,5]),
[iquote('0:Rew:16.0,59.0,5.0,59.0')] ).
cnf(973,plain,
equal(vmul(u,vd470),vplus(vmul(u,vd471),vmul(u,vd473))),
inference(spr,[status(thm),theory(equality)],[5,58]),
[iquote('0:SpR:5.0,58.0')] ).
cnf(983,plain,
~ equal(vplus(vmul(vd469,vd471),vmul(vd469,vd473)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[973,69]),
[iquote('0:Rew:973.0,69.0')] ).
cnf(996,plain,
~ equal(vplus(vmul(vd471,vd469),vmul(vd473,vd469)),vplus(vmul(vd471,vd469),vmul(vd473,vd469))),
inference(rew,[status(thm),theory(equality)],[16,983]),
[iquote('0:Rew:16.0,983.0,16.0,983.0')] ).
cnf(997,plain,
$false,
inference(obv,[status(thm),theory(equality)],[996]),
[iquote('0:Obv:996.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM851+1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 20:41:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.54
% 0.20/0.54 SPASS V 3.9
% 0.20/0.54 SPASS beiseite: Proof found.
% 0.20/0.54 % SZS status Theorem
% 0.20/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.54 SPASS derived 766 clauses, backtracked 0 clauses, performed 0 splits and kept 459 clauses.
% 0.20/0.54 SPASS allocated 85846 KBytes.
% 0.20/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.54 0:00:00.04 for the input.
% 0.20/0.54 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.54 0:00:00.01 for inferences.
% 0.20/0.54 0:00:00.00 for the backtracking.
% 0.20/0.54 0:00:00.08 for the reduction.
% 0.20/0.54
% 0.20/0.54
% 0.20/0.54 Here is a proof with depth 1, length 9 :
% 0.20/0.54 % SZS output start Refutation
% See solution above
% 0.20/0.54 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_
% 0.20/0.54
%------------------------------------------------------------------------------