TSTP Solution File: NUM857+2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM857+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 14:31:09 EDT 2022
% Result : Theorem 0.44s 0.68s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 14 unt; 1 nHn; 23 RR)
% Number of literals : 35 ( 0 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
geq(vd529,vd530),
file('NUM857+2.p',unknown),
[] ).
cnf(2,axiom,
geq(vd526,vd527),
file('NUM857+2.p',unknown),
[] ).
cnf(23,axiom,
( ~ greater(u,v)
| geq(u,v) ),
file('NUM857+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ equal(u,v)
| geq(u,v) ),
file('NUM857+2.p',unknown),
[] ).
cnf(28,axiom,
~ geq(vmul(vd526,vd529),vmul(vd527,vd530)),
file('NUM857+2.p',unknown),
[] ).
cnf(43,axiom,
( ~ geq(u,v)
| equal(u,v)
| greater(u,v) ),
file('NUM857+2.p',unknown),
[] ).
cnf(65,axiom,
( ~ geq(u,v)
| ~ greater(w,x)
| greater(vmul(u,w),vmul(v,x)) ),
file('NUM857+2.p',unknown),
[] ).
cnf(66,axiom,
( ~ greater(u,v)
| ~ geq(w,x)
| greater(vmul(u,w),vmul(v,x)) ),
file('NUM857+2.p',unknown),
[] ).
cnf(77,plain,
~ greater(vmul(vd526,vd529),vmul(vd527,vd530)),
inference(res,[status(thm),theory(equality)],[23,28]),
[iquote('0:Res:23.1,28.0')] ).
cnf(78,plain,
~ equal(vmul(vd527,vd530),vmul(vd526,vd529)),
inference(res,[status(thm),theory(equality)],[24,28]),
[iquote('0:Res:24.1,28.0')] ).
cnf(2042,plain,
( ~ greater(vd526,vd527)
| ~ geq(vd529,vd530) ),
inference(res,[status(thm),theory(equality)],[66,77]),
[iquote('0:Res:66.2,77.0')] ).
cnf(2044,plain,
~ greater(vd526,vd527),
inference(mrr,[status(thm)],[2042,1]),
[iquote('0:MRR:2042.1,1.0')] ).
cnf(2048,plain,
( ~ geq(vd526,vd527)
| equal(vd527,vd526) ),
inference(res,[status(thm),theory(equality)],[43,2044]),
[iquote('0:Res:43.2,2044.0')] ).
cnf(2049,plain,
equal(vd527,vd526),
inference(mrr,[status(thm)],[2048,2]),
[iquote('0:MRR:2048.0,2.0')] ).
cnf(2050,plain,
geq(vd526,vd526),
inference(rew,[status(thm),theory(equality)],[2049,2]),
[iquote('0:Rew:2049.0,2.0')] ).
cnf(2052,plain,
~ equal(vmul(vd526,vd530),vmul(vd526,vd529)),
inference(rew,[status(thm),theory(equality)],[2049,78]),
[iquote('0:Rew:2049.0,78.0')] ).
cnf(2053,plain,
~ greater(vmul(vd526,vd529),vmul(vd526,vd530)),
inference(rew,[status(thm),theory(equality)],[2049,77]),
[iquote('0:Rew:2049.0,77.0')] ).
cnf(2183,plain,
( ~ geq(vd526,vd526)
| ~ greater(vd529,vd530) ),
inference(res,[status(thm),theory(equality)],[65,2053]),
[iquote('0:Res:65.2,2053.0')] ).
cnf(2184,plain,
~ greater(vd529,vd530),
inference(mrr,[status(thm)],[2183,2050]),
[iquote('0:MRR:2183.0,2050.0')] ).
cnf(2188,plain,
( ~ geq(vd529,vd530)
| equal(vd530,vd529) ),
inference(res,[status(thm),theory(equality)],[43,2184]),
[iquote('0:Res:43.2,2184.0')] ).
cnf(2189,plain,
equal(vd530,vd529),
inference(mrr,[status(thm)],[2188,1]),
[iquote('0:MRR:2188.0,1.0')] ).
cnf(2193,plain,
~ equal(vmul(vd526,vd529),vmul(vd526,vd529)),
inference(rew,[status(thm),theory(equality)],[2189,2052]),
[iquote('0:Rew:2189.0,2052.0')] ).
cnf(2199,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2193]),
[iquote('0:Obv:2193.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM857+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 14:41:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.44/0.68
% 0.44/0.68 SPASS V 3.9
% 0.44/0.68 SPASS beiseite: Proof found.
% 0.44/0.68 % SZS status Theorem
% 0.44/0.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.68 SPASS derived 1871 clauses, backtracked 0 clauses, performed 0 splits and kept 865 clauses.
% 0.44/0.68 SPASS allocated 86517 KBytes.
% 0.44/0.68 SPASS spent 0:00:00.33 on the problem.
% 0.44/0.68 0:00:00.04 for the input.
% 0.44/0.68 0:00:00.03 for the FLOTTER CNF translation.
% 0.44/0.68 0:00:00.02 for inferences.
% 0.44/0.68 0:00:00.00 for the backtracking.
% 0.44/0.68 0:00:00.21 for the reduction.
% 0.44/0.68
% 0.44/0.68
% 0.44/0.68 Here is a proof with depth 3, length 23 :
% 0.44/0.68 % SZS output start Refutation
% See solution above
% 0.50/0.68 Formulae used in the proof : holds_a40_conjunct2_a40_antec_a40_323_a41__a41__a44__a32_531_a44__a32_0_a41_ holds_a40_conjunct1_a40_antec_a40_323_a41__a41__a44__a32_528_a44__a32_0_a41_ def_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_16_a41__a44__a32_1_a41_ holds_a40_conseq_a40_323_a41__a44__a32_532_a44__a32_0_a41_ ass_a40_cond_a40_318_a44__a32_0_a41__a44__a32_0_a41_
% 0.50/0.68
%------------------------------------------------------------------------------