TSTP Solution File: NUM845+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM845+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 14:31:00 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 11 unt; 0 nHn; 19 RR)
% Number of literals : 27 ( 0 equ; 12 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(25,axiom,
equal(vplus(u,v),vplus(v,u)),
file('NUM845+1.p',unknown),
[] ).
cnf(33,axiom,
equal(vplus(vsucc(u),v),vsucc(vplus(u,v))),
file('NUM845+1.p',unknown),
[] ).
cnf(34,axiom,
equal(vplus(u,vsucc(v)),vsucc(vplus(u,v))),
file('NUM845+1.p',unknown),
[] ).
cnf(37,axiom,
equal(vplus(vmul(vd411,skc1),skc1),vmul(vsucc(vd411),skc1)),
file('NUM845+1.p',unknown),
[] ).
cnf(54,axiom,
equal(vplus(vplus(u,v),w),vplus(u,vplus(v,w))),
file('NUM845+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(vplus(vmul(vd411,vsucc(skc1)),vsucc(skc1)),vmul(vsucc(vd411),vsucc(skc1))),
file('NUM845+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vmul(vsucc(vd411),u),vsucc(vd411)),vmul(vsucc(vd411),vsucc(u))) ),
file('NUM845+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vplus(vmul(vd411,u),u),vsucc(vd411)),vplus(vmul(vsucc(vd411),u),vsucc(vd411))) ),
file('NUM845+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vplus(vmul(vd411,u),vd411),vsucc(u)),vplus(vmul(vd411,vsucc(u)),vsucc(u))) ),
file('NUM845+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ equal(vplus(vmul(vd411,u),u),vmul(vsucc(vd411),u))
| equal(vplus(vmul(vd411,u),vplus(u,vsucc(vd411))),vplus(vmul(vd411,u),vplus(vsucc(vd411),u))) ),
file('NUM845+1.p',unknown),
[] ).
cnf(73,plain,
equal(vplus(skc1,vmul(vd411,skc1)),vmul(vsucc(vd411),skc1)),
inference(rew,[status(thm),theory(equality)],[25,37]),
[iquote('0:Rew:25.0,37.0')] ).
cnf(74,plain,
~ equal(vsucc(vplus(skc1,vmul(vd411,vsucc(skc1)))),vmul(vsucc(vd411),vsucc(skc1))),
inference(rew,[status(thm),theory(equality)],[33,56,25]),
[iquote('0:Rew:33.0,56.0,25.0,56.0')] ).
cnf(76,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(vd411,vmul(vsucc(vd411),u))),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[33,62,25]),
[iquote('0:Rew:33.0,62.1,25.0,62.1,25.0,62.0')] ).
cnf(77,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(vmul(vd411,u),vplus(u,vd411))),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[34,63,54,76,33,25]),
[iquote('0:Rew:34.0,63.1,34.0,63.1,54.0,63.1,76.1,63.1,33.0,63.1,25.0,63.1,25.0,63.0')] ).
cnf(78,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(vmul(vd411,u),vplus(vd411,u))),vsucc(vplus(u,vmul(vd411,vsucc(u))))) ),
inference(rew,[status(thm),theory(equality)],[34,64,54,33,25]),
[iquote('0:Rew:34.0,64.1,34.0,64.1,54.0,64.1,33.0,64.1,25.0,64.1,25.0,64.0')] ).
cnf(79,plain,
( ~ equal(vplus(u,vmul(vd411,u)),vmul(vsucc(vd411),u))
| equal(vsucc(vplus(u,vmul(vd411,vsucc(u)))),vmul(vsucc(vd411),vsucc(u))) ),
inference(rew,[status(thm),theory(equality)],[77,66,34,78,33,25]),
[iquote('0:Rew:77.1,66.1,34.0,66.1,34.0,66.1,78.1,66.1,34.0,66.1,33.0,66.1,25.0,66.0')] ).
cnf(95,plain,
~ equal(vplus(skc1,vmul(vd411,skc1)),vmul(vsucc(vd411),skc1)),
inference(res,[status(thm),theory(equality)],[79,74]),
[iquote('0:Res:79.1,74.0')] ).
cnf(112,plain,
~ equal(vmul(vsucc(vd411),skc1),vmul(vsucc(vd411),skc1)),
inference(rew,[status(thm),theory(equality)],[73,95]),
[iquote('0:Rew:73.0,95.0')] ).
cnf(113,plain,
$false,
inference(obv,[status(thm),theory(equality)],[112]),
[iquote('0:Obv:112.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM845+1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 07:35:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45
% 0.19/0.45 SPASS V 3.9
% 0.19/0.45 SPASS beiseite: Proof found.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 SPASS derived 18 clauses, backtracked 0 clauses, performed 0 splits and kept 62 clauses.
% 0.19/0.45 SPASS allocated 85318 KBytes.
% 0.19/0.45 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.45 0:00:00.04 for the input.
% 0.19/0.45 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45 0:00:00.00 for inferences.
% 0.19/0.45 0:00:00.00 for the backtracking.
% 0.19/0.45 0:00:00.00 for the reduction.
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 Here is a proof with depth 1, length 19 :
% 0.19/0.45 % SZS output start Refutation
% See solution above
% 0.19/0.45 Formulae used in the proof : ass_a40_cond_a40_61_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_52_a44__a32_0_a41__a44__a32_0_a41_ qu_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_3_a41__a44__a32_and_a40_holds_a40_definiens_a40_29_a41__a44__a32_45_a44__a32_0_a41__a44__a32_holds_a40_definiens_a40_29_a41__a44__a32_44_a44__a32_0_a41__a41__a41_ qu_a40_ind_a40_267_a41__a44__a32_imp_a40_267_a41__a41_ ass_a40_cond_a40_33_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_7_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_6_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_0_a41_ ass_a40_cond_a40_conseq_a40_263_a41__a44__a32_1_a41__a44__a32_4_a41_
% 0.19/0.45
%------------------------------------------------------------------------------