TSTP Solution File: GRP709-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP709-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sat Jul 16 11:49:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 3 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP709-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(u,mult(v,u)),w),mult(u,mult(v,mult(u,w)))),
file('GRP709-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP709-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,v),op_c),mult(u,mult(v,op_c))),
file('GRP709-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(mult(op_c,op_c),a),b),mult(mult(op_c,op_c),mult(a,b))),
file('GRP709-1.p',unknown),
[] ).
cnf(11,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(v,op_c))),
inference(rew,[status(thm),theory(equality)],[8,9]),
[iquote('0:Rew:8.0,9.0')] ).
cnf(134,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(op_c,v))),
inference(spr,[status(thm),theory(equality)],[8,11]),
[iquote('0:SpR:8.0,11.0')] ).
cnf(250,plain,
equal(mult(u,mult(unit,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(253,plain,
equal(mult(mult(op_c,mult(op_c,u)),v),mult(op_c,mult(u,mult(op_c,v)))),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(266,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[6,250]),
[iquote('0:Rew:6.0,250.0')] ).
cnf(267,plain,
~ equal(mult(mult(op_c,mult(op_c,a)),b),mult(mult(op_c,op_c),mult(a,b))),
inference(rew,[status(thm),theory(equality)],[266,10]),
[iquote('0:Rew:266.0,10.0')] ).
cnf(270,plain,
~ equal(mult(op_c,mult(op_c,mult(a,b))),mult(op_c,mult(op_c,mult(a,b)))),
inference(rew,[status(thm),theory(equality)],[134,267,253,266]),
[iquote('0:Rew:134.0,267.0,253.0,267.0,266.0,267.0')] ).
cnf(271,plain,
$false,
inference(obv,[status(thm),theory(equality)],[270]),
[iquote('0:Obv:270.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP709-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n008.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 : Mon Jun 13 23:17:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 225 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.19/0.43 SPASS allocated 63393 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.02 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 1, length 13 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : c06 c07 c08 c09 goals
% 0.19/0.43
%------------------------------------------------------------------------------