%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:48:49 EDT 2022
% Result : Unsatisfiable 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP665-11.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP665-11.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP665-11.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(rd(mult(u,v),u),mult(u,w)),mult(u,mult(v,w))),
file('GRP665-11.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(mult(u,v),ld(v,mult(w,v))),mult(mult(u,w),v)),
file('GRP665-11.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(op_c,u),mult(u,op_c)),
file('GRP665-11.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(x0__dfg,op_c),x1__dfg),mult(x0__dfg,mult(op_c,x1__dfg))),
file('GRP665-11.p',unknown),
[] ).
cnf(11,plain,
~ equal(mult(mult(op_c,x0__dfg),x1__dfg),mult(x0__dfg,mult(op_c,x1__dfg))),
inference(rew,[status(thm),theory(equality)],[9,10]),
[iquote('0:Rew:9.0,10.0')] ).
cnf(22,plain,
equal(rd(mult(u,op_c),u),op_c),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(53,plain,
equal(ld(op_c,mult(u,op_c)),u),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(146,plain,
equal(mult(op_c,mult(u,v)),mult(u,mult(op_c,v))),
inference(spr,[status(thm),theory(equality)],[22,7]),
[iquote('0:SpR:22.0,7.0')] ).
cnf(147,plain,
~ equal(mult(mult(op_c,x0__dfg),x1__dfg),mult(op_c,mult(x0__dfg,x1__dfg))),
inference(rew,[status(thm),theory(equality)],[146,11]),
[iquote('0:Rew:146.0,11.0')] ).
cnf(340,plain,
equal(mult(mult(u,op_c),v),mult(mult(u,v),op_c)),
inference(spr,[status(thm),theory(equality)],[53,8]),
[iquote('0:SpR:53.0,8.0')] ).
cnf(345,plain,
equal(mult(mult(u,op_c),ld(u,mult(v,u))),mult(mult(op_c,v),u)),
inference(spr,[status(thm),theory(equality)],[9,8]),
[iquote('0:SpR:9.0,8.0')] ).
cnf(354,plain,
equal(mult(mult(u,op_c),v),mult(op_c,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[9,340]),
[iquote('0:Rew:9.0,340.0')] ).
cnf(364,plain,
equal(mult(op_c,mult(u,ld(u,mult(v,u)))),mult(mult(op_c,v),u)),
inference(rew,[status(thm),theory(equality)],[354,345]),
[iquote('0:Rew:354.0,345.0')] ).
cnf(365,plain,
equal(mult(mult(op_c,u),v),mult(op_c,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[1,364]),
[iquote('0:Rew:1.0,364.0')] ).
cnf(366,plain,
$false,
inference(unc,[status(thm)],[365,147]),
[iquote('0:UnC:365.0,147.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GRP665-11 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.10 % Command : run_spass %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Mon Jun 13 04:00:41 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.38
% 0.14/0.38 SPASS V 3.9
% 0.14/0.38 SPASS beiseite: Proof found.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 SPASS derived 290 clauses, backtracked 0 clauses, performed 0 splits and kept 81 clauses.
% 0.14/0.38 SPASS allocated 63482 KBytes.
% 0.14/0.38 SPASS spent 0:00:00.07 on the problem.
% 0.14/0.38 0:00:00.03 for the input.
% 0.14/0.38 0:00:00.00 for the FLOTTER CNF translation.
% 0.14/0.38 0:00:00.00 for inferences.
% 0.14/0.38 0:00:00.00 for the backtracking.
% 0.14/0.38 0:00:00.02 for the reduction.
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 Here is a proof with depth 2, length 18 :
% 0.14/0.38 % SZS output start Refutation
% See solution above
% 0.14/0.38 Formulae used in the proof : f01 f02 f04 f07 f08 f09 goal
% 0.14/0.38
%------------------------------------------------------------------------------