TSTP Solution File: GRP684-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP684-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 11:48:58 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 18 ( 0 equ; 1 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(ld(u,mult(u,u)),u),
file('GRP684-1.p',unknown),
[] ).
cnf(2,axiom,
equal(rd(mult(u,u),u),u),
file('GRP684-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(u,ld(u,v)),ld(u,mult(u,v))),
file('GRP684-1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(rd(u,v),v),rd(mult(u,v),v)),
file('GRP684-1.p',unknown),
[] ).
cnf(6,axiom,
equal(rd(mult(mult(u,v),rd(w,x)),rd(w,x)),mult(u,rd(mult(v,x),x))),
file('GRP684-1.p',unknown),
[] ).
cnf(7,axiom,
equal(rd(mult(rd(u,u),v),v),ld(u,mult(u,ld(v,v)))),
file('GRP684-1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(rd(mult(a,mult(b,c)),mult(b,c)),rd(mult(a,c),c)),
file('GRP684-1.p',unknown),
[] ).
cnf(19,plain,
equal(rd(rd(mult(u,u),u),u),ld(u,mult(u,ld(u,u)))),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(20,plain,
equal(rd(u,u),ld(u,u)),
inference(rew,[status(thm),theory(equality)],[2,19,1,3]),
[iquote('0:Rew:2.0,19.0,1.0,19.0,3.0,19.0')] ).
cnf(25,plain,
equal(mult(ld(u,u),u),rd(mult(u,u),u)),
inference(spr,[status(thm),theory(equality)],[20,4]),
[iquote('0:SpR:20.0,4.0')] ).
cnf(27,plain,
equal(mult(ld(u,u),u),u),
inference(rew,[status(thm),theory(equality)],[2,25]),
[iquote('0:Rew:2.0,25.0')] ).
cnf(53,plain,
equal(mult(u,rd(mult(v,w),w)),rd(mult(mult(u,v),w),w)),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(65,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),mult(ld(u,u),rd(mult(u,w),w))),
inference(spr,[status(thm),theory(equality)],[27,6]),
[iquote('0:SpR:27.0,6.0')] ).
cnf(72,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(mult(ld(u,u),u),w),w)),
inference(rew,[status(thm),theory(equality)],[53,65]),
[iquote('0:Rew:53.0,65.0')] ).
cnf(73,plain,
equal(rd(mult(u,rd(v,w)),rd(v,w)),rd(mult(u,w),w)),
inference(rew,[status(thm),theory(equality)],[27,72]),
[iquote('0:Rew:27.0,72.0')] ).
cnf(102,plain,
equal(rd(mult(mult(u,v),v),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[2,53]),
[iquote('0:SpR:2.0,53.0')] ).
cnf(139,plain,
equal(rd(mult(u,mult(v,w)),mult(v,w)),rd(mult(u,w),w)),
inference(spr,[status(thm),theory(equality)],[102,73]),
[iquote('0:SpR:102.0,73.0')] ).
cnf(151,plain,
$false,
inference(unc,[status(thm)],[139,8]),
[iquote('0:UnC:139.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP684-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 12:19:53 EDT 2022
% 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 110 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.19/0.43 SPASS allocated 63473 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.08 on the problem.
% 0.19/0.43 0:00:00.03 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 4, length 18 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : c01 c02 c03 c04 c06 c07 goals
% 0.19/0.43
%------------------------------------------------------------------------------