%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP611-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:48:17 EDT 2022
% Result : Unsatisfiable 0.50s 0.67s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 24 RR)
% Number of literals : 24 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(inverse(double_divide(inverse(double_divide(inverse(double_divide(u,v)),w)),double_divide(u,w))),v),
file('GRP611-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP611-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP611-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),multiply(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(7,plain,
equal(multiply(double_divide(multiply(u,v),double_divide(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(multiply(double_divide(u,v),multiply(v,w)),double_divide(multiply(u,x),double_divide(x,w))),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(15,plain,
equal(double_divide(u,multiply(double_divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(32,plain,
equal(multiply(multiply(double_divide(multiply(u,v),w),u),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[15,2]),
[iquote('0:SpR:15.0,2.0')] ).
cnf(42,plain,
equal(double_divide(multiply(u,v),double_divide(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[6,15]),
[iquote('0:SpR:6.0,15.0')] ).
cnf(44,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[42,2]),
[iquote('0:SpR:42.0,2.0')] ).
cnf(130,plain,
equal(multiply(multiply(double_divide(u,v),multiply(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(174,plain,
equal(multiply(multiply(double_divide(u,v),multiply(double_divide(w,x),multiply(x,u))),w),inverse(v)),
inference(spr,[status(thm),theory(equality)],[130,32]),
[iquote('0:SpR:130.0,32.0')] ).
cnf(182,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,w)),x),u),multiply(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[4,130]),
[iquote('0:SpR:4.0,130.0')] ).
cnf(184,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,multiply(w,x))),inverse(w)),u),multiply(x,v)),
inference(spr,[status(thm),theory(equality)],[44,130]),
[iquote('0:SpR:44.0,130.0')] ).
cnf(195,plain,
equal(multiply(multiply(u,v),multiply(inverse(u),w)),multiply(v,w)),
inference(rew,[status(thm),theory(equality)],[182,184]),
[iquote('0:Rew:182.0,184.0')] ).
cnf(386,plain,
equal(multiply(u,multiply(inverse(double_divide(v,w)),x)),multiply(multiply(w,multiply(u,v)),x)),
inference(spr,[status(thm),theory(equality)],[4,195]),
[iquote('0:SpR:4.0,195.0')] ).
cnf(397,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(v,multiply(multiply(u,w),x))),
inference(rew,[status(thm),theory(equality)],[2,386]),
[iquote('0:Rew:2.0,386.0')] ).
cnf(409,plain,
equal(multiply(double_divide(u,v),multiply(multiply(double_divide(w,x),multiply(v,w)),u)),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,174]),
[iquote('0:Rew:397.0,174.0')] ).
cnf(418,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(multiply(double_divide(w,x),w),u))),inverse(x)),
inference(rew,[status(thm),theory(equality)],[397,409]),
[iquote('0:Rew:397.0,409.0')] ).
cnf(419,plain,
equal(multiply(double_divide(u,v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,418]),
[iquote('0:Rew:4.0,418.0')] ).
cnf(456,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[42,419]),
[iquote('0:SpR:42.0,419.0')] ).
cnf(646,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,456]),
[iquote('0:Rew:2.0,456.0')] ).
cnf(647,plain,
$false,
inference(unc,[status(thm)],[646,3]),
[iquote('0:UnC:646.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP611-1 : TPTP v8.1.0. Released v2.6.0.
% 0.14/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 02:26:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.50/0.67
% 0.50/0.67 SPASS V 3.9
% 0.50/0.67 SPASS beiseite: Proof found.
% 0.50/0.67 % SZS status Theorem
% 0.50/0.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.67 SPASS derived 754 clauses, backtracked 0 clauses, performed 0 splits and kept 488 clauses.
% 0.50/0.67 SPASS allocated 65087 KBytes.
% 0.50/0.67 SPASS spent 0:00:00.29 on the problem.
% 0.50/0.67 0:00:00.03 for the input.
% 0.50/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.50/0.67 0:00:00.01 for inferences.
% 0.50/0.67 0:00:00.00 for the backtracking.
% 0.50/0.67 0:00:00.23 for the reduction.
% 0.50/0.67
% 0.50/0.67
% 0.50/0.67 Here is a proof with depth 6, length 24 :
% 0.50/0.67 % SZS output start Refutation
% See solution above
% 0.50/0.67 Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 0.50/0.67
%------------------------------------------------------------------------------