%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Thu Jul 14 23:49:21 EDT 2022
% Result : Unsatisfiable 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 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 : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(inverse(inverse(a)),a),
file('BOO001-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(multiply(u,v,w),x,multiply(u,v,y)),multiply(u,v,multiply(w,x,y))),
file('BOO001-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v,v),v),
file('BOO001-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,u,v),u),
file('BOO001-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(u,v,inverse(v)),u),
file('BOO001-1.p',unknown),
[] ).
cnf(16,plain,
equal(multiply(u,v,multiply(w,multiply(u,v,x),x)),multiply(u,v,x)),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(20,plain,
equal(multiply(multiply(u,u,v),w,u),multiply(u,u,multiply(v,w,x))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(21,plain,
equal(multiply(multiply(u,v,w),x,v),multiply(u,v,multiply(w,x,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(25,plain,
equal(multiply(u,v,multiply(w,u,x)),multiply(w,u,multiply(u,v,x))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(28,plain,
equal(multiply(u,v,u),u),
inference(rew,[status(thm),theory(equality)],[4,20]),
[iquote('0:Rew:4.0,20.0,4.0,20.0')] ).
cnf(36,plain,
equal(multiply(multiply(u,v,w),x,u),multiply(u,v,multiply(w,x,u))),
inference(spr,[status(thm),theory(equality)],[28,2]),
[iquote('0:SpR:28.0,2.0')] ).
cnf(95,plain,
equal(multiply(u,v,multiply(w,u,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[6,16]),
[iquote('0:SpR:6.0,16.0')] ).
cnf(119,plain,
equal(multiply(u,v,multiply(w,x,multiply(y,u,inverse(v)))),multiply(multiply(u,v,w),x,u)),
inference(spr,[status(thm),theory(equality)],[95,2]),
[iquote('0:SpR:95.0,2.0')] ).
cnf(130,plain,
equal(multiply(u,v,multiply(w,x,multiply(y,u,inverse(v)))),multiply(u,v,multiply(w,x,u))),
inference(rew,[status(thm),theory(equality)],[36,119]),
[iquote('0:Rew:36.0,119.0')] ).
cnf(172,plain,
equal(multiply(u,v,multiply(w,inverse(v),multiply(x,u,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[21,95]),
[iquote('0:SpR:21.0,95.0')] ).
cnf(187,plain,
equal(multiply(u,v,multiply(w,inverse(v),u)),u),
inference(rew,[status(thm),theory(equality)],[130,172]),
[iquote('0:Rew:130.0,172.0')] ).
cnf(270,plain,
equal(multiply(u,inverse(u),multiply(v,u,v)),v),
inference(spr,[status(thm),theory(equality)],[25,187]),
[iquote('0:SpR:25.0,187.0')] ).
cnf(315,plain,
equal(multiply(u,inverse(u),v),v),
inference(rew,[status(thm),theory(equality)],[28,270]),
[iquote('0:Rew:28.0,270.0')] ).
cnf(358,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[315,6]),
[iquote('0:SpR:315.0,6.0')] ).
cnf(380,plain,
$false,
inference(unc,[status(thm)],[358,1]),
[iquote('0:UnC:358.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 19:29:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 272 clauses, backtracked 0 clauses, performed 0 splits and kept 86 clauses.
% 0.20/0.47 SPASS allocated 63563 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.04 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 20 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : prove_inverse_is_self_cancelling associativity ternary_multiply_1 ternary_multiply_2 right_inverse
% 0.20/0.47
%------------------------------------------------------------------------------