%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 11:47:55 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(u,divide(v,w)),divide(u,v)),w),
file('GRP532-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP532-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP532-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP532-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(10,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(17,plain,
equal(divide(u,divide(divide(v,divide(w,u)),v)),w),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(18,plain,
equal(inverse(divide(divide(u,v),u)),v),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(26,plain,
equal(divide(divide(u,inverse(v)),divide(u,divide(w,w))),v),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(31,plain,
equal(divide(multiply(u,v),divide(u,divide(w,w))),v),
inference(rew,[status(thm),theory(equality)],[5,26]),
[iquote('0:Rew:5.0,26.0')] ).
cnf(43,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(46,plain,
equal(multiply(divide(u,u),v),v),
inference(rew,[status(thm),theory(equality)],[43,10]),
[iquote('0:Rew:43.0,10.0')] ).
cnf(52,plain,
equal(divide(divide(u,v),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[18,43]),
[iquote('0:SpR:18.0,43.0')] ).
cnf(55,plain,
equal(divide(u,inverse(divide(v,u))),v),
inference(rew,[status(thm),theory(equality)],[52,17]),
[iquote('0:Rew:52.0,17.0')] ).
cnf(56,plain,
equal(multiply(u,divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[5,55]),
[iquote('0:Rew:5.0,55.0')] ).
cnf(62,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[56,46]),
[iquote('0:SpR:56.0,46.0')] ).
cnf(67,plain,
equal(divide(u,divide(v,w)),multiply(divide(u,v),w)),
inference(spr,[status(thm),theory(equality)],[1,56]),
[iquote('0:SpR:1.0,56.0')] ).
cnf(69,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[62,31]),
[iquote('0:Rew:62.0,31.0')] ).
cnf(77,plain,
equal(multiply(divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[67,62]),
[iquote('0:Rew:67.0,62.0')] ).
cnf(142,plain,
equal(multiply(u,v),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[69,77]),
[iquote('0:SpR:69.0,77.0')] ).
cnf(144,plain,
$false,
inference(unc,[status(thm)],[142,4]),
[iquote('0:UnC:142.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n014.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 : Mon Jun 13 23:52:36 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 112 clauses, backtracked 0 clauses, performed 0 splits and kept 54 clauses.
% 0.19/0.42 SPASS allocated 63247 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.42 0:00:00.03 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 3, length 21 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_4
% 0.19/0.42
%------------------------------------------------------------------------------