%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP048-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 11:45:00 EDT 2022
% Result : Unsatisfiable 5.73s 5.96s
% Output : Refutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 20 unt; 0 nHn; 45 RR)
% Number of literals : 81 ( 0 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equalish(a,b),
file('GRP048-2.p',unknown),
[] ).
cnf(2,axiom,
~ equalish(inverse(a),inverse(b)),
file('GRP048-2.p',unknown),
[] ).
cnf(3,axiom,
product(identity,u,u),
file('GRP048-2.p',unknown),
[] ).
cnf(4,axiom,
product(inverse(u),u,identity),
file('GRP048-2.p',unknown),
[] ).
cnf(5,axiom,
product(u,v,multiply(u,v)),
file('GRP048-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP048-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP048-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP048-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equalish(u,v)
| ~ product(w,x,u)
| product(w,x,v) ),
file('GRP048-2.p',unknown),
[] ).
cnf(10,plain,
( ~ product(u,v,inverse(b))
| ~ product(u,v,inverse(a)) ),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.2,2.0')] ).
cnf(12,plain,
( ~ equalish(u,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.1')] ).
cnf(14,plain,
( ~ equalish(multiply(u,v),w)
| product(u,v,w) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.1')] ).
cnf(17,plain,
( ~ equalish(u,v)
| ~ equalish(v,w)
| product(identity,u,w) ),
inference(res,[status(thm),theory(equality)],[12,9]),
[iquote('0:Res:12.1,9.1')] ).
cnf(18,plain,
( ~ product(identity,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.0')] ).
cnf(20,plain,
( ~ product(inverse(u),u,v)
| equalish(v,identity) ),
inference(res,[status(thm),theory(equality)],[4,6]),
[iquote('0:Res:4.0,6.0')] ).
cnf(21,plain,
( ~ product(u,v,w)
| equalish(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[5,6]),
[iquote('0:Res:5.0,6.0')] ).
cnf(28,plain,
( ~ product(u,v,w)
| ~ product(identity,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(30,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.0')] ).
cnf(41,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.0,7.0')] ).
cnf(44,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(x,w,multiply(y,v)) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.0,7.0')] ).
cnf(59,plain,
( ~ product(u,v,multiply(w,x))
| product(w,x,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[21,14]),
[iquote('0:Res:21.1,14.0')] ).
cnf(74,plain,
( ~ product(identity,inverse(u),v)
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[4,28]),
[iquote('0:Res:4.0,28.0')] ).
cnf(89,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[4,41]),
[iquote('0:Res:4.0,41.0')] ).
cnf(124,plain,
( ~ product(u,v,w)
| product(multiply(inverse(w),u),v,identity) ),
inference(res,[status(thm),theory(equality)],[5,30]),
[iquote('0:Res:5.0,30.1')] ).
cnf(217,plain,
( ~ product(u,identity,v)
| product(u,w,multiply(v,w)) ),
inference(res,[status(thm),theory(equality)],[3,44]),
[iquote('0:Res:3.0,44.0')] ).
cnf(247,plain,
product(multiply(identity,inverse(u)),u,identity),
inference(res,[status(thm),theory(equality)],[5,74]),
[iquote('0:Res:5.0,74.0')] ).
cnf(287,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[4,89]),
[iquote('0:Res:4.0,89.0')] ).
cnf(292,plain,
product(multiply(identity,inverse(inverse(u))),identity,u),
inference(res,[status(thm),theory(equality)],[247,89]),
[iquote('0:Res:247.0,89.0')] ).
cnf(515,plain,
( ~ product(inverse(u),identity,v)
| equalish(multiply(v,u),identity) ),
inference(res,[status(thm),theory(equality)],[217,20]),
[iquote('0:Res:217.1,20.0')] ).
cnf(586,plain,
( ~ equalish(b,u)
| product(identity,a,u) ),
inference(res,[status(thm),theory(equality)],[1,17]),
[iquote('0:Res:1.0,17.0')] ).
cnf(614,plain,
( ~ equalish(b,u)
| equalish(u,a) ),
inference(res,[status(thm),theory(equality)],[586,18]),
[iquote('0:Res:586.1,18.0')] ).
cnf(697,plain,
( ~ product(u,inverse(v),w)
| product(multiply(inverse(w),u),identity,v) ),
inference(res,[status(thm),theory(equality)],[124,89]),
[iquote('0:Res:124.1,89.0')] ).
cnf(3045,plain,
equalish(multiply(u,inverse(u)),identity),
inference(res,[status(thm),theory(equality)],[287,515]),
[iquote('0:Res:287.0,515.0')] ).
cnf(3065,plain,
product(u,inverse(u),identity),
inference(res,[status(thm),theory(equality)],[3045,14]),
[iquote('0:Res:3045.0,14.0')] ).
cnf(3085,plain,
product(u,identity,u),
inference(res,[status(thm),theory(equality)],[3065,89]),
[iquote('0:Res:3065.0,89.0')] ).
cnf(3124,plain,
( ~ product(u,identity,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[3085,6]),
[iquote('0:Res:3085.0,6.0')] ).
cnf(3128,plain,
product(u,v,multiply(multiply(u,v),identity)),
inference(res,[status(thm),theory(equality)],[3085,59]),
[iquote('0:Res:3085.0,59.0')] ).
cnf(5724,plain,
equalish(u,multiply(identity,inverse(inverse(u)))),
inference(res,[status(thm),theory(equality)],[292,3124]),
[iquote('0:Res:292.0,3124.0')] ).
cnf(6287,plain,
equalish(multiply(identity,inverse(inverse(b))),a),
inference(res,[status(thm),theory(equality)],[5724,614]),
[iquote('0:Res:5724.0,614.0')] ).
cnf(6296,plain,
product(identity,inverse(inverse(b)),a),
inference(res,[status(thm),theory(equality)],[6287,14]),
[iquote('0:Res:6287.0,14.0')] ).
cnf(6723,plain,
equalish(multiply(multiply(u,identity),identity),u),
inference(res,[status(thm),theory(equality)],[3128,3124]),
[iquote('0:Res:3128.0,3124.0')] ).
cnf(6919,plain,
product(multiply(u,identity),identity,u),
inference(res,[status(thm),theory(equality)],[6723,14]),
[iquote('0:Res:6723.0,14.0')] ).
cnf(6922,plain,
~ product(multiply(inverse(a),identity),identity,inverse(b)),
inference(res,[status(thm),theory(equality)],[6919,10]),
[iquote('0:Res:6919.0,10.1')] ).
cnf(9683,plain,
~ product(identity,inverse(inverse(b)),a),
inference(res,[status(thm),theory(equality)],[697,6922]),
[iquote('0:Res:697.1,6922.0')] ).
cnf(9684,plain,
$false,
inference(mrr,[status(thm)],[9683,6296]),
[iquote('0:MRR:9683.0,6296.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP048-2 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Tue Jun 14 13:58:31 EDT 2022
% 0.15/0.36 % CPUTime :
% 5.73/5.96
% 5.73/5.96 SPASS V 3.9
% 5.73/5.96 SPASS beiseite: Proof found.
% 5.73/5.96 % SZS status Theorem
% 5.73/5.96 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/5.96 SPASS derived 9649 clauses, backtracked 0 clauses, performed 0 splits and kept 6149 clauses.
% 5.73/5.96 SPASS allocated 69063 KBytes.
% 5.73/5.96 SPASS spent 0:00:05.54 on the problem.
% 5.73/5.96 0:00:00.03 for the input.
% 5.73/5.96 0:00:00.00 for the FLOTTER CNF translation.
% 5.73/5.96 0:00:00.08 for inferences.
% 5.73/5.96 0:00:00.00 for the backtracking.
% 5.73/5.96 0:00:05.36 for the reduction.
% 5.73/5.96
% 5.73/5.96
% 5.73/5.96 Here is a proof with depth 11, length 45 :
% 5.73/5.96 % SZS output start Refutation
% See solution above
% 5.73/5.96 Formulae used in the proof : a_equals_b prove_inverse_substitution left_identity left_inverse total_function1 total_function2 associativity1 associativity2 product_substitution3
% 5.73/5.96
%------------------------------------------------------------------------------