%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP045-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:44:59 EDT 2022
% Result : Unsatisfiable 2.36s 2.58s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 15 unt; 0 nHn; 39 RR)
% Number of literals : 74 ( 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equalish(a,b),
file('GRP045-2.p',unknown),
[] ).
cnf(2,axiom,
product(c,a,result),
file('GRP045-2.p',unknown),
[] ).
cnf(3,axiom,
~ product(c,b,result),
file('GRP045-2.p',unknown),
[] ).
cnf(4,axiom,
product(identity,u,u),
file('GRP045-2.p',unknown),
[] ).
cnf(5,axiom,
product(inverse(u),u,identity),
file('GRP045-2.p',unknown),
[] ).
cnf(6,axiom,
product(u,v,multiply(u,v)),
file('GRP045-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP045-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP045-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP045-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ equalish(u,v)
| ~ product(w,x,u)
| product(w,x,v) ),
file('GRP045-2.p',unknown),
[] ).
cnf(12,plain,
( ~ equalish(u,result)
| ~ product(c,b,u) ),
inference(res,[status(thm),theory(equality)],[10,3]),
[iquote('0:Res:10.2,3.0')] ).
cnf(16,plain,
( ~ equalish(u,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.1')] ).
cnf(18,plain,
( ~ equalish(multiply(u,v),w)
| product(u,v,w) ),
inference(res,[status(thm),theory(equality)],[6,10]),
[iquote('0:Res:6.0,10.1')] ).
cnf(20,plain,
( ~ product(identity,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.0')] ).
cnf(22,plain,
( ~ product(u,v,w)
| equalish(w,multiply(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(30,plain,
( ~ product(u,v,w)
| ~ product(identity,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(32,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(y,v,multiply(x,w)) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.0')] ).
cnf(36,plain,
( ~ equalish(u,v)
| ~ equalish(v,w)
| product(identity,u,w) ),
inference(res,[status(thm),theory(equality)],[16,10]),
[iquote('0:Res:16.1,10.1')] ).
cnf(38,plain,
( ~ equalish(u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[16,20]),
[iquote('0:Res:16.1,20.0')] ).
cnf(39,plain,
equalish(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[6,20]),
[iquote('0:Res:6.0,20.0')] ).
cnf(40,plain,
( ~ product(u,a,v)
| ~ product(w,u,c)
| product(w,v,result) ),
inference(res,[status(thm),theory(equality)],[2,8]),
[iquote('0:Res:2.0,8.0')] ).
cnf(42,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,8]),
[iquote('0:Res:4.0,8.0')] ).
cnf(46,plain,
equalish(b,a),
inference(res,[status(thm),theory(equality)],[1,38]),
[iquote('0:Res:1.0,38.0')] ).
cnf(49,plain,
equalish(u,multiply(identity,u)),
inference(res,[status(thm),theory(equality)],[39,38]),
[iquote('0:Res:39.0,38.0')] ).
cnf(83,plain,
( ~ product(u,v,w)
| equalish(multiply(u,v),w) ),
inference(res,[status(thm),theory(equality)],[22,38]),
[iquote('0:Res:22.1,38.0')] ).
cnf(138,plain,
( ~ product(identity,inverse(u),v)
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[5,30]),
[iquote('0:Res:5.0,30.0')] ).
cnf(164,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[5,42]),
[iquote('0:Res:5.0,42.0')] ).
cnf(310,plain,
( ~ product(u,identity,v)
| product(v,w,multiply(u,w)) ),
inference(res,[status(thm),theory(equality)],[4,32]),
[iquote('0:Res:4.0,32.0')] ).
cnf(590,plain,
product(multiply(identity,inverse(u)),u,identity),
inference(res,[status(thm),theory(equality)],[6,138]),
[iquote('0:Res:6.0,138.0')] ).
cnf(644,plain,
product(multiply(identity,inverse(inverse(u))),identity,u),
inference(res,[status(thm),theory(equality)],[590,164]),
[iquote('0:Res:590.0,164.0')] ).
cnf(931,plain,
( ~ product(u,identity,c)
| ~ equalish(multiply(u,b),result) ),
inference(res,[status(thm),theory(equality)],[310,12]),
[iquote('0:Res:310.1,12.1')] ).
cnf(1195,plain,
( ~ equalish(a,u)
| product(identity,b,u) ),
inference(res,[status(thm),theory(equality)],[46,36]),
[iquote('0:Res:46.0,36.0')] ).
cnf(1368,plain,
( ~ equalish(a,u)
| equalish(u,b) ),
inference(res,[status(thm),theory(equality)],[1195,20]),
[iquote('0:Res:1195.1,20.0')] ).
cnf(1390,plain,
equalish(multiply(identity,a),b),
inference(res,[status(thm),theory(equality)],[49,1368]),
[iquote('0:Res:49.0,1368.0')] ).
cnf(1402,plain,
product(identity,a,b),
inference(res,[status(thm),theory(equality)],[1390,18]),
[iquote('0:Res:1390.0,18.0')] ).
cnf(1421,plain,
( ~ product(u,identity,c)
| product(u,b,result) ),
inference(res,[status(thm),theory(equality)],[1402,40]),
[iquote('0:Res:1402.0,40.0')] ).
cnf(5098,plain,
( ~ product(u,b,result)
| ~ product(u,identity,c) ),
inference(res,[status(thm),theory(equality)],[83,931]),
[iquote('0:Res:83.1,931.1')] ).
cnf(5100,plain,
~ product(u,identity,c),
inference(mrr,[status(thm)],[5098,1421]),
[iquote('0:MRR:5098.0,1421.1')] ).
cnf(5101,plain,
$false,
inference(unc,[status(thm)],[5100,644]),
[iquote('0:UnC:5100.0,644.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP045-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Tue Jun 14 08:55:12 EDT 2022
% 0.11/0.32 % CPUTime :
% 2.36/2.58
% 2.36/2.58 SPASS V 3.9
% 2.36/2.58 SPASS beiseite: Proof found.
% 2.36/2.58 % SZS status Theorem
% 2.36/2.58 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.36/2.58 SPASS derived 5071 clauses, backtracked 0 clauses, performed 0 splits and kept 3680 clauses.
% 2.36/2.58 SPASS allocated 66381 KBytes.
% 2.36/2.58 SPASS spent 0:00:02.23 on the problem.
% 2.36/2.58 0:00:00.03 for the input.
% 2.36/2.58 0:00:00.00 for the FLOTTER CNF translation.
% 2.36/2.58 0:00:00.04 for inferences.
% 2.36/2.58 0:00:00.00 for the backtracking.
% 2.36/2.58 0:00:02.12 for the reduction.
% 2.36/2.58
% 2.36/2.58
% 2.36/2.58 Here is a proof with depth 8, length 39 :
% 2.36/2.58 % SZS output start Refutation
% See solution above
% 2.36/2.58 Formulae used in the proof : a_equals_b product_with_a prove_product_with_b left_identity left_inverse total_function1 total_function2 associativity1 associativity2 product_substitution3
% 2.36/2.58
%------------------------------------------------------------------------------