TSTP Solution File: CAT003-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT003-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Fri Jul 15 00:07:28 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 10 RR)
% Number of literals : 14 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ equal(compose(u,compose(a,b)),v)
| ~ equal(compose(w,compose(a,b)),v)
| equal(w,u) ),
file('CAT003-4.p',unknown),
[] ).
cnf(4,axiom,
equal(compose(g,a),compose(h,a)),
file('CAT003-4.p',unknown),
[] ).
cnf(5,axiom,
~ equal(g,h),
file('CAT003-4.p',unknown),
[] ).
cnf(14,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT003-4.p',unknown),
[] ).
cnf(18,plain,
( ~ equal(compose(h,compose(a,b)),u)
| ~ equal(compose(g,compose(a,b)),u) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.2,5.0')] ).
cnf(62,plain,
equal(compose(compose(h,a),u),compose(g,compose(a,u))),
inference(spr,[status(thm),theory(equality)],[4,14]),
[iquote('0:SpR:4.0,14.0')] ).
cnf(65,plain,
equal(compose(g,compose(a,u)),compose(h,compose(a,u))),
inference(rew,[status(thm),theory(equality)],[14,62]),
[iquote('0:Rew:14.0,62.0')] ).
cnf(66,plain,
( ~ equal(compose(h,compose(a,b)),u)
| ~ equal(compose(h,compose(a,b)),u) ),
inference(rew,[status(thm),theory(equality)],[65,18]),
[iquote('0:Rew:65.0,18.1')] ).
cnf(68,plain,
~ equal(compose(h,compose(a,b)),u),
inference(obv,[status(thm),theory(equality)],[66]),
[iquote('0:Obv:66.0')] ).
cnf(69,plain,
$false,
inference(aed,[status(thm),theory(equality)],[5,68]),
[iquote('0:AED:5.0,68.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 : Sun May 29 23:56:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41
% 0.20/0.41 SPASS V 3.9
% 0.20/0.41 SPASS beiseite: Proof found.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.41 SPASS derived 45 clauses, backtracked 0 clauses, performed 0 splits and kept 42 clauses.
% 0.20/0.41 SPASS allocated 75651 KBytes.
% 0.20/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.41 0:00:00.04 for the input.
% 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41 0:00:00.00 for inferences.
% 0.20/0.41 0:00:00.00 for the backtracking.
% 0.20/0.41 0:00:00.00 for the reduction.
% 0.20/0.41
% 0.20/0.41
% 0.20/0.41 Here is a proof with depth 1, length 10 :
% 0.20/0.41 % SZS output start Refutation
% See solution above
% 0.20/0.41 Formulae used in the proof : epimorphism ha_equals_ga prove_g_equals_h associativity_of_compose
% 0.20/0.41
%------------------------------------------------------------------------------