TSTP Solution File: CAT004-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 1.14s 1.35s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 13 ( 6 unt; 0 nHn; 13 RR)
% Number of literals : 22 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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,a),v)
| ~ equal(compose(w,a),v)
| equal(w,u) ),
file('CAT004-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(compose(u,b),v)
| ~ equal(compose(w,b),v)
| equal(w,u) ),
file('CAT004-3.p',unknown),
[] ).
cnf(5,axiom,
equal(compose(g,compose(a,b)),compose(h,compose(a,b))),
file('CAT004-3.p',unknown),
[] ).
cnf(6,axiom,
~ equal(g,h),
file('CAT004-3.p',unknown),
[] ).
cnf(15,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT004-3.p',unknown),
[] ).
cnf(28,plain,
( ~ equal(compose(h,a),u)
| ~ equal(compose(g,a),u) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.2,6.0')] ).
cnf(279,plain,
( ~ equal(compose(u,b),compose(v,b))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[3]),
[iquote('0:EqR:3.0')] ).
cnf(1605,plain,
( ~ equal(compose(u,compose(v,b)),compose(w,b))
| equal(compose(u,v),w) ),
inference(spl,[status(thm),theory(equality)],[15,279]),
[iquote('0:SpL:15.0,279.0')] ).
cnf(2168,plain,
~ equal(compose(g,a),compose(h,a)),
inference(eqr,[status(thm),theory(equality)],[28]),
[iquote('0:EqR:28.1')] ).
cnf(9610,plain,
( ~ equal(compose(h,compose(a,b)),compose(u,b))
| equal(compose(g,a),u) ),
inference(spl,[status(thm),theory(equality)],[5,1605]),
[iquote('0:SpL:5.0,1605.0')] ).
cnf(9619,plain,
( ~ equal(compose(h,compose(a,b)),compose(u,compose(v,b)))
| equal(compose(g,a),compose(u,v)) ),
inference(spl,[status(thm),theory(equality)],[15,9610]),
[iquote('0:SpL:15.0,9610.0')] ).
cnf(9699,plain,
equal(compose(g,a),compose(h,a)),
inference(eqr,[status(thm),theory(equality)],[9619]),
[iquote('0:EqR:9619.0')] ).
cnf(9705,plain,
$false,
inference(mrr,[status(thm)],[9699,2168]),
[iquote('0:MRR:9699.0,2168.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : CAT004-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 18:45:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.14/1.35
% 1.14/1.35 SPASS V 3.9
% 1.14/1.35 SPASS beiseite: Proof found.
% 1.14/1.35 % SZS status Theorem
% 1.14/1.35 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.14/1.35 SPASS derived 6540 clauses, backtracked 0 clauses, performed 6 splits and kept 1172 clauses.
% 1.14/1.35 SPASS allocated 81390 KBytes.
% 1.14/1.35 SPASS spent 0:00:00.81 on the problem.
% 1.14/1.35 0:00:00.04 for the input.
% 1.14/1.35 0:00:00.00 for the FLOTTER CNF translation.
% 1.14/1.35 0:00:00.08 for inferences.
% 1.14/1.35 0:00:00.02 for the backtracking.
% 1.14/1.35 0:00:00.65 for the reduction.
% 1.14/1.35
% 1.14/1.35
% 1.14/1.35 Here is a proof with depth 5, length 13 :
% 1.14/1.35 % SZS output start Refutation
% See solution above
% 1.14/1.35 Formulae used in the proof : cancellation_for_product1 cancellation_for_product2 h_ab_equals_g_ab prove_h_equals_g associativity_of_compose
% 1.14/1.35
%------------------------------------------------------------------------------