%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 00:07:27 EDT 2022
% Result : Unsatisfiable 0.42s 0.60s
% Output : Refutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 19 ( 0 equ; 10 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(a,u),v)
| ~ equal(compose(a,w),v)
| equal(w,u) ),
file('CAT002-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(compose(b,u),v)
| ~ equal(compose(b,w),v)
| equal(w,u) ),
file('CAT002-3.p',unknown),
[] ).
cnf(5,axiom,
equal(compose(compose(a,b),g),compose(compose(a,b),h)),
file('CAT002-3.p',unknown),
[] ).
cnf(6,axiom,
~ equal(g,h),
file('CAT002-3.p',unknown),
[] ).
cnf(15,axiom,
equal(compose(compose(u,v),w),compose(u,compose(v,w))),
file('CAT002-3.p',unknown),
[] ).
cnf(24,plain,
equal(compose(a,compose(b,g)),compose(a,compose(b,h))),
inference(rew,[status(thm),theory(equality)],[15,5]),
[iquote('0:Rew:15.0,5.0,15.0,5.0')] ).
cnf(30,plain,
( ~ equal(compose(b,h),u)
| ~ equal(compose(b,g),u) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.2,6.0')] ).
cnf(346,plain,
( ~ equal(compose(a,u),compose(a,v))
| equal(u,v) ),
inference(eqr,[status(thm),theory(equality)],[2]),
[iquote('0:EqR:2.0')] ).
cnf(1934,plain,
( ~ equal(compose(a,compose(b,h)),compose(a,u))
| equal(compose(b,g),u) ),
inference(spl,[status(thm),theory(equality)],[24,346]),
[iquote('0:SpL:24.0,346.0')] ).
cnf(2034,plain,
~ equal(compose(b,g),compose(b,h)),
inference(eqr,[status(thm),theory(equality)],[30]),
[iquote('0:EqR:30.1')] ).
cnf(2639,plain,
equal(compose(b,g),compose(b,h)),
inference(eqr,[status(thm),theory(equality)],[1934]),
[iquote('0:EqR:1934.0')] ).
cnf(2643,plain,
$false,
inference(mrr,[status(thm)],[2639,2034]),
[iquote('0:MRR:2639.0,2034.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 19:31:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.60
% 0.42/0.60 SPASS V 3.9
% 0.42/0.60 SPASS beiseite: Proof found.
% 0.42/0.60 % SZS status Theorem
% 0.42/0.60 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.60 SPASS derived 1998 clauses, backtracked 0 clauses, performed 4 splits and kept 434 clauses.
% 0.42/0.60 SPASS allocated 77241 KBytes.
% 0.42/0.60 SPASS spent 0:00:00.23 on the problem.
% 0.42/0.60 0:00:00.04 for the input.
% 0.42/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.42/0.60 0:00:00.03 for inferences.
% 0.42/0.60 0:00:00.01 for the backtracking.
% 0.42/0.60 0:00:00.14 for the reduction.
% 0.42/0.60
% 0.42/0.60
% 0.42/0.60 Here is a proof with depth 3, length 12 :
% 0.42/0.60 % SZS output start Refutation
% See solution above
% 0.42/0.60 Formulae used in the proof : cancellation_for_compose1 cancellation_for_compose2 ab_h_equals_ab_g prove_g_equals_h associativity_of_compose
% 0.42/0.60
%------------------------------------------------------------------------------