%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL897-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:08:39 PM UTC 2026
% Result : Unsatisfiable 44.46s 44.75s
% Output : Refutation 44.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(a43_(a43_(u,v),w),a43_(u,a43_(v,w))),
file('LCL897-10.p',unknown),
[] ).
cnf(2,axiom,
equal(a43_(u,v),a43_(v,u)),
file('LCL897-10.p',unknown),
[] ).
cnf(7,axiom,
equal(a32__a61__a32__a61__a62_(a43_(u,v),w),a32__a61__a32__a61__a62_(u,a32__a61__a32__a61__a62_(v,w))),
file('LCL897-10.p',unknown),
[] ).
cnf(8,axiom,
equal(a43_(u,a32__a61__a32__a61__a62_(u,v)),a43_(v,a32__a61__a32__a61__a62_(v,u))),
file('LCL897-10.p',unknown),
[] ).
cnf(9,axiom,
~ equal(a43_(a43_(a,a32__a61__a32__a61__a62_(a,b)),a32__a61__a32__a61__a62_(a43_(a,a32__a61__a32__a61__a62_(a,b)),c)),a43_(a,a32__a61__a32__a61__a62_(a,a43_(b,a32__a61__a32__a61__a62_(b,c))))),
file('LCL897-10.p',unknown),
[] ).
cnf(10,plain,
~ equal(a43_(a,a43_(a32__a61__a32__a61__a62_(a,b),a32__a61__a32__a61__a62_(a,a32__a61__a32__a61__a62_(a32__a61__a32__a61__a62_(a,b),c)))),a43_(a,a32__a61__a32__a61__a62_(a,a43_(b,a32__a61__a32__a61__a62_(b,c))))),
inference(rew,[status(thm),theory(equality)],[1,9,7]),
[iquote('0:Rew:1.0,9.0,7.0,9.0')] ).
cnf(49,plain,
equal(a43_(a43_(u,v),a32__a61__a32__a61__a62_(u,a32__a61__a32__a61__a62_(v,w))),a43_(w,a32__a61__a32__a61__a62_(w,a43_(u,v)))),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(54,plain,
equal(a32__a61__a32__a61__a62_(a43_(u,v),w),a32__a61__a32__a61__a62_(v,a32__a61__a32__a61__a62_(u,w))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(61,plain,
equal(a32__a61__a32__a61__a62_(u,a32__a61__a32__a61__a62_(v,w)),a32__a61__a32__a61__a62_(v,a32__a61__a32__a61__a62_(u,w))),
inference(rew,[status(thm),theory(equality)],[7,54]),
[iquote('0:Rew:7.0,54.0')] ).
cnf(65,plain,
equal(a43_(u,a43_(v,a32__a61__a32__a61__a62_(u,a32__a61__a32__a61__a62_(v,w)))),a43_(w,a32__a61__a32__a61__a62_(w,a43_(u,v)))),
inference(rew,[status(thm),theory(equality)],[1,49]),
[iquote('0:Rew:1.0,49.0')] ).
cnf(66,plain,
~ equal(a43_(c,a32__a61__a32__a61__a62_(c,a43_(a,a32__a61__a32__a61__a62_(a,b)))),a43_(a,a32__a61__a32__a61__a62_(a,a43_(b,a32__a61__a32__a61__a62_(b,c))))),
inference(rew,[status(thm),theory(equality)],[65,10]),
[iquote('0:Rew:65.0,10.0')] ).
cnf(94,plain,
equal(a43_(a43_(u,v),w),a43_(v,a43_(u,w))),
inference(spr,[status(thm),theory(equality)],[2,1]),
[iquote('0:SpR:2.0,1.0')] ).
cnf(101,plain,
equal(a43_(u,a43_(v,w)),a43_(v,a43_(u,w))),
inference(rew,[status(thm),theory(equality)],[1,94]),
[iquote('0:Rew:1.0,94.0')] ).
cnf(131,plain,
equal(a43_(u,a32__a61__a32__a61__a62_(v,a32__a61__a32__a61__a62_(u,w))),a43_(a32__a61__a32__a61__a62_(v,w),a32__a61__a32__a61__a62_(a32__a61__a32__a61__a62_(v,w),u))),
inference(spr,[status(thm),theory(equality)],[61,8]),
[iquote('0:SpR:61.0,8.0')] ).
cnf(2697,plain,
equal(a43_(u,a32__a61__a32__a61__a62_(u,a43_(v,w))),a43_(w,a43_(v,a32__a61__a32__a61__a62_(v,a32__a61__a32__a61__a62_(w,u))))),
inference(spr,[status(thm),theory(equality)],[65,101]),
[iquote('0:SpR:65.0,101.0')] ).
cnf(2813,plain,
equal(a43_(u,a43_(a32__a61__a32__a61__a62_(u,v),a32__a61__a32__a61__a62_(u,a32__a61__a32__a61__a62_(a32__a61__a32__a61__a62_(u,v),w)))),a43_(w,a32__a61__a32__a61__a62_(w,a43_(v,a32__a61__a32__a61__a62_(v,u))))),
inference(spr,[status(thm),theory(equality)],[8,65]),
[iquote('0:SpR:8.0,65.0')] ).
cnf(26595,plain,
equal(a43_(u,a43_(a32__a61__a32__a61__a62_(u,v),a32__a61__a32__a61__a62_(w,a32__a61__a32__a61__a62_(a32__a61__a32__a61__a62_(u,v),x)))),a43_(v,a32__a61__a32__a61__a62_(v,a43_(a32__a61__a32__a61__a62_(w,x),u)))),
inference(spr,[status(thm),theory(equality)],[131,2697]),
[iquote('0:SpR:131.0,2697.0')] ).
cnf(26674,plain,
equal(a43_(u,a32__a61__a32__a61__a62_(u,a43_(a32__a61__a32__a61__a62_(v,w),v))),a43_(w,a32__a61__a32__a61__a62_(w,a43_(u,a32__a61__a32__a61__a62_(u,v))))),
inference(rew,[status(thm),theory(equality)],[26595,2813]),
[iquote('0:Rew:26595.0,2813.0')] ).
cnf(26675,plain,
equal(a43_(u,a32__a61__a32__a61__a62_(u,a43_(v,a32__a61__a32__a61__a62_(v,w)))),a43_(w,a32__a61__a32__a61__a62_(w,a43_(u,a32__a61__a32__a61__a62_(u,v))))),
inference(rew,[status(thm),theory(equality)],[2,26674]),
[iquote('0:Rew:2.0,26674.0')] ).
cnf(26676,plain,
$false,
inference(unc,[status(thm)],[26675,66]),
[iquote('0:UnC:26675.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL897-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 4 15:29:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 44.46/44.75
% 44.46/44.75 SPASS V 3.9
% 44.46/44.75 SPASS beiseite: Proof found.
% 44.46/44.75 % SZS status Theorem
% 44.46/44.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.46/44.75 SPASS derived 15749 clauses, backtracked 0 clauses, performed 0 splits and kept 3228 clauses.
% 44.46/44.75 SPASS allocated 95152 KBytes.
% 44.46/44.75 SPASS spent 0:0:43.25 on the problem.
% 44.46/44.75 0:00:00.06 for the input.
% 44.46/44.75 0:00:00.00 for the FLOTTER CNF translation.
% 44.46/44.75 0:00:00.29 for inferences.
% 44.46/44.75 0:00:00.00 for the backtracking.
% 44.46/44.75 0:0:42.84 for the reduction.
% 44.46/44.75
% 44.46/44.75
% 44.46/44.75 Here is a proof with depth 3, length 20 :
% 44.46/44.75 % SZS output start Refutation
% See solution above
% 44.46/44.75 Formulae used in the proof : sos_01 sos_02 sos_07 sos_08 goals_09
% 44.46/44.75
%------------------------------------------------------------------------------