%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Theorem 22.65s 22.99s
% Output : Refutation 22.65s
% 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(5,axiom,
equal(a43_(u,v),a43_(v,u)),
file('LCL897+1.p',unknown),
[] ).
cnf(6,axiom,
equal(a43_(a43_(u,v),w),a43_(u,a43_(v,w))),
file('LCL897+1.p',unknown),
[] ).
cnf(7,axiom,
equal(a61__a61__a62_(a43_(u,v),w),a61__a61__a62_(u,a61__a61__a62_(v,w))),
file('LCL897+1.p',unknown),
[] ).
cnf(8,axiom,
equal(a43_(u,a61__a61__a62_(u,v)),a43_(v,a61__a61__a62_(v,u))),
file('LCL897+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(a43_(a43_(a,a61__a61__a62_(a,b)),a61__a61__a62_(a43_(a,a61__a61__a62_(a,b)),c)),a43_(a,a61__a61__a62_(a,a43_(b,a61__a61__a62_(b,c))))),
file('LCL897+1.p',unknown),
[] ).
cnf(10,plain,
~ equal(a43_(a,a43_(a61__a61__a62_(a,b),a61__a61__a62_(a,a61__a61__a62_(a61__a61__a62_(a,b),c)))),a43_(a,a61__a61__a62_(a,a43_(b,a61__a61__a62_(b,c))))),
inference(rew,[status(thm),theory(equality)],[6,9,7]),
[iquote('0:Rew:6.0,9.0,7.0,9.0')] ).
cnf(49,plain,
equal(a43_(a43_(u,v),a61__a61__a62_(u,a61__a61__a62_(v,w))),a43_(w,a61__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(a61__a61__a62_(a43_(u,v),w),a61__a61__a62_(v,a61__a61__a62_(u,w))),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(61,plain,
equal(a61__a61__a62_(u,a61__a61__a62_(v,w)),a61__a61__a62_(v,a61__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,a61__a61__a62_(u,a61__a61__a62_(v,w)))),a43_(w,a61__a61__a62_(w,a43_(u,v)))),
inference(rew,[status(thm),theory(equality)],[6,49]),
[iquote('0:Rew:6.0,49.0')] ).
cnf(66,plain,
~ equal(a43_(c,a61__a61__a62_(c,a43_(a,a61__a61__a62_(a,b)))),a43_(a,a61__a61__a62_(a,a43_(b,a61__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)],[5,6]),
[iquote('0:SpR:5.0,6.0')] ).
cnf(101,plain,
equal(a43_(u,a43_(v,w)),a43_(v,a43_(u,w))),
inference(rew,[status(thm),theory(equality)],[6,94]),
[iquote('0:Rew:6.0,94.0')] ).
cnf(131,plain,
equal(a43_(u,a61__a61__a62_(v,a61__a61__a62_(u,w))),a43_(a61__a61__a62_(v,w),a61__a61__a62_(a61__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,a61__a61__a62_(u,a43_(v,w))),a43_(w,a43_(v,a61__a61__a62_(v,a61__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_(a61__a61__a62_(u,v),a61__a61__a62_(u,a61__a61__a62_(a61__a61__a62_(u,v),w)))),a43_(w,a61__a61__a62_(w,a43_(v,a61__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_(a61__a61__a62_(u,v),a61__a61__a62_(w,a61__a61__a62_(a61__a61__a62_(u,v),x)))),a43_(v,a61__a61__a62_(v,a43_(a61__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,a61__a61__a62_(u,a43_(a61__a61__a62_(v,w),v))),a43_(w,a61__a61__a62_(w,a43_(u,a61__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,a61__a61__a62_(u,a43_(v,a61__a61__a62_(v,w)))),a43_(w,a61__a61__a62_(w,a43_(u,a61__a61__a62_(u,v))))),
inference(rew,[status(thm),theory(equality)],[5,26674]),
[iquote('0:Rew:5.0,26674.0')] ).
cnf(26676,plain,
$false,
inference(unc,[status(thm)],[26675,66]),
[iquote('0:UnC:26675.0,66.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 5 15:06:57 UTC 2026
% 0.04/0.30 % CPUTime :
% 22.65/22.99
% 22.65/22.99 SPASS V 3.9
% 22.65/22.99 SPASS beiseite: Proof found.
% 22.65/22.99 % SZS status Theorem
% 22.65/22.99 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.65/22.99 SPASS derived 15749 clauses, backtracked 0 clauses, performed 0 splits and kept 3228 clauses.
% 22.65/22.99 SPASS allocated 117124 KBytes.
% 22.65/22.99 SPASS spent 0:0:22.09 on the problem.
% 22.65/22.99 0:00:00.03 for the input.
% 22.65/22.99 0:00:00.02 for the FLOTTER CNF translation.
% 22.65/22.99 0:00:00.12 for inferences.
% 22.65/22.99 0:00:00.00 for the backtracking.
% 22.65/22.99 0:0:21.89 for the reduction.
% 22.65/22.99
% 22.65/22.99
% 22.65/22.99 Here is a proof with depth 3, length 20 :
% 22.65/22.99 % SZS output start Refutation
% See solution above
% 22.65/22.99 Formulae used in the proof : sos_02 sos_01 sos_07 sos_08 goals_09
% 22.65/22.99
%------------------------------------------------------------------------------