%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 01:06:47 PM UTC 2026
% Result : Unsatisfiable 0.40s 0.68s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 19 unt; 0 nHn; 33 RR)
% Number of literals : 47 ( 0 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ordered(u,v)
| ordered(implies__dfg(u,w),implies__dfg(v,w)) ),
file('LCL109-5.p',unknown),
[] ).
cnf(4,axiom,
( ~ ordered(u,implies__dfg(v,w))
| ordered(v,implies__dfg(u,w)) ),
file('LCL109-5.p',unknown),
[] ).
cnf(9,axiom,
~ equal(big_V(implies__dfg(x__dfg,y__dfg),implies__dfg(y__dfg,x__dfg)),truth),
file('LCL109-5.p',unknown),
[] ).
cnf(10,axiom,
equal(implies__dfg(truth,u),u),
file('LCL109-5.p',unknown),
[] ).
cnf(12,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL109-5.p',unknown),
[] ).
cnf(13,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL109-5.p',unknown),
[] ).
cnf(14,axiom,
equal(implies__dfg(implies__dfg(u,v),v),big_V(u,v)),
file('LCL109-5.p',unknown),
[] ).
cnf(16,axiom,
( ~ ordered(u,v)
| equal(implies__dfg(u,v),truth) ),
file('LCL109-5.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(implies__dfg(u,v),truth)
| ordered(u,v) ),
file('LCL109-5.p',unknown),
[] ).
cnf(20,plain,
equal(big_V(u,v),big_V(v,u)),
inference(rew,[status(thm),theory(equality)],[14,12]),
[iquote('0:Rew:14.0,12.0,14.0,12.0')] ).
cnf(28,plain,
( ~ ordered(truth,u)
| equal(truth,u) ),
inference(spr,[status(thm),theory(equality)],[16,10]),
[iquote('0:SpR:16.1,10.0')] ).
cnf(34,plain,
( ~ ordered(implies__dfg(u,v),v)
| equal(big_V(u,v),truth) ),
inference(spr,[status(thm),theory(equality)],[14,16]),
[iquote('0:SpR:14.0,16.1')] ).
cnf(37,plain,
equal(implies__dfg(u,u),big_V(truth,u)),
inference(spr,[status(thm),theory(equality)],[10,14]),
[iquote('0:SpR:10.0,14.0')] ).
cnf(46,plain,
( ~ ordered(u,u)
| equal(big_V(truth,u),truth) ),
inference(spr,[status(thm),theory(equality)],[37,16]),
[iquote('0:SpR:37.0,16.1')] ).
cnf(48,plain,
( ~ equal(big_V(truth,u),truth)
| ordered(u,u) ),
inference(spl,[status(thm),theory(equality)],[37,17]),
[iquote('0:SpL:37.0,17.0')] ).
cnf(57,plain,
( ~ ordered(u,u)
| equal(big_V(u,truth),truth) ),
inference(spr,[status(thm),theory(equality)],[46,20]),
[iquote('0:SpR:46.1,20.0')] ).
cnf(96,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[10,13]),
[iquote('0:SpR:10.0,13.0')] ).
cnf(124,plain,
( ~ equal(truth,truth)
| ordered(implies__dfg(not__dfg(u),not__dfg(truth)),u) ),
inference(spl,[status(thm),theory(equality)],[96,17]),
[iquote('0:SpL:96.0,17.0')] ).
cnf(129,plain,
ordered(implies__dfg(not__dfg(u),not__dfg(truth)),u),
inference(obv,[status(thm),theory(equality)],[124]),
[iquote('0:Obv:124.0')] ).
cnf(160,plain,
( ~ ordered(u,truth)
| ordered(implies__dfg(u,v),v) ),
inference(spr,[status(thm),theory(equality)],[10,1]),
[iquote('0:SpR:10.0,1.1')] ).
cnf(161,plain,
( ~ ordered(u,v)
| ordered(implies__dfg(u,v),big_V(truth,v)) ),
inference(spr,[status(thm),theory(equality)],[37,1]),
[iquote('0:SpR:37.0,1.1')] ).
cnf(172,plain,
( ~ ordered(u,v)
| ordered(truth,big_V(truth,v)) ),
inference(rew,[status(thm),theory(equality)],[16,161]),
[iquote('0:Rew:16.1,161.1')] ).
cnf(253,plain,
ordered(truth,big_V(truth,u)),
inference(res,[status(thm),theory(equality)],[129,172]),
[iquote('0:Res:129.0,172.0')] ).
cnf(294,plain,
equal(big_V(truth,u),truth),
inference(res,[status(thm),theory(equality)],[253,28]),
[iquote('0:Res:253.0,28.0')] ).
cnf(300,plain,
( ~ equal(truth,truth)
| ordered(u,u) ),
inference(rew,[status(thm),theory(equality)],[294,48]),
[iquote('0:Rew:294.0,48.0')] ).
cnf(319,plain,
ordered(u,u),
inference(obv,[status(thm),theory(equality)],[300]),
[iquote('0:Obv:300.0')] ).
cnf(320,plain,
equal(big_V(u,truth),truth),
inference(mrr,[status(thm)],[57,319]),
[iquote('0:MRR:57.0,319.0')] ).
cnf(333,plain,
ordered(u,implies__dfg(implies__dfg(u,v),v)),
inference(res,[status(thm),theory(equality)],[319,4]),
[iquote('0:Res:319.0,4.0')] ).
cnf(335,plain,
ordered(u,big_V(u,v)),
inference(rew,[status(thm),theory(equality)],[14,333]),
[iquote('0:Rew:14.0,333.0')] ).
cnf(481,plain,
ordered(u,truth),
inference(spr,[status(thm),theory(equality)],[320,335]),
[iquote('0:SpR:320.0,335.0')] ).
cnf(484,plain,
ordered(implies__dfg(u,v),v),
inference(mrr,[status(thm)],[160,481]),
[iquote('0:MRR:160.0,481.0')] ).
cnf(490,plain,
equal(big_V(u,v),truth),
inference(mrr,[status(thm)],[34,484]),
[iquote('0:MRR:34.0,484.0')] ).
cnf(491,plain,
$false,
inference(unc,[status(thm)],[490,9]),
[iquote('0:UnC:490.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_spass %d %s
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 4 19:53:11 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.40/0.68
% 0.40/0.68 SPASS V 3.9
% 0.40/0.68 SPASS beiseite: Proof found.
% 0.40/0.68 % SZS status Theorem
% 0.40/0.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.68 SPASS derived 354 clauses, backtracked 0 clauses, performed 0 splits and kept 192 clauses.
% 0.40/0.68 SPASS allocated 63645 KBytes.
% 0.40/0.68 SPASS spent 0:00:00.21 on the problem.
% 0.40/0.68 0:00:00.09 for the input.
% 0.40/0.68 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.68 0:00:00.01 for inferences.
% 0.40/0.68 0:00:00.00 for the backtracking.
% 0.40/0.68 0:00:00.06 for the reduction.
% 0.40/0.68
% 0.40/0.68
% 0.40/0.68 Here is a proof with depth 4, length 33 :
% 0.40/0.68 % SZS output start Refutation
% See solution above
% 0.40/0.68 Formulae used in the proof : lemma_1 lemma_3_2 prove_mv_4 wajsberg_1 wajsberg_3 wajsberg_4 big_V_definition partial_order_definition1 partial_order_definition2
% 0.40/0.68
%------------------------------------------------------------------------------