%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n031.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 01:06:38 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 16 RR)
% Number of literals : 22 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
file('LCL035-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,falsehood)),x),y),implies__dfg(implies__dfg(y,u),implies__dfg(w,u)))),
file('LCL035-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(falsehood,a)),
file('LCL035-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,falsehood)),x),y))
| is_a_theorem(implies__dfg(implies__dfg(y,u),implies__dfg(w,u))) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
cnf(8,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),implies__dfg(y,implies__dfg(v,x)))),
inference(sor,[status(thm)],[7,2]),
[iquote('0:SoR:7.0,2.0')] ).
cnf(9,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(falsehood,v)),w),implies__dfg(x,w))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(falsehood,w))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(12,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(falsehood,v)),w))
| is_a_theorem(implies__dfg(x,w)) ),
inference(res,[status(thm),theory(equality)],[9,1]),
[iquote('0:Res:9.0,1.1')] ).
cnf(13,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(falsehood,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[7,11]),
[iquote('0:SoR:7.0,11.0')] ).
cnf(38,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(falsehood,w)))),
inference(sor,[status(thm)],[12,13]),
[iquote('0:SoR:12.0,13.0')] ).
cnf(42,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(falsehood,v),w),implies__dfg(x,w)))),
inference(sor,[status(thm)],[12,2]),
[iquote('0:SoR:12.0,2.0')] ).
cnf(58,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(falsehood,w))) ),
inference(res,[status(thm),theory(equality)],[38,1]),
[iquote('0:Res:38.0,1.1')] ).
cnf(65,plain,
is_a_theorem(implies__dfg(u,implies__dfg(falsehood,v))),
inference(ems,[status(thm)],[58,42]),
[iquote('0:EmS:58.0,42.0')] ).
cnf(79,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(falsehood,v)) ),
inference(res,[status(thm),theory(equality)],[65,1]),
[iquote('0:Res:65.0,1.1')] ).
cnf(81,plain,
is_a_theorem(implies__dfg(falsehood,u)),
inference(ems,[status(thm)],[79,65]),
[iquote('0:EmS:79.0,65.0')] ).
cnf(91,plain,
$false,
inference(unc,[status(thm)],[81,3]),
[iquote('0:UnC:81.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.08/0.36 % Computer : n031.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 06:09:39 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 84 clauses, backtracked 0 clauses, performed 0 splits and kept 40 clauses.
% 0.20/0.48 SPASS allocated 75703 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.10 on the problem.
% 0.20/0.48 0:00:00.06 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.00 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 10, length 16 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : condensed_detachment c0_CAMeredith prove_c0_4
% 0.20/0.48
%------------------------------------------------------------------------------