%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 01:06:43 PM UTC 2026
% Result : Unsatisfiable 21.17s 21.40s
% Output : Refutation 21.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 20 RR)
% Number of literals : 31 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 9 ( 9 usr; 8 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('LCL080-2.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL080-2.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
file('LCL080-2.p',unknown),
[] ).
cnf(5,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL080-2.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),c),implies__dfg(implies__dfg(c,a),implies__dfg(e,a)))),
file('LCL080-2.p',unknown),
[] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,u)) ),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.0,1.1')] ).
cnf(15,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(u) ),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.0,1.1')] ).
cnf(16,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(u,w))) ),
inference(res,[status(thm),theory(equality)],[5,1]),
[iquote('0:Res:5.0,1.1')] ).
cnf(19,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[16,14]),
[iquote('0:SoR:16.0,14.1')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x),implies__dfg(implies__dfg(w,u),x))),
inference(sor,[status(thm)],[16,5]),
[iquote('0:SoR:16.0,5.0')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(u,w),u),v))),
inference(sor,[status(thm)],[16,4]),
[iquote('0:SoR:16.0,4.0')] ).
cnf(30,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(implies__dfg(u,w),x))) ),
inference(sor,[status(thm)],[16,19]),
[iquote('0:SoR:16.0,19.1')] ).
cnf(35,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,w),u),v)) ),
inference(res,[status(thm),theory(equality)],[21,1]),
[iquote('0:Res:21.0,1.1')] ).
cnf(57,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),x))
| is_a_theorem(implies__dfg(implies__dfg(w,u),x)) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(99,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
inference(sor,[status(thm)],[35,3]),
[iquote('0:SoR:35.0,3.0')] ).
cnf(177,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[15,30]),
[iquote('0:SoR:15.0,30.1')] ).
cnf(288,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[57,177]),
[iquote('0:SoR:57.0,177.1')] ).
cnf(2590,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),v)),implies__dfg(u,implies__dfg(x,v)))),
inference(sor,[status(thm)],[288,99]),
[iquote('0:SoR:288.0,99.0')] ).
cnf(23440,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(implies__dfg(w,u),implies__dfg(x,u)))),
inference(sor,[status(thm)],[57,2590]),
[iquote('0:SoR:57.0,2590.0')] ).
cnf(23488,plain,
$false,
inference(unc,[status(thm)],[23440,6]),
[iquote('0:UnC:23440.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL080-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_spass %d %s
% 0.18/0.42 % Computer : n020.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 5 08:41:42 UTC 2026
% 0.18/0.42 % CPUTime :
% 21.17/21.40
% 21.17/21.40 SPASS V 3.9
% 21.17/21.40 SPASS beiseite: Proof found.
% 21.17/21.40 % SZS status Theorem
% 21.17/21.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.17/21.40 SPASS derived 23147 clauses, backtracked 0 clauses, performed 0 splits and kept 6284 clauses.
% 21.17/21.40 SPASS allocated 98642 KBytes.
% 21.17/21.40 SPASS spent 0:0:20.47 on the problem.
% 21.17/21.40 0:00:00.05 for the input.
% 21.17/21.40 0:00:00.00 for the FLOTTER CNF translation.
% 21.17/21.40 0:00:00.51 for inferences.
% 21.17/21.40 0:00:00.00 for the backtracking.
% 21.17/21.40 0:0:19.80 for the reduction.
% 21.17/21.40
% 21.17/21.40
% 21.17/21.40 Here is a proof with depth 7, length 20 :
% 21.17/21.40 % SZS output start Refutation
% See solution above
% 21.17/21.41 Formulae used in the proof : condensed_detachment ic_2 ic_3 ic_4 prove_ic_JLukasiewicz
% 21.17/21.41
%------------------------------------------------------------------------------