%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL029-1 : 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 01:06:37 PM UTC 2026
% Result : Unsatisfiable 3.95s 4.20s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of clauses : 30 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 46 ( 0 equ; 17 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 : 7 ( 7 usr; 6 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('LCL029-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
file('LCL029-1.p',unknown),
[] ).
cnf(3,axiom,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
file('LCL029-1.p',unknown),
[] ).
cnf(4,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
file('LCL029-1.p',unknown),
[] ).
cnf(5,axiom,
is_a_theorem(implies__dfg(falsehood,u)),
file('LCL029-1.p',unknown),
[] ).
cnf(6,axiom,
~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,falsehood),falsehood),a)),
file('LCL029-1.p',unknown),
[] ).
cnf(14,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(15,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(19,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)],[2,1]),
[iquote('0:Res:2.0,1.1')] ).
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)],[19,2]),
[iquote('0:SoR:19.0,2.0')] ).
cnf(21,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
inference(sor,[status(thm)],[19,3]),
[iquote('0:SoR:19.0,3.0')] ).
cnf(22,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
inference(sor,[status(thm)],[19,15]),
[iquote('0:SoR:19.0,15.1')] ).
cnf(24,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(falsehood,v))),
inference(sor,[status(thm)],[19,5]),
[iquote('0:SoR:19.0,5.0')] ).
cnf(28,plain,
is_a_theorem(implies__dfg(u,u)),
inference(sor,[status(thm)],[14,21]),
[iquote('0:SoR:14.0,21.0')] ).
cnf(34,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)],[19,22]),
[iquote('0:SoR:19.0,22.1')] ).
cnf(35,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,v)) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.1,1.1')] ).
cnf(75,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(w,implies__dfg(falsehood,v))) ),
inference(sor,[status(thm)],[35,24]),
[iquote('0:SoR:35.1,24.0')] ).
cnf(92,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(102,plain,
is_a_theorem(implies__dfg(u,implies__dfg(falsehood,v))),
inference(sor,[status(thm)],[75,28]),
[iquote('0:SoR:75.0,28.0')] ).
cnf(112,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(falsehood,u),v),implies__dfg(w,v))),
inference(sor,[status(thm)],[19,102]),
[iquote('0:SoR:19.0,102.0')] ).
cnf(210,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
inference(sor,[status(thm)],[14,34]),
[iquote('0:SoR:14.0,34.1')] ).
cnf(224,plain,
( ~ is_a_theorem(u)
| ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(v) ),
inference(res,[status(thm),theory(equality)],[210,1]),
[iquote('0:Res:210.1,1.1')] ).
cnf(363,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
inference(sor,[status(thm)],[92,4]),
[iquote('0:SoR:92.0,4.0')] ).
cnf(383,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
| is_a_theorem(implies__dfg(u,v)) ),
inference(sor,[status(thm)],[224,363]),
[iquote('0:SoR:224.1,363.0')] ).
cnf(510,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(falsehood,u),v),v)),
inference(sor,[status(thm)],[383,112]),
[iquote('0:SoR:383.0,112.0')] ).
cnf(584,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(implies__dfg(falsehood,w),u),v))),
inference(sor,[status(thm)],[19,510]),
[iquote('0:SoR:19.0,510.0')] ).
cnf(1021,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(falsehood,w),u),v)) ),
inference(sor,[status(thm)],[224,584]),
[iquote('0:SoR:224.1,584.0')] ).
cnf(5453,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(falsehood,u),implies__dfg(implies__dfg(v,w),v)),v)),
inference(sor,[status(thm)],[1021,4]),
[iquote('0:SoR:1021.0,4.0')] ).
cnf(5625,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),u)),
inference(sor,[status(thm)],[92,5453]),
[iquote('0:SoR:92.0,5453.0')] ).
cnf(5639,plain,
$false,
inference(unc,[status(thm)],[5625,6]),
[iquote('0:UnC:5625.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 12:32:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 3.95/4.20
% 3.95/4.20 SPASS V 3.9
% 3.95/4.20 SPASS beiseite: Proof found.
% 3.95/4.20 % SZS status Theorem
% 3.95/4.20 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/4.20 SPASS derived 5573 clauses, backtracked 0 clauses, performed 0 splits and kept 1855 clauses.
% 3.95/4.20 SPASS allocated 82729 KBytes.
% 3.95/4.20 SPASS spent 0:00:03.70 on the problem.
% 3.95/4.20 0:00:00.06 for the input.
% 3.95/4.20 0:00:00.00 for the FLOTTER CNF translation.
% 3.95/4.20 0:00:00.20 for inferences.
% 3.95/4.20 0:00:00.00 for the backtracking.
% 3.95/4.20 0:00:03.37 for the reduction.
% 3.95/4.20
% 3.95/4.20
% 3.95/4.20 Here is a proof with depth 11, length 30 :
% 3.95/4.20 % SZS output start Refutation
% See solution above
% 3.95/4.20 Formulae used in the proof : condensed_detachment c0_1 c0_2 c0_3 c0_4 prove_c0_5
% 3.95/4.20
%------------------------------------------------------------------------------