%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 01:06:45 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.94s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 52 ( 32 unt; 0 nHn; 52 RR)
% Number of literals : 73 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 14 ( 14 usr; 13 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('LCL091-1.p',unknown),
[] ).
cnf(2,axiom,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)),implies__dfg(implies__dfg(x,u),implies__dfg(y,implies__dfg(w,u))))),
file('LCL091-1.p',unknown),
[] ).
cnf(3,axiom,
~ is_a_theorem(implies__dfg(a,implies__dfg(b,a))),
file('LCL091-1.p',unknown),
[] ).
cnf(7,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(implies__dfg(x,u),implies__dfg(y,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(u,implies__dfg(v,w)),implies__dfg(w,x)),implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(w,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(implies__dfg(u,v),implies__dfg(v,w)),implies__dfg(x,implies__dfg(y,v))),implies__dfg(z,implies__dfg(x1,implies__dfg(x,implies__dfg(y,v)))))),
inference(sor,[status(thm)],[7,8]),
[iquote('0:SoR:7.0,8.0')] ).
cnf(10,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(w,x)))
| is_a_theorem(implies__dfg(y,implies__dfg(implies__dfg(z,w),implies__dfg(w,x)))) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.1')] ).
cnf(11,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(implies__dfg(x,y),implies__dfg(y,w)))))),
inference(sor,[status(thm)],[10,8]),
[iquote('0:SoR:10.0,8.0')] ).
cnf(14,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(implies__dfg(x,y),implies__dfg(y,w))))) ),
inference(res,[status(thm),theory(equality)],[11,1]),
[iquote('0:Res:11.0,1.1')] ).
cnf(15,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(x,v))))),
inference(ems,[status(thm)],[14,11]),
[iquote('0:EmS:14.0,11.0')] ).
cnf(18,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(v,w)),x),implies__dfg(y,implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,15]),
[iquote('0:SoR:7.0,15.0')] ).
cnf(20,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(y,x),implies__dfg(x,z))),implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(y,x),implies__dfg(x,z)))))),
inference(sor,[status(thm)],[7,9]),
[iquote('0:SoR:7.0,9.0')] ).
cnf(29,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(x,implies__dfg(y,w)))))),
inference(sor,[status(thm)],[10,18]),
[iquote('0:SoR:10.0,18.0')] ).
cnf(35,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(x,implies__dfg(y,w))))) ),
inference(res,[status(thm),theory(equality)],[29,1]),
[iquote('0:Res:29.0,1.1')] ).
cnf(36,plain,
is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(w,implies__dfg(x,v))))),
inference(ems,[status(thm)],[35,29]),
[iquote('0:EmS:35.0,29.0')] ).
cnf(43,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(y,implies__dfg(w,x)))),
inference(sor,[status(thm)],[7,36]),
[iquote('0:SoR:7.0,36.0')] ).
cnf(45,plain,
( ~ is_a_theorem(implies__dfg(u,v))
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(x,v)))) ),
inference(res,[status(thm),theory(equality)],[36,1]),
[iquote('0:Res:36.0,1.1')] ).
cnf(53,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(x,implies__dfg(y,implies__dfg(u,implies__dfg(v,w)))))),
inference(sor,[status(thm)],[45,43]),
[iquote('0:SoR:45.0,43.0')] ).
cnf(61,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,x))),implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))),implies__dfg(x2,implies__dfg(x3,implies__dfg(y,implies__dfg(z,implies__dfg(x1,w))))))),
inference(sor,[status(thm)],[7,20]),
[iquote('0:SoR:7.0,20.0')] ).
cnf(65,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(implies__dfg(y,x),implies__dfg(x,z))))
| is_a_theorem(implies__dfg(x1,implies__dfg(x2,implies__dfg(implies__dfg(y,x),implies__dfg(x,z))))) ),
inference(res,[status(thm),theory(equality)],[20,1]),
[iquote('0:Res:20.0,1.1')] ).
cnf(100,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),x),implies__dfg(x,implies__dfg(y,x)))))),
inference(sor,[status(thm)],[65,2]),
[iquote('0:SoR:65.0,2.0')] ).
cnf(119,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,y)))),implies__dfg(z,implies__dfg(implies__dfg(x1,y),implies__dfg(y,x2)))),implies__dfg(x3,implies__dfg(x4,implies__dfg(z,implies__dfg(implies__dfg(x1,y),implies__dfg(y,x2))))))),
inference(sor,[status(thm)],[7,61]),
[iquote('0:SoR:7.0,61.0')] ).
cnf(124,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,x))),implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))))
| is_a_theorem(implies__dfg(x2,implies__dfg(x3,implies__dfg(y,implies__dfg(z,implies__dfg(x1,w)))))) ),
inference(res,[status(thm),theory(equality)],[61,1]),
[iquote('0:Res:61.0,1.1')] ).
cnf(172,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),x),implies__dfg(x,implies__dfg(y,x))))) ),
inference(res,[status(thm),theory(equality)],[100,1]),
[iquote('0:Res:100.0,1.1')] ).
cnf(228,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),implies__dfg(y,implies__dfg(implies__dfg(z,w),w)))))),
inference(sor,[status(thm)],[124,2]),
[iquote('0:SoR:124.0,2.0')] ).
cnf(297,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,x),implies__dfg(x,y)))),implies__dfg(z,implies__dfg(x1,implies__dfg(x2,implies__dfg(x3,x))))),implies__dfg(x4,implies__dfg(x5,implies__dfg(z,implies__dfg(x1,implies__dfg(x2,implies__dfg(x3,x)))))))),
inference(sor,[status(thm)],[7,119]),
[iquote('0:SoR:7.0,119.0')] ).
cnf(361,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),w),implies__dfg(w,implies__dfg(x,w))))),
inference(ems,[status(thm)],[172,53]),
[iquote('0:EmS:172.0,53.0')] ).
cnf(396,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),w),implies__dfg(w,implies__dfg(x,w)))) ),
inference(res,[status(thm),theory(equality)],[361,1]),
[iquote('0:Res:361.0,1.1')] ).
cnf(398,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),v),implies__dfg(v,implies__dfg(w,v)))),
inference(ems,[status(thm)],[396,53]),
[iquote('0:EmS:396.0,53.0')] ).
cnf(424,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(x,implies__dfg(v,implies__dfg(w,v))))),
inference(sor,[status(thm)],[7,398]),
[iquote('0:SoR:7.0,398.0')] ).
cnf(509,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(implies__dfg(w,x),w),implies__dfg(y,implies__dfg(implies__dfg(z,w),w))))) ),
inference(res,[status(thm),theory(equality)],[228,1]),
[iquote('0:Res:228.0,1.1')] ).
cnf(550,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))
| is_a_theorem(implies__dfg(x,implies__dfg(v,implies__dfg(w,v)))) ),
inference(res,[status(thm),theory(equality)],[424,1]),
[iquote('0:Res:424.0,1.1')] ).
cnf(896,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,implies__dfg(implies__dfg(y,v),v))))),
inference(ems,[status(thm)],[509,297]),
[iquote('0:EmS:509.0,297.0')] ).
cnf(957,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,implies__dfg(implies__dfg(y,v),v)))) ),
inference(res,[status(thm),theory(equality)],[896,1]),
[iquote('0:Res:896.0,1.1')] ).
cnf(1066,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,implies__dfg(implies__dfg(x,u),u)))),
inference(ems,[status(thm)],[957,297]),
[iquote('0:EmS:957.0,297.0')] ).
cnf(1122,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
| is_a_theorem(implies__dfg(w,implies__dfg(implies__dfg(x,u),u))) ),
inference(res,[status(thm),theory(equality)],[1066,1]),
[iquote('0:Res:1066.0,1.1')] ).
cnf(1157,plain,
is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(w,implies__dfg(x,x))),implies__dfg(w,implies__dfg(x,x))))),
inference(sor,[status(thm)],[1122,43]),
[iquote('0:SoR:1122.0,43.0')] ).
cnf(1178,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(w,implies__dfg(x,x))),implies__dfg(w,implies__dfg(x,x)))) ),
inference(res,[status(thm),theory(equality)],[1157,1]),
[iquote('0:Res:1157.0,1.1')] ).
cnf(1220,plain,
is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,w))),implies__dfg(v,implies__dfg(w,w)))),
inference(ems,[status(thm)],[1178,1066]),
[iquote('0:EmS:1178.0,1066.0')] ).
cnf(1271,plain,
is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,implies__dfg(x,v)))),
inference(sor,[status(thm)],[7,1220]),
[iquote('0:SoR:7.0,1220.0')] ).
cnf(1286,plain,
( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w))))
| is_a_theorem(implies__dfg(v,implies__dfg(w,w))) ),
inference(res,[status(thm),theory(equality)],[1220,1]),
[iquote('0:Res:1220.0,1.1')] ).
cnf(1595,plain,
( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
| is_a_theorem(implies__dfg(w,implies__dfg(x,v))) ),
inference(res,[status(thm),theory(equality)],[1271,1]),
[iquote('0:Res:1271.0,1.1')] ).
cnf(1734,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,implies__dfg(x,x))))),
inference(sor,[status(thm)],[1595,1220]),
[iquote('0:SoR:1595.0,1220.0')] ).
cnf(1804,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,implies__dfg(x,x)))) ),
inference(res,[status(thm),theory(equality)],[1734,1]),
[iquote('0:Res:1734.0,1.1')] ).
cnf(1806,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
inference(ems,[status(thm)],[1804,1271]),
[iquote('0:EmS:1804.0,1271.0')] ).
cnf(1860,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
inference(mrr,[status(thm)],[1286,1806]),
[iquote('0:MRR:1286.0,1806.0')] ).
cnf(1882,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,v)) ),
inference(res,[status(thm),theory(equality)],[1860,1]),
[iquote('0:Res:1860.0,1.1')] ).
cnf(1906,plain,
is_a_theorem(implies__dfg(u,u)),
inference(ems,[status(thm)],[1882,1271]),
[iquote('0:EmS:1882.0,1271.0')] ).
cnf(1973,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
inference(sor,[status(thm)],[550,1906]),
[iquote('0:SoR:550.0,1906.0')] ).
cnf(2077,plain,
( ~ is_a_theorem(u)
| is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
inference(res,[status(thm),theory(equality)],[1973,1]),
[iquote('0:Res:1973.0,1.1')] ).
cnf(2078,plain,
is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
inference(ems,[status(thm)],[2077,1906]),
[iquote('0:EmS:2077.0,1906.0')] ).
cnf(2129,plain,
$false,
inference(unc,[status(thm)],[2078,3]),
[iquote('0:UnC:2078.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL091-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 22:44:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.64/0.94
% 0.64/0.94 SPASS V 3.9
% 0.64/0.94 SPASS beiseite: Proof found.
% 0.64/0.94 % SZS status Theorem
% 0.64/0.94 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.94 SPASS derived 2096 clauses, backtracked 0 clauses, performed 0 splits and kept 399 clauses.
% 0.64/0.94 SPASS allocated 78866 KBytes.
% 0.64/0.94 SPASS spent 0:00:00.56 on the problem.
% 0.64/0.94 0:00:00.06 for the input.
% 0.64/0.94 0:00:00.00 for the FLOTTER CNF translation.
% 0.64/0.94 0:00:00.09 for inferences.
% 0.64/0.94 0:00:00.00 for the backtracking.
% 0.64/0.94 0:00:00.36 for the reduction.
% 0.64/0.94
% 0.64/0.94
% 0.64/0.94 Here is a proof with depth 21, length 52 :
% 0.64/0.94 % SZS output start Refutation
% See solution above
% 0.64/0.98 Formulae used in the proof : condensed_detachment ic_JLukasiewicz_5 prove_ic_2
% 0.64/0.98
%------------------------------------------------------------------------------