%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL036-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 01:06:38 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.48s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 13 unt; 4 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 44 ~; 41 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 123 ( 123 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z,U,V] : is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(X2,falsehood)),X3),X4),implies(implies(X4,X0),implies(X2,X0)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(implies(implies(implies(a,falsehood),falsehood),a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(implies(X4,X0),implies(X2,X0)))
| ~ is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,falsehood)),X3),X4)) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3)),implies(X4,implies(X1,X3)))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(falsehood,X1)),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(X4,implies(X1,X3)))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3))) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f12,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(falsehood,X2))),
inference(resolution,[status(thm)],[f10,f8]) ).
fof(f14,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(falsehood,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f22,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f29,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f23]) ).
fof(f34,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f161,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f167,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X2),implies(X3,X2))),
inference(resolution,[status(thm)],[f161,f8]) ).
fof(f171,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f161,f5]) ).
fof(f172,definition,
! [X1,X2] :
( sQ11_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f173,plain,
! [X0,X1] :
( ~ sQ11_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f171,f22,f172]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ11_spl
| is_a_theorem(implies(implies(implies(X0,implies(implies(implies(X1,X2),implies(X3,falsehood)),X4)),X1),implies(X3,X1))) ),
inference(resolution,[status(thm)],[f173,f8]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f167,f5]) ).
fof(f605,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(implies(X1,X3),implies(X0,falsehood)),X2))) ),
inference(resolution,[status(thm)],[f177,f8]) ).
fof(f762,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ11_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X4,implies(X3,X1))))) ),
inference(resolution,[status(thm)],[f605,f212]) ).
fof(f777,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ11_spl
| is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X4,implies(X3,X1))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f762,f5]) ).
fof(f780,definition,
! [X1,X2,X3,X4] :
( sQ34_spl
<=> is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X4,implies(X3,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f781,plain,
! [X0,X1,X2,X3] :
( ~ sQ34_spl
| is_a_theorem(implies(implies(implies(X0,X1),implies(X2,falsehood)),implies(X3,implies(X2,X0)))) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f783,plain,
( ~ sQ11_spl
| sQ34_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f777,f22,f780,f172]) ).
fof(f806,plain,
! [X0,X1,X2,X3] :
( ~ sQ34_spl
| is_a_theorem(implies(X3,implies(X2,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,falsehood))) ),
inference(resolution,[status(thm)],[f781,f5]) ).
fof(f874,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| ~ sQ34_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X3,X1)))) ),
inference(resolution,[status(thm)],[f806,f605]) ).
fof(f888,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| ~ sQ34_spl
| is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X3,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f874,f5]) ).
fof(f891,definition,
! [X1,X2,X3] :
( sQ37_spl
<=> is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X3,X1))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f892,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(implies(X0,X1),implies(X2,falsehood)),implies(X2,X0))) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f894,plain,
( ~ sQ11_spl
| ~ sQ34_spl
| sQ37_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f888,f22,f891,f780,f172]) ).
fof(f896,plain,
! [X0,X1,X2,X3] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),X1),implies(X3,X1))) ),
inference(resolution,[status(thm)],[f892,f8]) ).
fof(f900,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,falsehood))) ),
inference(resolution,[status(thm)],[f892,f5]) ).
fof(f932,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f896,f8]) ).
fof(f943,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(implies(implies(X0,falsehood),X1),X2),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f932,f8]) ).
fof(f2167,plain,
! [X0,X1] :
( ~ sQ37_spl
| is_a_theorem(implies(X0,implies(implies(X0,falsehood),X1))) ),
inference(resolution,[status(thm)],[f943,f900]) ).
fof(f2189,plain,
! [X0,X1] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(implies(X0,X1),falsehood),X0)) ),
inference(resolution,[status(thm)],[f2167,f900]) ).
fof(f2200,plain,
( ~ sQ37_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f2189]) ).
fof(f2214,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f2200]) ).
fof(f2215,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f175,f783,f894,f2214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:02:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.48 % Refutation found
% 0.11/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.51 % Elapsed time: 0.127236 seconds
% 0.11/0.51 % CPU time: 0.755524 seconds
% 0.11/0.51 % Total memory used: 71.091 MB
% 0.11/0.51 % Net memory used: 69.366 MB
%------------------------------------------------------------------------------