%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL088-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 01:06:46 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 7 unt; 4 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 165 ( 82 ~; 79 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 6 ( 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 : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [P,Q,R,S,T] : is_a_theorem(implies(implies(implies(P,Q),implies(R,S)),implies(T,implies(implies(S,P),implies(R,P))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox2/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(X0,X1),implies(X2,X3)),implies(X4,implies(implies(X3,X0),implies(X2,X0))))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(X4,implies(implies(X3,X0),implies(X2,X0))))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f9,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(implies(X0,implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4))))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4,X5] :
( is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f12,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f13,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,definition,
! [X1,X2,X3,X4,X5] :
( sQ1_spl
<=> is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3)),implies(X4,implies(X1,X3)))) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f12,f15]) ).
fof(f19,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f13]) ).
fof(f22,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| 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)],[f16,f5]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3))) ),
inference(resolution,[status(thm)],[f23,f5]) ).
fof(f29,definition,
! [X0,X1,X2,X3] :
( sQ2_spl
<=> ( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X1,X3))) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( ~ sQ1_spl
| sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f28,f29,f12,f15]) ).
fof(f33,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ2_spl
| is_a_theorem(implies(implies(X0,X1),implies(X1,implies(X0,X1)))) ),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,X1)))) ),
inference(resolution,[status(thm)],[f30,f6]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ2_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X2,X1)))) ),
inference(resolution,[status(thm)],[f33,f8]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f34,f5]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f39,f30]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f43,f5]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ2_spl
| is_a_theorem(implies(X3,implies(implies(X2,X4),implies(X1,X4))))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f48,f8]) ).
fof(f93,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X1,X0))) ),
inference(resolution,[status(thm)],[f36,f30]) ).
fof(f100,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[f93,f30]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X1),implies(X3,X1)))) ),
inference(resolution,[status(thm)],[f100,f8]) ).
fof(f105,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f100,f5]) ).
fof(f106,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X2,implies(implies(X1,X3),implies(X0,X3))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f75,f105]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),implies(X2,X0))) ),
inference(resolution,[status(thm)],[f104,f30]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f138,f5]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f149,f5]) ).
fof(f154,definition,
! [X0,X1] :
( sQ13_spl
<=> ( is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ13_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f153,f154,f12,f15,f29]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f106,f30]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f234,f155]) ).
fof(f256,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ13_spl
| is_a_theorem(implies(implies(implies(X0,X1),X0),X0)) ),
inference(resolution,[status(thm)],[f252,f138]) ).
fof(f276,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7,f256]) ).
fof(f277,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
$false,
inference(sat_refutation,[status(thm)],[f18,f22,f32,f157,f277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL088-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n019.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 00:04:49 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.083360 seconds
% 0.13/0.43 % CPU time: 0.451627 seconds
% 0.13/0.43 % Total memory used: 64.340 MB
% 0.13/0.43 % Net memory used: 63.217 MB
%------------------------------------------------------------------------------