%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL092-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 : Thu Sep 24 01:06:47 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.64s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 6 unt; 5 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 299 ( 149 ~; 145 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 204 ( 204 !; 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(implies(S,P),implies(T,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(implies(X3,X0),implies(X4,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(implies(X3,X0),implies(X4,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] :
( is_a_theorem(implies(X4,implies(X2,X0)))
| ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f8,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3,X4] :
( is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f9,f5]) ).
fof(f11,definition,
! [X0,X1,X2,X3] :
( sQ0_spl
<=> ( is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
! [X4] :
( sQ1_spl
<=> ~ is_a_theorem(X4) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f15,plain,
! [X0] :
( ~ sQ1_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f11,f14]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ0_spl
| is_a_theorem(implies(X5,implies(implies(X0,X1),implies(X2,implies(X3,X1)))))
| ~ is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,implies(X3,X1))),X4),implies(X5,implies(implies(X1,X6),implies(X3,X0))))) ),
inference(resolution,[status(thm)],[f12,f6]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(X2,X6),implies(X1,X5)))
| is_a_theorem(implies(X4,implies(X0,implies(X1,X2))))
| ~ is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),X3),implies(X4,implies(X5,X2)))) ),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(implies(X4,X1),X5),implies(implies(X2,X6),implies(implies(X1,X2),implies(X3,implies(X4,X2))))))
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,implies(X4,X2))))) ),
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f23,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ0_spl
| is_a_theorem(implies(X5,implies(X0,implies(implies(X1,X2),implies(X2,X3)))))
| ~ is_a_theorem(implies(implies(implies(X0,implies(implies(X1,X2),implies(X2,X3))),X4),implies(X5,implies(implies(X6,implies(X7,X2)),implies(X2,X3))))) ),
inference(resolution,[status(thm)],[f19,f6]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(implies(X3,implies(X4,X2)),X5),implies(implies(X1,X2),implies(X4,X1))))
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,implies(X4,X2))))) ),
inference(resolution,[status(thm)],[f21,f8]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X2),implies(X2,implies(X3,X2))))) ),
inference(resolution,[status(thm)],[f26,f6]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ0_spl
| ~ is_a_theorem(implies(implies(X1,X5),implies(X4,implies(X3,implies(X4,X2)))))
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,implies(X4,X2))))) ),
inference(resolution,[status(thm)],[f26,f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),implies(X1,X2)),implies(implies(implies(X1,X2),X1),implies(X3,implies(X4,X1))))) ),
inference(resolution,[status(thm)],[f28,f18]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,implies(implies(implies(X1,X2),X2),implies(X3,implies(X2,X2))))) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f40,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f15]) ).
fof(f41,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(X1,X2),X2),implies(X3,implies(X2,X2))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f32,f5]) ).
fof(f48,definition,
! [X1,X2,X3] :
( sQ3_spl
<=> is_a_theorem(implies(implies(implies(X1,X2),X2),implies(X3,implies(X2,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| is_a_theorem(implies(implies(implies(X0,X1),X1),implies(X2,implies(X1,X1)))) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f47,f14,f48,f11]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| is_a_theorem(implies(X2,implies(X1,X1)))
| ~ is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f49,f5]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,implies(X4,X1))))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f31,f5]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| is_a_theorem(implies(X3,implies(X4,X1)))
| ~ is_a_theorem(implies(implies(X1,X2),X1))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f69,f5]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(X0,X4),implies(X3,implies(X2,X4))))
| ~ is_a_theorem(X5)
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X3,implies(X2,X4))))) ),
inference(resolution,[status(thm)],[f29,f5]) ).
fof(f101,definition,
! [X0,X1,X2,X3,X4] :
( sQ6_spl
<=> ( is_a_theorem(implies(implies(X0,X4),implies(X3,implies(X2,X4))))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X3,implies(X2,X4))))) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| is_a_theorem(implies(implies(X0,X4),implies(X3,implies(X2,X4))))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X3,implies(X2,X4))))) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f100,f101,f14,f11]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| is_a_theorem(implies(X3,implies(X2,X4)))
| ~ is_a_theorem(implies(X0,X4))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X3,implies(X2,X4))))) ),
inference(resolution,[status(thm)],[f102,f5]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| is_a_theorem(implies(X2,implies(implies(X3,X0),X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f106,f6]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| is_a_theorem(implies(implies(X3,X0),X0))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f108,f5]) ).
fof(f122,definition,
! [X0,X1,X3] :
( sQ7_spl
<=> ( is_a_theorem(implies(implies(X3,X0),X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| is_a_theorem(implies(implies(X2,X0),X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( ~ sQ6_spl
| sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f121,f122,f14,f101]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ7_spl
| is_a_theorem(implies(X2,implies(X0,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f123,f52]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f123,f5]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| is_a_theorem(implies(X2,implies(X3,X0)))
| ~ is_a_theorem(implies(implies(X0,X0),X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f129,f81]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| is_a_theorem(implies(X2,implies(X3,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f123]) ).
fof(f202,plain,
! [X0,X1,X2,X3] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(X2,implies(X3,X0)))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f139,f132]) ).
fof(f208,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f139]) ).
fof(f213,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f208]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ3_spl
| is_a_theorem(implies(implies(implies(X0,implies(X1,X0)),X0),implies(X0,implies(X1,X0)))) ),
inference(resolution,[status(thm)],[f213,f31]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[f224,f213]) ).
fof(f314,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(implies(X0,X1),implies(X1,implies(implies(X2,X3),implies(X3,X1))))) ),
inference(resolution,[status(thm)],[f23,f6]) ).
fof(f454,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(implies(X0,implies(implies(X0,X1),implies(X2,implies(X3,X1))))) ),
inference(resolution,[status(thm)],[f314,f18]) ).
fof(f457,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ sQ0_spl
| is_a_theorem(implies(implies(X2,X1),implies(X1,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f314,f106]) ).
fof(f532,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| ~ sQ0_spl
| is_a_theorem(implies(X2,implies(implies(implies(X0,X3),X1),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f454,f106]) ).
fof(f556,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f457,f213]) ).
fof(f633,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| is_a_theorem(implies(implies(implies(X0,X2),X1),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f532,f213]) ).
fof(f642,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(a,a)) ),
inference(resolution,[status(thm)],[f633,f7]) ).
fof(f649,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f633,f213]) ).
fof(f654,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(X0,a)) ),
inference(resolution,[status(thm)],[f642,f556]) ).
fof(f697,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f649,f239]) ).
fof(f708,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl
| $false ),
inference(resolution,[status(thm)],[f697,f654]) ).
fof(f711,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f712,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f41,f51,f104,f125,f711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL092-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n020.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 00:05:23 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.12/5.64 % Refutation found
% 0.12/5.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.65 % Elapsed time: 0.280284 seconds
% 0.12/5.65 % CPU time: 2.068183 seconds
% 0.12/5.65 % Total memory used: 86.214 MB
% 0.12/5.65 % Net memory used: 80.753 MB
%------------------------------------------------------------------------------