%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL090-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 0.13s 5.78s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 13 unt; 9 def)
% Number of atoms : 142 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 157 ( 78 ~; 70 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 10 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 185 ( 185 !; 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,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ is_a_theorem(implies(a,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(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(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(f19,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| is_a_theorem(X0)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X3,X0))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f12,f5]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,implies(a,a)))
| ~ is_a_theorem(implies(implies(implies(a,a),X0),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f19,f7]) ).
fof(f27,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(a,a),X0),implies(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(a,a),X0),implies(X1,X2))) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f34,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f15]) ).
fof(f35,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(implies(implies(implies(X0,implies(X1,X2)),implies(X2,X3)),implies(X4,implies(implies(X5,X2),implies(X2,X3))))),
inference(resolution,[status(thm)],[f8,f6]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( is_a_theorem(implies(X7,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)],[f9,f6]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5] :
( is_a_theorem(implies(X4,implies(implies(X5,X2),implies(X2,X3))))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f38,f5]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X4,X2)))))),
inference(resolution,[status(thm)],[f46,f38]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f47,f28]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(implies(X0,implies(implies(X1,implies(X2,X3)),implies(implies(X2,X3),implies(X3,implies(implies(X4,X5),implies(X5,X3))))))),
inference(resolution,[status(thm)],[f47,f46]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(implies(implies(implies(X0,implies(implies(X1,X2),implies(X2,X0))),X3),implies(X4,implies(implies(X5,X0),X3)))),
inference(resolution,[status(thm)],[f47,f8]) ).
fof(f59,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f48]) ).
fof(f60,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X5,X2)))))),
inference(resolution,[status(thm)],[f46,f50]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( is_a_theorem(implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X5,X2)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f101,f5]) ).
fof(f110,definition,
! [X1,X2,X3,X4,X5] :
( sQ6_spl
<=> is_a_theorem(implies(implies(X1,X2),implies(X2,implies(implies(X3,X4),implies(X5,X2))))) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| is_a_theorem(implies(implies(X0,X1),implies(X1,implies(implies(X2,X3),implies(X4,X1))))) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ6_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f109,f14,f110]) ).
fof(f178,definition,
! [X2,X3] :
( sQ18_spl
<=> ~ is_a_theorem(implies(X2,X3)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ is_a_theorem(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f182,plain,
( ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f50,f179]) ).
fof(f192,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f208,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ6_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X3)),X4),implies(X5,implies(X3,X4)))) ),
inference(resolution,[status(thm)],[f8,f111]) ).
fof(f303,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| is_a_theorem(implies(X0,implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3)))))) ),
inference(resolution,[status(thm)],[f41,f208]) ).
fof(f356,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f303,f5]) ).
fof(f359,definition,
! [X1,X2,X3,X4] :
( sQ22_spl
<=> is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,implies(X3,X3))))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f360,plain,
! [X0,X1,X2,X3] :
( ~ sQ22_spl
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(X3,implies(X2,X2))))) ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( ~ sQ6_spl
| sQ22_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f356,f14,f359,f110]) ).
fof(f373,plain,
! [X0,X1,X2,X3] :
( ~ sQ22_spl
| is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X2,X2))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f360,f5]) ).
fof(f376,definition,
! [X1,X2,X3] :
( sQ23_spl
<=> is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X2,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f377,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| is_a_theorem(implies(implies(X0,X1),implies(X2,implies(X1,X1)))) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,plain,
( ~ sQ22_spl
| sQ23_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f373,f14,f376,f359]) ).
fof(f382,plain,
! [X0,X1,X2,X3] :
( ~ sQ23_spl
| is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,implies(X3,X1)))) ),
inference(resolution,[status(thm)],[f377,f8]) ).
fof(f418,plain,
! [X0,X1,X2,X3] :
( ~ sQ23_spl
| is_a_theorem(implies(X2,implies(X3,X1)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f382,f5]) ).
fof(f426,plain,
! [X0,X1,X2,X3] :
( ~ sQ23_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,implies(X3,X3))))) ),
inference(resolution,[status(thm)],[f418,f377]) ).
fof(f447,plain,
! [X0,X1,X2,X3] :
( ~ sQ23_spl
| is_a_theorem(implies(X1,implies(X2,implies(X3,X3))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f426,f5]) ).
fof(f450,definition,
! [X1,X2,X3] :
( sQ24_spl
<=> is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ23_spl
| sQ24_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f447,f14,f450,f376]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| is_a_theorem(implies(X1,implies(X2,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f451,f5]) ).
fof(f470,definition,
! [X1,X2] :
( sQ25_spl
<=> is_a_theorem(implies(X1,implies(X2,X2))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f471,plain,
! [X0,X1] :
( ~ sQ25_spl
| is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( ~ sQ24_spl
| sQ25_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f467,f14,f470,f450]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ25_spl
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(a,a),X0),implies(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[f21,f471]) ).
fof(f476,plain,
( ~ sQ0_spl
| ~ sQ25_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f474,f27,f470,f11]) ).
fof(f477,plain,
$false,
inference(sat_refutation,[status(thm)],[f17,f35,f60,f113,f192,f362,f379,f453,f473,f476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL090-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.58 % Computer : n006.cluster.edu
% 0.08/5.58 % Model : x86_64 x86_64
% 0.08/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.58 % Memory : 8046.5625MB
% 0.08/5.58 % OS : Linux 6.8.0-71-generic
% 0.08/5.58 % CPULimit : 300
% 0.08/5.58 % WCLimit : 300
% 0.08/5.58 % DateTime : Mon Sep 21 00:04:18 UTC 2026
% 0.08/5.58 % CPUTime :
% 0.08/5.59 % Drodi V4.1.1
% 0.13/5.78 % Refutation found
% 0.13/5.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.80 % Elapsed time: 0.208239 seconds
% 0.13/5.80 % CPU time: 1.489539 seconds
% 0.13/5.80 % Total memory used: 81.992 MB
% 0.13/5.80 % Net memory used: 77.291 MB
%------------------------------------------------------------------------------