%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL071-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 01:06:44 PM UTC 2026
% Result : Unsatisfiable 56.75s 7.65s
% Output : CNFRefutation 56.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 15 unt; 6 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 264 ( 130 ~; 128 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 164 ( 164 !; 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] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,U] : is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(not(a),a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(X0,implies(not(X1),X2)),implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(not(a),a),a)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f14,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X0)))),
inference(resolution,[status(thm)],[f13,f12]) ).
fof(f15,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f13,f7]) ).
fof(f17,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f15,f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f17,f7]) ).
fof(f27,definition,
! [X0] :
( sQ0_spl
<=> ~ is_a_theorem(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0] :
( ~ sQ0_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,definition,
! [X1,X2] :
( sQ1_spl
<=> is_a_theorem(implies(X1,implies(X2,X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f27,f30]) ).
fof(f34,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f28]) ).
fof(f39,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f69,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(not(X0),X1),implies(X2,implies(implies(X3,X1),implies(implies(X0,X3),X1))))),
inference(resolution,[status(thm)],[f12,f10]) ).
fof(f87,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(implies(X0,X1)),implies(X1,X2))),
inference(resolution,[status(thm)],[f19,f8]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(not(X0),implies(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f19,f31]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| is_a_theorem(implies(X1,implies(X0,X2)))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[status(thm)],[f96,f7]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X2),implies(implies(X1,X3),X2)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f55,f7]) ).
fof(f117,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X2,implies(implies(X3,X1),implies(implies(X0,X3),X1))))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f69,f7]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X3,X1),implies(implies(X0,X3),X1)))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f117,f7]) ).
fof(f160,definition,
! [X0,X1,X3] :
( sQ12_spl
<=> ( is_a_theorem(implies(implies(X3,X1),implies(implies(X0,X3),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(implies(X2,X1),implies(implies(X0,X2),X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ0_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f159,f160,f27]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(implies(X0,X2),X1))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f161,f7]) ).
fof(f168,plain,
( ~ sQ12_spl
| ~ is_a_theorem(implies(a,a))
| ~ is_a_theorem(implies(not(not(a)),a)) ),
inference(resolution,[status(thm)],[f166,f11]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f166,f7]) ).
fof(f172,definition,
( sQ13_spl
<=> is_a_theorem(implies(not(not(a)),a)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ13_spl
| ~ is_a_theorem(implies(not(not(a)),a)) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ14_spl
<=> is_a_theorem(implies(a,a)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ14_spl
| ~ is_a_theorem(implies(a,a)) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f168,f172,f175,f160]) ).
fof(f184,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X1,X3),X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f114,f7]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X0))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f171,f87]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f188,f8]) ).
fof(f239,plain,
! [X0,X1,X2,X3] :
( ~ sQ12_spl
| is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),implies(X2,X3))) ),
inference(resolution,[status(thm)],[f188,f17]) ).
fof(f245,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f218,f8]) ).
fof(f270,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f245,f171]) ).
fof(f273,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(not(X0),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f245,f19]) ).
fof(f276,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f273,f171]) ).
fof(f288,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ is_a_theorem(implies(not(X0),implies(X2,X1)))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) ),
inference(resolution,[status(thm)],[f239,f161]) ).
fof(f433,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f276,f245]) ).
fof(f441,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,implies(not(X0),X0)))
| is_a_theorem(implies(implies(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f433,f114]) ).
fof(f642,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f184,f7]) ).
fof(f647,plain,
( sQ14_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f245]) ).
fof(f648,plain,
( sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f647]) ).
fof(f707,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f441,f7]) ).
fof(f712,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f245]) ).
fof(f727,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ is_a_theorem(implies(not(X0),implies(not(X1),X1)))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f712,f288]) ).
fof(f834,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X1,not(X0)))
| ~ is_a_theorem(implies(X0,implies(X1,not(X0)))) ),
inference(resolution,[status(thm)],[f727,f14]) ).
fof(f843,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[f834,f273]) ).
fof(f943,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f843,f270]) ).
fof(f944,plain,
! [X0,X1] :
( ~ sQ12_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(not(not(X0)),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f843,f276]) ).
fof(f1306,plain,
! [X0] :
( ~ sQ12_spl
| is_a_theorem(not(not(implies(X0,X0)))) ),
inference(resolution,[status(thm)],[f943,f87]) ).
fof(f1316,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ12_spl
| is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))) ),
inference(resolution,[status(thm)],[f1306,f99]) ).
fof(f4598,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ12_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X3,X3),X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f642,f1316]) ).
fof(f4658,definition,
! [X1,X2,X3] :
( sQ183_spl
<=> ( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X3,X3),X1))
| ~ is_a_theorem(implies(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f4659,plain,
! [X0,X1,X2] :
( ~ sQ183_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f4658]) ).
fof(f4661,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| sQ183_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f4598,f27,f4658,f160,f30]) ).
fof(f5130,plain,
! [X0,X1,X2] :
( ~ sQ183_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f4659,f8]) ).
fof(f5185,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ sQ183_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f4659,f245]) ).
fof(f6041,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ sQ183_spl
| is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f161,f5185]) ).
fof(f7133,plain,
! [X0,X1] :
( ~ sQ183_spl
| ~ sQ12_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),implies(X1,X0))) ),
inference(resolution,[status(thm)],[f6041,f5130]) ).
fof(f10395,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ12_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f944,f96]) ).
fof(f10466,plain,
! [X0] :
( ~ sQ183_spl
| ~ sQ12_spl
| ~ sQ1_spl
| is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f10395,f7133]) ).
fof(f10483,plain,
( sQ13_spl
| ~ sQ183_spl
| ~ sQ12_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f174,f10466]) ).
fof(f10533,plain,
( sQ13_spl
| ~ sQ183_spl
| ~ sQ12_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f10483]) ).
fof(f10534,plain,
$false,
inference(sat_refutation,[status(thm)],[f33,f39,f163,f178,f648,f4661,f10533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL071-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 00:08:07 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 56.75/7.65 % Refutation found
% 56.75/7.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 56.75/7.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 56.75/7.70 % Elapsed time: 7.271743 seconds
% 56.75/7.70 % CPU time: 57.190266 seconds
% 56.75/7.70 % Total memory used: 321.502 MB
% 56.75/7.70 % Net memory used: 269.030 MB
%------------------------------------------------------------------------------