%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL390-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 01:07:35 PM UTC 2026
% Result : Unsatisfiable 226.98s 37.21s
% Output : CNFRefutation 226.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 7
% Syntax : Number of formulae : 98 ( 45 unt; 2 def)
% Number of atoms : 162 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 130 ( 66 ~; 62 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 200 ( 200 !; 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(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
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(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
~ is_a_theorem(implies(implies(not(x),y),implies(implies(x,y),y))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f7,f9]) ).
fof(f13,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f7,f10]) ).
fof(f23,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f23,f7]) ).
fof(f26,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f25,f12]) ).
fof(f28,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(x,y),y)))
| ~ is_a_theorem(implies(implies(not(x),y),X0)) ),
inference(resolution,[status(thm)],[f25,f11]) ).
fof(f29,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f7]) ).
fof(f117,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[f23,f9]) ).
fof(f118,plain,
! [X0,X1,X2,X3] : is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))),
inference(resolution,[status(thm)],[f23,f8]) ).
fof(f119,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[f23,f10]) ).
fof(f120,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X1),X2),implies(implies(X0,X1),X2))),
inference(resolution,[status(thm)],[f117,f23]) ).
fof(f123,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f117,f7]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,implies(implies(not(X1),X2),X3))) ),
inference(resolution,[status(thm)],[f119,f29]) ).
fof(f130,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f119,f7]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(X1,X3)))
| ~ is_a_theorem(implies(X0,implies(implies(not(X1),X2),X3))) ),
inference(resolution,[status(thm)],[f25,f119]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[f25,f9]) ).
fof(f139,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,implies(not(X1),X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f25,f10]) ).
fof(f163,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f130,f9]) ).
fof(f165,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(resolution,[status(thm)],[f130,f8]) ).
fof(f180,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X0)),X1)),
inference(resolution,[status(thm)],[f163,f13]) ).
fof(f188,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))),
inference(resolution,[status(thm)],[f180,f23]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(implies(X2,X0),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[f118,f7]) ).
fof(f329,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),implies(not(X0),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f165,f7]) ).
fof(f342,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(not(implies(X1,X1)),X2))),
inference(resolution,[status(thm)],[f188,f130]) ).
fof(f362,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f342,f136]) ).
fof(f460,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(X0,y),implies(implies(x,y),y)))
| ~ is_a_theorem(implies(X0,not(x))) ),
inference(resolution,[status(thm)],[f23,f28]) ).
fof(f516,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f26,f362]) ).
fof(f564,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,implies(not(X1),X2))) ),
inference(resolution,[status(thm)],[f130,f329]) ).
fof(f566,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f130,f23]) ).
fof(f628,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f136,f23]) ).
fof(f639,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f136,f564]) ).
fof(f645,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[f639,f9]) ).
fof(f660,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X2)))),
inference(resolution,[status(thm)],[f639,f362]) ).
fof(f668,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X1)),X2)) ),
inference(resolution,[status(thm)],[f660,f26]) ).
fof(f733,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X0),X1),implies(X2,X1))),
inference(resolution,[status(thm)],[f668,f8]) ).
fof(f782,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(resolution,[status(thm)],[f733,f136]) ).
fof(f793,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,implies(implies(X1,X1),X2))) ),
inference(resolution,[status(thm)],[f782,f25]) ).
fof(f851,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f139,f516]) ).
fof(f873,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X2,implies(not(X0),X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f25]) ).
fof(f874,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X0),X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f7]) ).
fof(f1055,plain,
! [X0,X1] : is_a_theorem(implies(implies(implies(implies(not(X0),X0),X0),X1),X1)),
inference(resolution,[status(thm)],[f628,f645]) ).
fof(f1060,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(implies(not(X0),X1),X2),X2)) ),
inference(resolution,[status(thm)],[f628,f564]) ).
fof(f1419,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(implies(X2,X2),X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f874,f851]) ).
fof(f1476,plain,
! [X0,X1,X2,X3] :
( is_a_theorem(implies(X0,implies(implies(X1,X2),X3)))
| ~ is_a_theorem(implies(X0,implies(implies(implies(not(X1),X1),X2),X3))) ),
inference(resolution,[status(thm)],[f120,f25]) ).
fof(f1959,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(implies(implies(X2,X2),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f793,f23]) ).
fof(f2136,definition,
( sQ78_spl
<=> is_a_theorem(implies(y,implies(implies(x,y),y))) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f2138,plain,
( sQ78_spl
| ~ is_a_theorem(implies(y,implies(implies(x,y),y))) ),
inference(component_clause,[status(thm)],[f2136]) ).
fof(f3432,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[f278,f1055]) ).
fof(f3438,plain,
! [X0,X1,X2] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X0,not(X1)),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f278,f1060]) ).
fof(f3515,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f3432,f278]) ).
fof(f3620,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f3438,f136]) ).
fof(f3794,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f3620,f1959]) ).
fof(f3881,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(not(X1),X1)),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f3794,f136]) ).
fof(f4246,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[f3515,f130]) ).
fof(f4265,plain,
( sQ78_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2138,f4246]) ).
fof(f4286,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[f4246,f135]) ).
fof(f4294,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f4265]) ).
fof(f4325,plain,
! [X0,X1,X2] : is_a_theorem(implies(X0,implies(X1,implies(X2,X1)))),
inference(resolution,[status(thm)],[f4286,f639]) ).
fof(f4411,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,implies(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f4325,f1419]) ).
fof(f6474,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(resolution,[status(thm)],[f4411,f8]) ).
fof(f7472,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[f128,f3515]) ).
fof(f7666,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f6474,f7]) ).
fof(f7749,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f7666,f3515]) ).
fof(f7838,plain,
! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[f7749,f135]) ).
fof(f7858,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f7838,f136]) ).
fof(f7868,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(resolution,[status(thm)],[f7858,f628]) ).
fof(f7900,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[f7858,f25]) ).
fof(f8214,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f7868,f130]) ).
fof(f8270,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f8214,f25]) ).
fof(f12881,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X0),implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f1476,f7749]) ).
fof(f13052,plain,
! [X0] : is_a_theorem(implies(not(not(not(not(X0)))),X0)),
inference(resolution,[status(thm)],[f7900,f7858]) ).
fof(f13087,plain,
! [X0] : is_a_theorem(implies(X0,not(not(not(not(X0)))))),
inference(resolution,[status(thm)],[f13052,f7472]) ).
fof(f13182,plain,
! [X0,X1] : is_a_theorem(implies(not(not(not(X0))),implies(X0,X1))),
inference(resolution,[status(thm)],[f13087,f566]) ).
fof(f14764,plain,
! [X0,X1] :
( is_a_theorem(implies(not(X1),X0))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f8270,f7472]) ).
fof(f20251,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),not(not(X0)))),
inference(resolution,[status(thm)],[f14764,f13182]) ).
fof(f20473,plain,
! [X0,X1,X2] : is_a_theorem(implies(not(X0),implies(not(implies(X0,X1)),X2))),
inference(resolution,[status(thm)],[f20251,f566]) ).
fof(f23821,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(not(X0),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f20473,f873]) ).
fof(f25992,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f3881,f278]) ).
fof(f44983,plain,
! [X0,X1] : is_a_theorem(implies(not(not(X0)),implies(implies(X0,X1),X1))),
inference(resolution,[status(thm)],[f23821,f12881]) ).
fof(f45180,plain,
! [X0,X1] : is_a_theorem(implies(not(implies(implies(X0,X1),X1)),not(X0))),
inference(resolution,[status(thm)],[f44983,f14764]) ).
fof(f46836,plain,
( ~ is_a_theorem(implies(not(implies(implies(x,y),y)),not(x)))
| ~ is_a_theorem(implies(y,implies(implies(x,y),y))) ),
inference(resolution,[status(thm)],[f25992,f460]) ).
fof(f47054,definition,
( sQ747_spl
<=> is_a_theorem(implies(not(implies(implies(x,y),y)),not(x))) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f47056,plain,
( sQ747_spl
| ~ is_a_theorem(implies(not(implies(implies(x,y),y)),not(x))) ),
inference(component_clause,[status(thm)],[f47054]) ).
fof(f47057,plain,
( ~ sQ747_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f46836,f2136,f47054]) ).
fof(f47062,plain,
( sQ747_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f47056,f45180]) ).
fof(f47063,plain,
sQ747_spl,
inference(contradiction_clause,[status(thm)],[f47062]) ).
fof(f47064,plain,
$false,
inference(sat_refutation,[status(thm)],[f4294,f47057,f47063]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL390-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n020.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.35 % CPULimit : 300
% 0.07/5.35 % WCLimit : 300
% 0.07/5.35 % DateTime : Mon Sep 21 00:27:37 UTC 2026
% 0.07/5.35 % CPUTime :
% 0.07/5.36 % Drodi V4.1.1
% 226.98/37.21 % Refutation found
% 226.98/37.21 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 226.98/37.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 219.62/38.41 % Elapsed time: 32.847303 seconds
% 219.62/38.41 % CPU time: 244.760866 seconds
% 219.62/38.41 % Total memory used: 849.970 MB
% 219.62/38.41 % Net memory used: 748.779 MB
%------------------------------------------------------------------------------