%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL199-3 : TPTP v9.3.1. Released v2.3.0.
% 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 01:07:06 PM UTC 2026
% Result : Unsatisfiable 8.62s 1.61s
% Output : CNFRefutation 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 33 unt; 2 def)
% Number of atoms : 157 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 137 ( 71 ~; 64 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 172 ( 172 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(implies(not(or(p,q)),not(p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [Y] :
( ~ theorem(Y)
| ! [X] :
( ~ theorem(implies(Y,X))
| theorem(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
~ theorem(implies(not(or(p,q)),not(p))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] : theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f21,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f26,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f30,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f18,f21]) ).
fof(f38,definition,
! [X1] :
( sQ1_spl
<=> ~ theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f39,plain,
! [X0] :
( ~ sQ1_spl
| ~ theorem(X0) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f53,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f54,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f26]) ).
fof(f55,plain,
! [X0,X1] : theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f15,f26]) ).
fof(f56,plain,
! [X0,X1] :
( ~ theorem(X0)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f53,f32]) ).
fof(f57,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f53]) ).
fof(f60,plain,
! [X0,X1] :
( ~ theorem(not(X0))
| theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f15,f56]) ).
fof(f70,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f83,plain,
! [X0,X1] : theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f54]) ).
fof(f86,plain,
! [X0,X1] :
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f55,f18]) ).
fof(f90,plain,
! [X0,X1] :
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f15,f57]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f44,f18]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f70,f18]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f91,f32]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f15,f91]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f134]) ).
fof(f155,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f83,f39]) ).
fof(f166,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f267,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(or(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f133,f30]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ~ theorem(or(not(X0),X2))
| theorem(implies(X0,or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f133]) ).
fof(f270,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X0,X2))
| theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f268]) ).
fof(f289,plain,
! [X0,X1] :
( theorem(or(not(X0),X1))
| ~ theorem(or(implies(X0,X1),X1)) ),
inference(paramodulation,[status(thm)],[f15,f267]) ).
fof(f290,plain,
! [X0,X1] :
( theorem(implies(X0,X1))
| ~ theorem(or(implies(X0,X1),X1)) ),
inference(forward_demodulation,[status(thm)],[f15,f289]) ).
fof(f302,plain,
! [X0,X1,X2] :
( ~ theorem(X0)
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f270,f18]) ).
fof(f303,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X0,X2))
| theorem(implies(X0,implies(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f270]) ).
fof(f358,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X1))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f302,f26]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f126,f18]) ).
fof(f636,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f91,f358]) ).
fof(f643,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(or(not(X0),or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f91]) ).
fof(f645,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,implies(X0,X2)))
| theorem(implies(X0,or(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f643]) ).
fof(f669,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(or(X0,or(X1,X0))) ),
inference(resolution,[status(thm)],[f636,f30]) ).
fof(f751,plain,
! [X0,X1] :
( theorem(or(not(X1),X0))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(paramodulation,[status(thm)],[f15,f669]) ).
fof(f752,plain,
! [X0,X1] :
( theorem(implies(X1,X0))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f15,f751]) ).
fof(f976,plain,
! [X0,X1] : theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f136,f21]) ).
fof(f981,plain,
! [X0,X1] : theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f976,f290]) ).
fof(f983,plain,
! [X0] : theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f976,f752]) ).
fof(f990,plain,
! [X0] : theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[f983,f90]) ).
fof(f1452,plain,
! [X0,X1,X2] :
( ~ theorem(or(X0,or(X2,not(X1))))
| theorem(or(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f526,f55]) ).
fof(f1457,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f526,f20]) ).
fof(f1459,plain,
! [X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[f526,f990]) ).
fof(f1556,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(or(not(X0),X1)) ),
inference(paramodulation,[status(thm)],[f15,f1457]) ).
fof(f1558,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(implies(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f15,f1556]) ).
fof(f1727,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| theorem(implies(or(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f1558,f126]) ).
fof(f1949,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(X1)
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1727,f18]) ).
fof(f2078,plain,
! [X0] :
( ~ theorem(or(not(not(X0)),X0))
| theorem(not(not(X0))) ),
inference(resolution,[status(thm)],[f1949,f990]) ).
fof(f2109,plain,
! [X0,X1] :
( ~ theorem(not(X1))
| ~ theorem(or(X0,X1))
| theorem(X0) ),
inference(resolution,[status(thm)],[f1949,f60]) ).
fof(f2114,plain,
! [X0] :
( ~ theorem(implies(not(X0),X0))
| theorem(not(not(X0))) ),
inference(forward_demodulation,[status(thm)],[f15,f2078]) ).
fof(f2149,plain,
! [X0,X1] :
( ~ theorem(implies(X1,X0))
| ~ theorem(not(not(X1)))
| theorem(X0) ),
inference(resolution,[status(thm)],[f2109,f57]) ).
fof(f3026,plain,
! [X0] : theorem(not(not(implies(X0,X0)))),
inference(resolution,[status(thm)],[f2114,f981]) ).
fof(f4333,plain,
! [X0,X1] :
( theorem(implies(not(X1),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f1459,f86]) ).
fof(f4355,plain,
~ theorem(or(not(p),or(p,q))),
inference(resolution,[status(thm)],[f4333,f19]) ).
fof(f4373,plain,
~ theorem(implies(p,or(p,q))),
inference(forward_demodulation,[status(thm)],[f15,f4355]) ).
fof(f4535,plain,
! [X0,X1] :
( ~ theorem(implies(implies(X1,X1),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f2149,f3026]) ).
fof(f4559,plain,
! [X0,X1,X2] :
( ~ theorem(implies(implies(X2,X2),X1))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f4535,f303]) ).
fof(f5100,plain,
! [X0,X1] : theorem(implies(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[f4559,f54]) ).
fof(f5146,plain,
! [X0,X1,X2] :
( ~ theorem(X2)
| theorem(or(X0,or(X1,not(X1)))) ),
inference(resolution,[status(thm)],[f5100,f302]) ).
fof(f5158,definition,
! [X0,X1] :
( sQ86_spl
<=> theorem(or(X0,or(X1,not(X1)))) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f5159,plain,
! [X0,X1] :
( ~ sQ86_spl
| theorem(or(X0,or(X1,not(X1)))) ),
inference(component_clause,[status(thm)],[f5158]) ).
fof(f5161,plain,
( sQ1_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f5146,f5158,f38]) ).
fof(f5185,plain,
! [X0,X1] :
( ~ sQ86_spl
| theorem(or(X0,or(X1,not(X0)))) ),
inference(resolution,[status(thm)],[f5159,f91]) ).
fof(f5959,plain,
! [X0,X1] :
( ~ sQ86_spl
| theorem(or(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f1452,f5185]) ).
fof(f5978,plain,
! [X0,X1] :
( ~ sQ86_spl
| theorem(implies(X0,or(X0,X1))) ),
inference(resolution,[status(thm)],[f5959,f645]) ).
fof(f5983,plain,
( ~ sQ86_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4373,f5978]) ).
fof(f5999,plain,
~ sQ86_spl,
inference(contradiction_clause,[status(thm)],[f5983]) ).
fof(f6000,plain,
$false,
inference(sat_refutation,[status(thm)],[f166,f5161,f5999]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL199-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 00:10:49 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 8.62/1.61 % Refutation found
% 8.62/1.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.62/1.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.96/1.64 % Elapsed time: 1.278215 seconds
% 6.96/1.64 % CPU time: 9.720311 seconds
% 6.96/1.64 % Total memory used: 160.535 MB
% 6.96/1.64 % Net memory used: 145.900 MB
%------------------------------------------------------------------------------