%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL225-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 01:07:13 PM UTC 2026
% Result : Unsatisfiable 115.81s 15.03s
% Output : CNFRefutation 115.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 40 unt; 2 def)
% Number of atoms : 157 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 131 ( 66 ~; 63 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 184 ( 184 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ theorem(implies(implies(p,implies(q,r)),implies(implies(p,q),implies(p,r)))),
file('/export/starexec/sandbox/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(implies(p,implies(q,r)),implies(implies(p,q),implies(p,r)))),
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] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f22,plain,
! [X0,X1] : theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f23,plain,
! [X0,X1] :
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f22,f18]) ).
fof(f45,plain,
! [X0,X1] : theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f48,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f45,f18]) ).
fof(f49,plain,
! [X0,X1] : theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f15,f45]) ).
fof(f78,plain,
! [X0,X1,X2] : theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f79,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f83,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f79]) ).
fof(f87,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f88,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f90,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f88]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f78,f18]) ).
fof(f94,plain,
! [X0,X1,X2] : theorem(implies(or(X0,implies(X1,X2)),or(not(X1),or(X0,X2)))),
inference(paramodulation,[status(thm)],[f15,f78]) ).
fof(f98,plain,
! [X0,X1,X2] : theorem(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f94]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[f87,f18]) ).
fof(f117,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f15,f87]) ).
fof(f119,plain,
! [X0,X1,X2] : theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f15,f117]) ).
fof(f156,plain,
! [X0,X1] :
( ~ axiom(implies(X1,X0))
| ~ theorem(X1)
| theorem(X0) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f179,plain,
! [X0,X1] :
( theorem(X1)
| ~ axiom(implies(X0,or(X1,X1)))
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f156,f21]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ theorem(X1)
| theorem(X2)
| ~ axiom(implies(X0,implies(X1,X2)))
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[f156,f18]) ).
fof(f195,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f15,f83]) ).
fof(f197,plain,
! [X0,X1,X2] : axiom(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f15,f195]) ).
fof(f368,plain,
! [X0] :
( theorem(X0)
| ~ theorem(or(or(X0,X0),or(X0,X0))) ),
inference(resolution,[status(thm)],[f179,f10]) ).
fof(f405,plain,
! [X0] :
( theorem(X0)
| ~ theorem(or(X0,or(or(X0,X0),X0))) ),
inference(resolution,[status(thm)],[f92,f368]) ).
fof(f406,plain,
! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(or(X0,X1),X1))) ),
inference(resolution,[status(thm)],[f92,f21]) ).
fof(f408,plain,
! [X0,X1,X2] :
( ~ theorem(or(not(X1),or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(paramodulation,[status(thm)],[f15,f92]) ).
fof(f410,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f408]) ).
fof(f445,plain,
! [X0] :
( ~ theorem(or(or(or(X0,X0),X0),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f405,f48]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f116,f18]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(implies(X0,X1),or(not(X0),X2))) ),
inference(paramodulation,[status(thm)],[f15,f116]) ).
fof(f528,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X1,X2))
| theorem(implies(implies(X0,X1),implies(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f15,f526]) ).
fof(f606,plain,
! [X0,X1,X2] :
( ~ theorem(implies(X2,X0))
| theorem(implies(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f183,f90]) ).
fof(f661,plain,
! [X0,X1,X2] :
( ~ theorem(X1)
| theorem(implies(X0,X2))
| ~ theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[f197,f183]) ).
fof(f751,plain,
! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f406,f23]) ).
fof(f774,plain,
! [X0,X1] :
( ~ theorem(or(X1,or(X0,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f751,f48]) ).
fof(f787,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f774,f92]) ).
fof(f805,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(or(not(X0),X1)) ),
inference(paramodulation,[status(thm)],[f15,f787]) ).
fof(f807,plain,
! [X0,X1] :
( ~ theorem(implies(X0,or(X1,X1)))
| theorem(implies(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f15,f805]) ).
fof(f1067,plain,
! [X0,X1,X2,X3] :
( ~ theorem(implies(X0,or(X3,X1)))
| theorem(or(X3,X2))
| ~ theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f525,f410]) ).
fof(f1366,plain,
! [X0,X1,X2,X3] :
( ~ theorem(implies(X3,X1))
| theorem(implies(implies(X0,X3),X2))
| ~ theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f606,f528]) ).
fof(f1375,plain,
! [X0,X1] :
( theorem(implies(or(X0,X0),X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f606,f20]) ).
fof(f1384,plain,
! [X0,X1,X2] :
( theorem(implies(X1,X2))
| ~ theorem(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f606,f22]) ).
fof(f1742,plain,
! [X0,X1,X2] :
( ~ theorem(or(X2,X0))
| theorem(implies(implies(X0,X1),or(X2,X1))) ),
inference(resolution,[status(thm)],[f661,f87]) ).
fof(f1924,plain,
! [X0,X1] :
( ~ theorem(or(X0,X0))
| theorem(X1)
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1375,f18]) ).
fof(f2141,plain,
! [X0,X1] : theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[f1384,f45]) ).
fof(f2173,plain,
! [X0,X1,X2] :
( theorem(implies(X0,X2))
| ~ theorem(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f2141,f606]) ).
fof(f2749,plain,
! [X0,X1,X2] :
( theorem(or(X2,X1))
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f1067,f22]) ).
fof(f3470,plain,
! [X0,X1,X2] : theorem(implies(X0,implies(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[f2173,f98]) ).
fof(f3530,plain,
! [X0,X1,X2] : theorem(implies(not(X0),implies(X1,implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f15,f3470]) ).
fof(f4159,plain,
! [X0] :
( ~ theorem(implies(implies(q,r),X0))
| ~ theorem(implies(implies(p,X0),implies(implies(p,q),implies(p,r)))) ),
inference(resolution,[status(thm)],[f1366,f19]) ).
fof(f5821,plain,
! [X0,X1] :
( theorem(implies(implies(X1,X0),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f1742,f807]) ).
fof(f5930,definition,
( sQ110_spl
<=> theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f5932,plain,
( sQ110_spl
| ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(component_clause,[status(thm)],[f5930]) ).
fof(f6211,plain,
( sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5932,f119]) ).
fof(f6212,plain,
sQ110_spl,
inference(contradiction_clause,[status(thm)],[f6211]) ).
fof(f7081,plain,
! [X0,X1] :
( theorem(X1)
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f2749,f445]) ).
fof(f7629,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[f7081,f49]) ).
fof(f7639,plain,
! [X0,X1] :
( ~ axiom(implies(or(X1,not(X1)),X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[f7629,f156]) ).
fof(f9437,plain,
! [X0,X1] : theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[f7639,f11]) ).
fof(f9455,plain,
! [X0,X1] : theorem(or(or(X0,not(X0)),X1)),
inference(resolution,[status(thm)],[f9437,f48]) ).
fof(f14590,plain,
! [X0,X1] :
( theorem(X1)
| ~ theorem(implies(or(X0,not(X0)),X1)) ),
inference(resolution,[status(thm)],[f1924,f9455]) ).
fof(f14651,plain,
! [X0,X1] :
( ~ theorem(implies(not(X0),X1))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f14590,f116]) ).
fof(f15111,plain,
! [X0,X1] :
( theorem(or(X1,X0))
| ~ theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[f14651,f48]) ).
fof(f16338,plain,
! [X0,X1,X2] : theorem(or(implies(X0,implies(X1,X2)),X1)),
inference(resolution,[status(thm)],[f15111,f3530]) ).
fof(f29741,plain,
( ~ theorem(or(implies(implies(p,q),implies(p,r)),p))
| ~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
inference(resolution,[status(thm)],[f4159,f5821]) ).
fof(f29769,definition,
( sQ476_spl
<=> theorem(or(implies(implies(p,q),implies(p,r)),p)) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f29771,plain,
( sQ476_spl
| ~ theorem(or(implies(implies(p,q),implies(p,r)),p)) ),
inference(component_clause,[status(thm)],[f29769]) ).
fof(f29772,plain,
( ~ sQ476_spl
| ~ sQ110_spl ),
inference(split_clause,[status(thm)],[f29741,f5930,f29769]) ).
fof(f29777,plain,
( sQ476_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29771,f16338]) ).
fof(f29778,plain,
sQ476_spl,
inference(contradiction_clause,[status(thm)],[f29777]) ).
fof(f29779,plain,
$false,
inference(sat_refutation,[status(thm)],[f6212,f29772,f29778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL225-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:16:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 115.81/15.03 % Refutation found
% 115.81/15.03 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 115.81/15.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.37/15.13 % Elapsed time: 14.753705 seconds
% 7.37/15.13 % CPU time: 116.536686 seconds
% 7.37/15.13 % Total memory used: 447.595 MB
% 7.37/15.13 % Net memory used: 392.753 MB
%------------------------------------------------------------------------------