%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:57:48 PM UTC 2026
% Result : Theorem 18.01s 2.81s
% Output : CNFRefutation 18.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 131 ( 19 unt; 11 def)
% Number of atoms : 395 ( 47 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 443 ( 179 ~; 204 |; 40 &)
% ( 18 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 172 ( 162 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
=> leq(X3,X2) )
& leq(X2,X1)
& leq(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1,X2] :
( ismeetu(X2,X0,X1)
<=> ! [X3] :
( ( leq(X3,X1)
& leq(X3,X0) )
<=> leq(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ismeet(X0,X1,X2)
<=> ismeetu(X0,X1,X2) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ismeet(X2,X0,X1)
<=> ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X1)
& leq(X3,X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X3,X2)
& leq(X3,X1)
& leq(X3,X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [X0,X1,X2] :
( ( ~ leq(sK0_skl(X2,X1,X0),X2)
& leq(sK0_skl(X2,X1,X0),X1)
& leq(sK0_skl(X2,X1,X0),X0) )
| ~ leq(X2,X1)
| ~ leq(X2,X0)
| ismeet(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) )
& leq(X2,X1)
& leq(X2,X0) )
| ~ ismeet(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X3,sK0_skl(X2,X1,X0))],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( leq(X0,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X0,X1,X2] :
( leq(sK0_skl(X0,X2,X1),X1)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f40,plain,
! [X0,X1,X2] :
( leq(sK0_skl(X0,X2,X1),X2)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ leq(sK0_skl(X0,X2,X1),X0)
| ~ leq(X0,X2)
| ~ leq(X0,X1)
| ismeet(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ismeetu(X2,X0,X1) )
& ( ! [X3] :
( ( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
( ! [X0,X1,X2] :
( ? [X3] :
( ( leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ismeetu(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [X0,X1,X2] :
( ( ( leq(sK1_skl(X2,X1,X0),X2)
| ( leq(sK1_skl(X2,X1,X0),X1)
& leq(sK1_skl(X2,X1,X0),X0) ) )
& ( ~ leq(sK1_skl(X2,X1,X0),X2)
| ~ leq(sK1_skl(X2,X1,X0),X1)
| ~ leq(sK1_skl(X2,X1,X0),X0) ) )
| ismeetu(X2,X0,X1) )
& ! [X0,X1,X2] :
( ( ! [X3] :
( ~ leq(X3,X2)
| ( leq(X3,X1)
& leq(X3,X0) ) )
& ! [X3] :
( leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X0) ) )
| ~ ismeetu(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X3,sK1_skl(X2,X1,X0))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( leq(X3,X0)
| ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X1)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X0)
| leq(X3,X2)
| ~ ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ leq(sK1_skl(X0,X2,X1),X0)
| ~ leq(sK1_skl(X0,X2,X1),X2)
| ~ leq(sK1_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f49,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,X1),X0)
| leq(sK1_skl(X0,X2,X1),X1)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f50,plain,
! [X0,X1,X2] :
( leq(sK1_skl(X0,X2,X1),X0)
| leq(sK1_skl(X0,X2,X1),X2)
| ismeetu(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ismeet(X0,X1,X2)
<~> ismeetu(X0,X1,X2) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ( ~ ismeetu(X0,X1,X2)
| ~ ismeet(X0,X1,X2) )
& ( ismeetu(X0,X1,X2)
| ismeet(X0,X1,X2) ) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
( ( ~ ismeetu(sK2_skl,sK3_skl,sK4_skl)
| ~ ismeet(sK2_skl,sK3_skl,sK4_skl) )
& ( ismeetu(sK2_skl,sK3_skl,sK4_skl)
| ismeet(sK2_skl,sK3_skl,sK4_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl),skolemize(X2,sK4_skl)],[f52]) ).
fof(f54,plain,
( ismeetu(sK2_skl,sK3_skl,sK4_skl)
| ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
( ~ ismeetu(sK2_skl,sK3_skl,sK4_skl)
| ~ ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ0_spl
<=> ismeet(sK2_skl,sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ0_spl
| ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f58,plain,
( sQ0_spl
| ~ ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ1_spl
<=> ismeetu(sK2_skl,sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ1_spl
| ismeetu(sK2_skl,sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( sQ1_spl
| ~ ismeetu(sK2_skl,sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f56,f59]) ).
fof(f63,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f56,f59]) ).
fof(f70,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f79,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f84,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f86,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f93,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f18,f84]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ ismeet(X0,X2,X1)
| addition(X0,X1) = X1 ),
inference(resolution,[status(thm)],[f30,f37]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ ismeet(X0,X1,X2)
| addition(X0,X1) = X1 ),
inference(resolution,[status(thm)],[f30,f36]) ).
fof(f121,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f17,f86]) ).
fof(f280,definition,
( sQ3_spl
<=> addition(zero,sK2_skl) = sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ3_spl
| addition(zero,sK2_skl) != sK2_skl ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f347,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f121,f79]) ).
fof(f409,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f18,f347]) ).
fof(f410,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f121,f409]) ).
fof(f659,plain,
( sQ0_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl)
| ~ leq(sK2_skl,sK4_skl)
| ~ leq(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f41,f58]) ).
fof(f667,definition,
( sQ7_spl
<=> leq(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( sQ7_spl
| ~ leq(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,definition,
( sQ8_spl
<=> leq(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( sQ8_spl
| ~ leq(sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f670]) ).
fof(f673,definition,
( sQ9_spl
<=> leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( sQ9_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f676,plain,
( sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f659,f667,f670,f673,f56]) ).
fof(f677,plain,
( sQ3_spl
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f70,f282]) ).
fof(f678,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f677]) ).
fof(f679,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( ~ sQ0_spl
| addition(sK2_skl,sK3_skl) = sK3_skl ),
inference(resolution,[status(thm)],[f57,f113]) ).
fof(f682,plain,
( ~ sQ0_spl
| addition(sK2_skl,sK4_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f57,f112]) ).
fof(f683,plain,
( ~ sQ0_spl
| addition(sK3_skl,sK2_skl) = sK3_skl ),
inference(paramodulation,[status(thm)],[f17,f681]) ).
fof(f687,plain,
! [X0] :
( ~ sQ0_spl
| addition(sK2_skl,addition(X0,sK3_skl)) = addition(X0,sK3_skl) ),
inference(paramodulation,[status(thm)],[f681,f93]) ).
fof(f697,plain,
( ~ sQ0_spl
| addition(sK4_skl,sK2_skl) = sK4_skl ),
inference(paramodulation,[status(thm)],[f17,f682]) ).
fof(f1015,plain,
( sQ1_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl)
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl)
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f48,f61]) ).
fof(f1019,definition,
( sQ10_spl
<=> leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1021,plain,
( sQ10_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f1019]) ).
fof(f1022,definition,
( sQ11_spl
<=> leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1024,plain,
( sQ11_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f1022]) ).
fof(f1025,definition,
( sQ12_spl
<=> leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( ~ sQ12_spl
| leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f1025]) ).
fof(f1027,plain,
( sQ12_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f1025]) ).
fof(f1028,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1015,f1019,f1022,f1025,f59]) ).
fof(f1037,plain,
! [X0,X1] :
( sQ12_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),X1)
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),X0)
| ~ ismeet(sK2_skl,X0,X1) ),
inference(resolution,[status(thm)],[f1027,f38]) ).
fof(f1066,plain,
! [X0] :
( ~ sQ0_spl
| addition(X0,sK3_skl) = addition(sK3_skl,addition(X0,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f687,f410]) ).
fof(f2385,plain,
( ~ sQ0_spl
| sQ12_spl
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl)
| ~ leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f1037,f57]) ).
fof(f2387,plain,
( ~ sQ0_spl
| sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2385,f1019,f1022,f1025,f56]) ).
fof(f2388,plain,
( sQ11_spl
| leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl)
| ismeetu(sK2_skl,sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f1024,f50]) ).
fof(f2389,plain,
( sQ11_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) != sK4_skl ),
inference(resolution,[status(thm)],[f1024,f31]) ).
fof(f2396,plain,
( sQ11_spl
| sQ12_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2388,f59,f1025,f1022]) ).
fof(f2402,plain,
( sQ10_spl
| leq(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl)
| ismeetu(sK2_skl,sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f1021,f49]) ).
fof(f2403,plain,
( sQ10_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) != sK3_skl ),
inference(resolution,[status(thm)],[f1021,f31]) ).
fof(f2410,plain,
( sQ10_spl
| sQ12_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2402,f59,f1025,f1019]) ).
fof(f2412,plain,
! [X0,X1] :
( sQ9_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),X1)
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),X0)
| ~ ismeetu(sK2_skl,X0,X1) ),
inference(resolution,[status(thm)],[f675,f45]) ).
fof(f2762,plain,
! [X0] :
( ~ sQ0_spl
| addition(X0,sK4_skl) = addition(sK4_skl,addition(X0,sK2_skl)) ),
inference(paramodulation,[status(thm)],[f682,f79]) ).
fof(f2791,plain,
( ~ sQ12_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK2_skl) = sK2_skl ),
inference(resolution,[status(thm)],[f1026,f30]) ).
fof(f4810,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) = addition(sK3_skl,sK2_skl) ),
inference(paramodulation,[status(thm)],[f2791,f1066]) ).
fof(f4832,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) = sK3_skl ),
inference(forward_demodulation,[status(thm)],[f683,f4810]) ).
fof(f4833,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4832,f2403]) ).
fof(f4834,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f4833]) ).
fof(f4837,plain,
! [X0,X1] :
( sQ8_spl
| ~ leq(sK2_skl,X0)
| ~ ismeetu(X0,X1,sK4_skl) ),
inference(resolution,[status(thm)],[f672,f47]) ).
fof(f4845,plain,
! [X0,X1] :
( sQ7_spl
| ~ leq(sK2_skl,X0)
| ~ ismeetu(X0,sK3_skl,X1) ),
inference(resolution,[status(thm)],[f669,f46]) ).
fof(f5897,plain,
( ~ sQ1_spl
| sQ8_spl
| ~ leq(sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f4837,f60]) ).
fof(f5899,plain,
( ~ sQ1_spl
| sQ8_spl
| addition(sK2_skl,sK2_skl) != sK2_skl ),
inference(resolution,[status(thm)],[f5897,f31]) ).
fof(f5906,plain,
( ~ sQ1_spl
| sQ8_spl
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f20,f5899]) ).
fof(f5907,plain,
( ~ sQ1_spl
| sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5906]) ).
fof(f5908,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f5907]) ).
fof(f6000,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ leq(sK2_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f4845,f60]) ).
fof(f6002,plain,
( ~ sQ1_spl
| sQ7_spl
| addition(sK2_skl,sK2_skl) != sK2_skl ),
inference(resolution,[status(thm)],[f6000,f31]) ).
fof(f6009,plain,
( ~ sQ1_spl
| sQ7_spl
| sK2_skl != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f20,f6002]) ).
fof(f6010,plain,
( ~ sQ1_spl
| sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6009]) ).
fof(f6011,plain,
( ~ sQ1_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f6010]) ).
fof(f9422,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) = addition(sK4_skl,sK2_skl) ),
inference(paramodulation,[status(thm)],[f2791,f2762]) ).
fof(f9453,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| addition(sK1_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f697,f9422]) ).
fof(f9454,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9453,f2389]) ).
fof(f9455,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f9454]) ).
fof(f10417,plain,
( ~ sQ1_spl
| sQ9_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl)
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f2412,f60]) ).
fof(f10419,definition,
( sQ56_spl
<=> leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f10421,plain,
( sQ56_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f10419]) ).
fof(f10422,definition,
( sQ57_spl
<=> leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f10424,plain,
( sQ57_spl
| ~ leq(sK0_skl(sK2_skl,sK4_skl,sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f10422]) ).
fof(f10425,plain,
( ~ sQ1_spl
| sQ9_spl
| ~ sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f10417,f10419,f10422,f673,f59]) ).
fof(f10439,plain,
( sQ56_spl
| ~ leq(sK2_skl,sK4_skl)
| ~ leq(sK2_skl,sK3_skl)
| ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f10421,f39]) ).
fof(f10447,plain,
( sQ56_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10439,f56,f667,f670,f10419]) ).
fof(f10448,plain,
( sQ57_spl
| ~ leq(sK2_skl,sK4_skl)
| ~ leq(sK2_skl,sK3_skl)
| ismeet(sK2_skl,sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f10424,f40]) ).
fof(f10456,plain,
( sQ57_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10448,f56,f667,f670,f10422]) ).
fof(f10457,plain,
$false,
inference(sat_refutation,[status(thm)],[f62,f63,f676,f679,f1028,f2387,f2396,f2410,f4834,f5908,f6011,f9455,f10425,f10447,f10456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE029+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:39:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 18.01/2.81 % Refutation found
% 18.01/2.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.01/2.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.51/2.87 % Elapsed time: 2.479447 seconds
% 13.51/2.87 % CPU time: 19.043082 seconds
% 13.51/2.87 % Total memory used: 187.727 MB
% 13.51/2.87 % Net memory used: 182.918 MB
%------------------------------------------------------------------------------