%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU304+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:20:06 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 115 ( 15 unt; 16 def)
% Number of atoms : 394 ( 48 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 476 ( 197 ~; 202 |; 41 &)
% ( 20 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 17 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 99 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet_commut(A,C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [A] :
( ( latt_str(A)
& ~ empty_carrier(A) )
=> ( meet_absorbing(A)
<=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> join(A,meet(A,B,C),C) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> element(meet_commut(A,B,C),the_carrier(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f245,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& meet_semilatt_str(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> meet_commut(A,B,C) = meet(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f339,conjecture,
! [A] :
( ( latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> below(A,meet_commut(A,B,C),B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f340,negated_conjecture,
~ ! [A] :
( ( latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> below(A,meet_commut(A,B,C),B) ) ) ),
inference(negated_conjecture,[status(cth)],[f339]) ).
fof(f502,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f503,plain,
! [X0,X1,X2] :
( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f502]) ).
fof(f773,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( below(A,B,C)
<=> join(A,B,C) = C )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f774,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( join(A,B,C) != C
| below(A,B,C) )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f773]) ).
fof(f776,plain,
! [X0,X1,X2] :
( join(X0,X1,X2) != X2
| below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f774]) ).
fof(f977,plain,
! [A] :
( ( meet_absorbing(A)
<=> ! [B] :
( ! [C] :
( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f978,plain,
! [A] :
( ( ( ? [B] :
( ? [C] :
( join(A,meet(A,B,C),C) != C
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
| meet_absorbing(A) )
& ( ! [B] :
( ! [C] :
( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ meet_absorbing(A) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f977]) ).
fof(f979,plain,
! [A] :
( ( ( ( join(A,meet(A,sK83_skl(A),sK84_skl(A)),sK84_skl(A)) != sK84_skl(A)
& element(sK84_skl(A),the_carrier(A))
& element(sK83_skl(A),the_carrier(A)) )
| meet_absorbing(A) )
& ( ! [B] :
( ! [C] :
( join(A,meet(A,B,C),C) = C
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ meet_absorbing(A) ) )
| ~ latt_str(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl,sK84_skl]),skolemize(B,sK83_skl(A)),skolemize(C,sK84_skl(A))],[f978]) ).
fof(f980,plain,
! [X0,X1,X2] :
( join(X0,meet(X0,X1,X2),X2) = X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_absorbing(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f979]) ).
fof(f1040,plain,
! [A,B,C] :
( element(meet_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f122]) ).
fof(f1041,plain,
! [X0,X1,X2] :
( element(meet_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1040]) ).
fof(f1069,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f141]) ).
fof(f1070,plain,
! [X0] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1069]) ).
fof(f1071,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f1069]) ).
fof(f1408,plain,
! [A,B,C] :
( meet_commut(A,B,C) = meet(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ meet_semilatt_str(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f245]) ).
fof(f1409,plain,
! [X0,X1,X2] :
( meet_commut(X0,X1,X2) = meet(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1408]) ).
fof(f1918,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ below(A,meet_commut(A,B,C),B)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& latt_str(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f340]) ).
fof(f1919,plain,
( ~ below(sK254_skl,meet_commut(sK254_skl,sK255_skl,sK256_skl),sK255_skl)
& element(sK256_skl,the_carrier(sK254_skl))
& element(sK255_skl,the_carrier(sK254_skl))
& latt_str(sK254_skl)
& meet_absorbing(sK254_skl)
& meet_commutative(sK254_skl)
& ~ empty_carrier(sK254_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254_skl,sK255_skl,sK256_skl]),skolemize(A,sK254_skl),skolemize(B,sK255_skl),skolemize(C,sK256_skl)],[f1918]) ).
fof(f1920,plain,
~ empty_carrier(sK254_skl),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1921,plain,
meet_commutative(sK254_skl),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1922,plain,
meet_absorbing(sK254_skl),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1923,plain,
latt_str(sK254_skl),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1924,plain,
element(sK255_skl,the_carrier(sK254_skl)),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1925,plain,
element(sK256_skl,the_carrier(sK254_skl)),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f1926,plain,
~ below(sK254_skl,meet_commut(sK254_skl,sK255_skl,sK256_skl),sK255_skl),
inference(cnf_transformation,[status(thm)],[f1919]) ).
fof(f3077,plain,
! [X0,X1] :
( meet_commut(sK254_skl,X0,X1) = meet_commut(sK254_skl,X1,X0)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl))
| ~ meet_semilatt_str(sK254_skl)
| ~ meet_commutative(sK254_skl) ),
inference(resolution,[status(thm)],[f503,f1920]) ).
fof(f3078,definition,
( sQ57_spl
<=> meet_commutative(sK254_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
( sQ57_spl
| ~ meet_commutative(sK254_skl) ),
inference(component_clause,[status(thm)],[f3078]) ).
fof(f3081,definition,
( sQ58_spl
<=> meet_semilatt_str(sK254_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f3083,plain,
( sQ58_spl
| ~ meet_semilatt_str(sK254_skl) ),
inference(component_clause,[status(thm)],[f3081]) ).
fof(f3084,definition,
! [X0,X1] :
( sQ59_spl
<=> ( meet_commut(sK254_skl,X0,X1) = meet_commut(sK254_skl,X1,X0)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f3085,plain,
! [X0,X1] :
( ~ sQ59_spl
| meet_commut(sK254_skl,X0,X1) = meet_commut(sK254_skl,X1,X0)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3084]) ).
fof(f3087,plain,
( sQ59_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3077,f3078,f3081,f3084]) ).
fof(f3089,plain,
! [X0] :
( ~ sQ59_spl
| meet_commut(sK254_skl,X0,sK255_skl) = meet_commut(sK254_skl,sK255_skl,X0)
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3085,f1924]) ).
fof(f3090,plain,
( ~ sQ59_spl
| meet_commut(sK254_skl,sK256_skl,sK255_skl) = meet_commut(sK254_skl,sK255_skl,sK256_skl) ),
inference(resolution,[status(thm)],[f3089,f1925]) ).
fof(f3092,plain,
( ~ sQ59_spl
| ~ below(sK254_skl,meet_commut(sK254_skl,sK256_skl,sK255_skl),sK255_skl) ),
inference(backward_demodulation,[status(thm)],[f3090,f1926]) ).
fof(f3094,definition,
( sQ60_spl
<=> element(sK255_skl,the_carrier(sK254_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f3096,plain,
( sQ60_spl
| ~ element(sK255_skl,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3094]) ).
fof(f3101,plain,
( sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3096,f1924]) ).
fof(f3102,plain,
sQ60_spl,
inference(contradiction_clause,[status(thm)],[f3101]) ).
fof(f3103,plain,
( sQ58_spl
| ~ latt_str(sK254_skl) ),
inference(resolution,[status(thm)],[f3083,f1070]) ).
fof(f3104,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3103,f1923]) ).
fof(f3105,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f3104]) ).
fof(f3106,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3080,f1921]) ).
fof(f3107,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f3106]) ).
fof(f3115,plain,
! [X0,X1] :
( join(sK254_skl,X0,X1) != X1
| below(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl))
| ~ join_semilatt_str(sK254_skl) ),
inference(resolution,[status(thm)],[f776,f1920]) ).
fof(f3116,definition,
( sQ62_spl
<=> join_semilatt_str(sK254_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f3118,plain,
( sQ62_spl
| ~ join_semilatt_str(sK254_skl) ),
inference(component_clause,[status(thm)],[f3116]) ).
fof(f3119,definition,
! [X0,X1] :
( sQ63_spl
<=> ( join(sK254_skl,X0,X1) != X1
| below(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f3120,plain,
! [X0,X1] :
( ~ sQ63_spl
| join(sK254_skl,X0,X1) != X1
| below(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3119]) ).
fof(f3122,plain,
( sQ63_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f3115,f3116,f3119]) ).
fof(f3123,plain,
! [X0,X1] :
( join(sK254_skl,meet(sK254_skl,X0,X1),X1) = X1
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl))
| ~ meet_absorbing(sK254_skl)
| ~ latt_str(sK254_skl) ),
inference(resolution,[status(thm)],[f980,f1920]) ).
fof(f3124,definition,
( sQ64_spl
<=> latt_str(sK254_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f3126,plain,
( sQ64_spl
| ~ latt_str(sK254_skl) ),
inference(component_clause,[status(thm)],[f3124]) ).
fof(f3127,definition,
( sQ65_spl
<=> meet_absorbing(sK254_skl) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f3129,plain,
( sQ65_spl
| ~ meet_absorbing(sK254_skl) ),
inference(component_clause,[status(thm)],[f3127]) ).
fof(f3130,definition,
! [X0,X1] :
( sQ66_spl
<=> ( join(sK254_skl,meet(sK254_skl,X0,X1),X1) = X1
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f3131,plain,
! [X0,X1] :
( ~ sQ66_spl
| join(sK254_skl,meet(sK254_skl,X0,X1),X1) = X1
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3130]) ).
fof(f3133,plain,
( sQ66_spl
| ~ sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f3123,f3124,f3127,f3130]) ).
fof(f3134,plain,
! [X0,X1] :
( element(meet_commut(sK254_skl,X0,X1),the_carrier(sK254_skl))
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl))
| ~ meet_semilatt_str(sK254_skl)
| ~ meet_commutative(sK254_skl) ),
inference(resolution,[status(thm)],[f1041,f1920]) ).
fof(f3135,definition,
! [X0,X1] :
( sQ67_spl
<=> ( element(meet_commut(sK254_skl,X0,X1),the_carrier(sK254_skl))
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f3136,plain,
! [X0,X1] :
( ~ sQ67_spl
| element(meet_commut(sK254_skl,X0,X1),the_carrier(sK254_skl))
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3135]) ).
fof(f3138,plain,
( sQ67_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3134,f3078,f3081,f3135]) ).
fof(f3139,plain,
( sQ62_spl
| ~ latt_str(sK254_skl) ),
inference(resolution,[status(thm)],[f3118,f1071]) ).
fof(f3140,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3139,f1923]) ).
fof(f3141,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f3140]) ).
fof(f3143,plain,
! [X0] :
( ~ sQ66_spl
| join(sK254_skl,meet(sK254_skl,X0,sK255_skl),sK255_skl) = sK255_skl
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3131,f1924]) ).
fof(f3146,plain,
! [X0] :
( ~ sQ67_spl
| element(meet_commut(sK254_skl,X0,sK256_skl),the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3136,f1925]) ).
fof(f3149,plain,
( ~ sQ67_spl
| element(meet_commut(sK254_skl,sK255_skl,sK256_skl),the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3146,f1924]) ).
fof(f3150,plain,
( ~ sQ67_spl
| ~ sQ59_spl
| element(meet_commut(sK254_skl,sK256_skl,sK255_skl),the_carrier(sK254_skl)) ),
inference(forward_demodulation,[status(thm)],[f3090,f3149]) ).
fof(f3185,plain,
! [X0,X1] :
( meet_commut(sK254_skl,X0,X1) = meet(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl))
| ~ meet_semilatt_str(sK254_skl)
| ~ meet_commutative(sK254_skl) ),
inference(resolution,[status(thm)],[f1409,f1920]) ).
fof(f3186,definition,
! [X0,X1] :
( sQ68_spl
<=> ( meet_commut(sK254_skl,X0,X1) = meet(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f3187,plain,
! [X0,X1] :
( ~ sQ68_spl
| meet_commut(sK254_skl,X0,X1) = meet(sK254_skl,X0,X1)
| ~ element(X1,the_carrier(sK254_skl))
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3186]) ).
fof(f3189,plain,
( sQ68_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3185,f3078,f3081,f3186]) ).
fof(f3190,plain,
( ~ sQ59_spl
| ~ sQ63_spl
| join(sK254_skl,meet_commut(sK254_skl,sK256_skl,sK255_skl),sK255_skl) != sK255_skl
| ~ element(sK255_skl,the_carrier(sK254_skl))
| ~ element(meet_commut(sK254_skl,sK256_skl,sK255_skl),the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3120,f3092]) ).
fof(f3192,definition,
( sQ69_spl
<=> element(meet_commut(sK254_skl,sK256_skl,sK255_skl),the_carrier(sK254_skl)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f3194,plain,
( sQ69_spl
| ~ element(meet_commut(sK254_skl,sK256_skl,sK255_skl),the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3192]) ).
fof(f3195,definition,
( sQ70_spl
<=> join(sK254_skl,meet_commut(sK254_skl,sK256_skl,sK255_skl),sK255_skl) = sK255_skl ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f3197,plain,
( sQ70_spl
| join(sK254_skl,meet_commut(sK254_skl,sK256_skl,sK255_skl),sK255_skl) != sK255_skl ),
inference(component_clause,[status(thm)],[f3195]) ).
fof(f3198,plain,
( ~ sQ59_spl
| ~ sQ63_spl
| ~ sQ70_spl
| ~ sQ60_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f3190,f3192,f3094,f3195,f3119,f3084]) ).
fof(f3206,plain,
( sQ69_spl
| ~ sQ67_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3194,f3150]) ).
fof(f3207,plain,
( sQ69_spl
| ~ sQ67_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f3206]) ).
fof(f3241,plain,
! [X0] :
( ~ sQ68_spl
| meet_commut(sK254_skl,X0,sK256_skl) = meet(sK254_skl,X0,sK256_skl)
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3187,f1925]) ).
fof(f3242,plain,
! [X0] :
( ~ sQ68_spl
| meet_commut(sK254_skl,X0,sK255_skl) = meet(sK254_skl,X0,sK255_skl)
| ~ element(X0,the_carrier(sK254_skl)) ),
inference(resolution,[status(thm)],[f3187,f1924]) ).
fof(f3261,plain,
( ~ sQ59_spl
| ~ sQ68_spl
| meet_commut(sK254_skl,sK256_skl,sK255_skl) = meet(sK254_skl,sK255_skl,sK256_skl)
| ~ element(sK255_skl,the_carrier(sK254_skl)) ),
inference(paramodulation,[status(thm)],[f3090,f3241]) ).
fof(f3262,definition,
( sQ73_spl
<=> meet_commut(sK254_skl,sK256_skl,sK255_skl) = meet(sK254_skl,sK255_skl,sK256_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f3263,plain,
( ~ sQ73_spl
| meet_commut(sK254_skl,sK256_skl,sK255_skl) = meet(sK254_skl,sK255_skl,sK256_skl) ),
inference(component_clause,[status(thm)],[f3262]) ).
fof(f3265,plain,
( ~ sQ59_spl
| ~ sQ68_spl
| sQ73_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f3261,f3094,f3262,f3186,f3084]) ).
fof(f3268,plain,
( sQ70_spl
| ~ sQ73_spl
| join(sK254_skl,meet(sK254_skl,sK255_skl,sK256_skl),sK255_skl) != sK255_skl ),
inference(backward_demodulation,[status(thm)],[f3263,f3197]) ).
fof(f3303,plain,
( ~ sQ66_spl
| join(sK254_skl,meet(sK254_skl,sK256_skl,sK255_skl),sK255_skl) = sK255_skl ),
inference(resolution,[status(thm)],[f3143,f1925]) ).
fof(f3305,plain,
( ~ sQ73_spl
| ~ sQ68_spl
| meet(sK254_skl,sK255_skl,sK256_skl) = meet(sK254_skl,sK256_skl,sK255_skl)
| ~ element(sK256_skl,the_carrier(sK254_skl)) ),
inference(paramodulation,[status(thm)],[f3263,f3242]) ).
fof(f3306,definition,
( sQ77_spl
<=> element(sK256_skl,the_carrier(sK254_skl)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3308,plain,
( sQ77_spl
| ~ element(sK256_skl,the_carrier(sK254_skl)) ),
inference(component_clause,[status(thm)],[f3306]) ).
fof(f3309,definition,
( sQ78_spl
<=> meet(sK254_skl,sK255_skl,sK256_skl) = meet(sK254_skl,sK256_skl,sK255_skl) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3310,plain,
( ~ sQ78_spl
| meet(sK254_skl,sK255_skl,sK256_skl) = meet(sK254_skl,sK256_skl,sK255_skl) ),
inference(component_clause,[status(thm)],[f3309]) ).
fof(f3312,plain,
( ~ sQ73_spl
| ~ sQ68_spl
| sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f3305,f3306,f3309,f3186,f3262]) ).
fof(f3313,plain,
( sQ77_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3308,f1925]) ).
fof(f3314,plain,
sQ77_spl,
inference(contradiction_clause,[status(thm)],[f3313]) ).
fof(f3316,plain,
( sQ70_spl
| ~ sQ73_spl
| ~ sQ78_spl
| join(sK254_skl,meet(sK254_skl,sK256_skl,sK255_skl),sK255_skl) != sK255_skl ),
inference(backward_demodulation,[status(thm)],[f3310,f3268]) ).
fof(f3321,plain,
( sQ70_spl
| ~ sQ73_spl
| ~ sQ78_spl
| ~ sQ66_spl
| sK255_skl != sK255_skl ),
inference(forward_demodulation,[status(thm)],[f3303,f3316]) ).
fof(f3322,plain,
( sQ70_spl
| ~ sQ73_spl
| ~ sQ78_spl
| ~ sQ66_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3321]) ).
fof(f3323,plain,
( sQ70_spl
| ~ sQ73_spl
| ~ sQ78_spl
| ~ sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f3322]) ).
fof(f3324,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3126,f1923]) ).
fof(f3325,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f3324]) ).
fof(f3326,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3129,f1922]) ).
fof(f3327,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f3326]) ).
fof(f3328,plain,
$false,
inference(sat_refutation,[status(thm)],[f3087,f3102,f3105,f3107,f3122,f3133,f3138,f3141,f3189,f3198,f3207,f3265,f3312,f3314,f3323,f3325,f3327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU304+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:15:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 0.14/0.45 % Refutation found
% 0.14/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.49 % Elapsed time: 0.127708 seconds
% 0.14/0.49 % CPU time: 0.341879 seconds
% 0.14/0.49 % Total memory used: 163.865 MB
% 0.14/0.49 % Net memory used: 162.995 MB
%------------------------------------------------------------------------------