%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU119+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:19:15 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 112 ( 8 unt; 17 def)
% Number of atoms : 329 ( 56 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 357 ( 140 ~; 145 |; 50 &)
% ( 21 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 150 ( 131 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f20,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( ( ( ( in(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( ~ in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f32,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
( ! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ! [A,B] :
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f43,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
| ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f47,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
| sP0_prd(B,A) ),
inference(formula_renaming,[status(thm)],[f45,f46]) ).
fof(f48,plain,
( ? [A,B] :
( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
| ? [A,B] : sP0_prd(B,A) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ( disjoint(sK6_skl,sK7_skl)
& in(sK8_skl,sK7_skl)
& in(sK8_skl,sK6_skl) )
| sP0_prd(sK5_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f48]) ).
fof(f50,plain,
( in(sK8_skl,sK6_skl)
| sP0_prd(sK5_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
( in(sK8_skl,sK7_skl)
| sP0_prd(sK5_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
( disjoint(sK6_skl,sK7_skl)
| sP0_prd(sK5_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [A,B] :
( ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B)
| sP0_prd(B,A) )
& ( ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
( ! [A,B] :
( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B)
| sP0_prd(B,A) )
& ! [A,B] :
( ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
( ! [A,B] :
( ( in(sK9_skl(B,A),B)
& in(sK9_skl(B,A),A) )
| disjoint(A,B)
| sP0_prd(B,A) )
& ! [A,B] :
( ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) )
| ~ sP0_prd(B,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(C,sK9_skl(B,A))],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ disjoint(X1,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ in(X2,X0)
| ~ in(X2,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,definition,
( sQ0_spl
<=> sP0_prd(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ0_spl
| sP0_prd(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> in(sK8_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| in(sK8_skl,sK6_skl) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f60,f63]) ).
fof(f67,definition,
( sQ2_spl
<=> in(sK8_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ2_spl
| in(sK8_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f60,f67]) ).
fof(f71,definition,
( sQ3_spl
<=> disjoint(sK6_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ3_spl
| disjoint(sK6_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f60,f71]) ).
fof(f75,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f76,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f77,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f79,plain,
( ~ sQ0_spl
| ~ disjoint(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f56,f61]) ).
fof(f80,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(X0,sK5_skl)
| ~ in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f57,f61]) ).
fof(f93,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| in(sK0_skl(set_intersection2(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f76,f22]) ).
fof(f99,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| in(sK0_skl(set_intersection2(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f77,f22]) ).
fof(f145,plain,
! [X0,X1] :
( ~ disjoint(X1,X0)
| set_intersection2(X0,X1) = empty_set ),
inference(resolution,[status(thm)],[f34,f44]) ).
fof(f147,plain,
! [X0,X1] :
( set_intersection2(X1,X0) != empty_set
| disjoint(X0,X1) ),
inference(paramodulation,[status(thm)],[f17,f35]) ).
fof(f246,plain,
! [X0] :
( ~ sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,X0)),sK4_skl)
| set_intersection2(sK5_skl,X0) = empty_set ),
inference(resolution,[status(thm)],[f93,f80]) ).
fof(f249,plain,
! [X0] : set_intersection2(empty_set,X0) = empty_set,
inference(resolution,[status(thm)],[f93,f75]) ).
fof(f257,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(paramodulation,[status(thm)],[f17,f249]) ).
fof(f260,plain,
! [X0] :
( set_intersection2(empty_set,X0) = empty_set
| in(sK0_skl(empty_set),empty_set) ),
inference(paramodulation,[status(thm)],[f249,f93]) ).
fof(f268,plain,
! [X0] :
( empty_set != empty_set
| disjoint(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f249,f147]) ).
fof(f269,plain,
! [X0] :
( empty_set != empty_set
| disjoint(empty_set,X0) ),
inference(paramodulation,[status(thm)],[f249,f35]) ).
fof(f279,definition,
( sQ9_spl
<=> in(sK0_skl(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ9_spl
| in(sK0_skl(empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
! [X0] :
( sQ10_spl
<=> set_intersection2(empty_set,X0) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f260,f279,f282]) ).
fof(f296,definition,
! [X0] :
( sQ11_spl
<=> disjoint(X0,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f299,definition,
( sQ12_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ12_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f268,f296,f299]) ).
fof(f303,definition,
! [X0] :
( sQ13_spl
<=> disjoint(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ12_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f269,f303,f299]) ).
fof(f315,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f301]) ).
fof(f316,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f75]) ).
fof(f318,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f425,plain,
( ~ sQ0_spl
| set_intersection2(sK5_skl,sK4_skl) = empty_set
| set_intersection2(sK5_skl,sK4_skl) = empty_set ),
inference(resolution,[status(thm)],[f246,f99]) ).
fof(f429,definition,
( sQ14_spl
<=> set_intersection2(sK5_skl,sK4_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ14_spl
| set_intersection2(sK5_skl,sK4_skl) = empty_set ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ0_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f425,f429,f60]) ).
fof(f437,plain,
( ~ sQ14_spl
| disjoint(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f430,f147]) ).
fof(f465,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f79]) ).
fof(f466,plain,
( ~ sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f469,plain,
( ~ sQ3_spl
| set_intersection2(sK7_skl,sK6_skl) = empty_set ),
inference(resolution,[status(thm)],[f72,f145]) ).
fof(f470,plain,
( ~ sQ3_spl
| set_intersection2(sK6_skl,sK7_skl) = empty_set ),
inference(resolution,[status(thm)],[f72,f34]) ).
fof(f504,plain,
! [X0] :
( set_intersection2(X0,empty_set) = empty_set
| in(sK0_skl(empty_set),empty_set) ),
inference(paramodulation,[status(thm)],[f257,f99]) ).
fof(f548,definition,
! [X0] :
( sQ16_spl
<=> set_intersection2(X0,empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ16_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f504,f279,f548]) ).
fof(f847,plain,
( ~ sQ3_spl
| set_intersection2(sK7_skl,sK6_skl) = empty_set
| in(sK0_skl(empty_set),sK6_skl) ),
inference(paramodulation,[status(thm)],[f469,f99]) ).
fof(f848,plain,
( ~ sQ3_spl
| set_intersection2(sK7_skl,sK6_skl) = empty_set
| in(sK0_skl(empty_set),sK7_skl) ),
inference(paramodulation,[status(thm)],[f469,f93]) ).
fof(f855,plain,
! [X0] :
( ~ sQ3_spl
| ~ in(X0,sK6_skl)
| ~ in(X0,sK7_skl)
| in(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f469,f78]) ).
fof(f857,plain,
( ~ sQ3_spl
| empty_set != empty_set
| disjoint(sK7_skl,sK6_skl) ),
inference(paramodulation,[status(thm)],[f469,f35]) ).
fof(f923,definition,
( sQ17_spl
<=> in(sK0_skl(empty_set),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f926,definition,
( sQ18_spl
<=> set_intersection2(sK7_skl,sK6_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( ~ sQ3_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f847,f923,f926,f71]) ).
fof(f930,definition,
( sQ19_spl
<=> in(sK0_skl(empty_set),sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ3_spl
| sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f848,f930,f926,f71]) ).
fof(f944,plain,
! [X0] :
( ~ sQ3_spl
| ~ in(X0,sK6_skl)
| ~ in(X0,sK7_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f855,f75]) ).
fof(f946,definition,
( sQ20_spl
<=> disjoint(sK7_skl,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f857,f946,f299,f71]) ).
fof(f973,plain,
( ~ sQ3_spl
| set_intersection2(sK6_skl,sK7_skl) = empty_set
| in(sK0_skl(empty_set),sK7_skl) ),
inference(paramodulation,[status(thm)],[f470,f99]) ).
fof(f974,plain,
( ~ sQ3_spl
| set_intersection2(sK6_skl,sK7_skl) = empty_set
| in(sK0_skl(empty_set),sK6_skl) ),
inference(paramodulation,[status(thm)],[f470,f93]) ).
fof(f1047,definition,
( sQ21_spl
<=> set_intersection2(sK6_skl,sK7_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1050,plain,
( ~ sQ3_spl
| sQ21_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f973,f930,f1047,f71]) ).
fof(f1051,plain,
( ~ sQ3_spl
| sQ21_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f974,f923,f1047,f71]) ).
fof(f1285,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ in(sK8_skl,sK6_skl) ),
inference(resolution,[status(thm)],[f944,f68]) ).
fof(f1300,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1285,f64]) ).
fof(f1301,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1300]) ).
fof(f1302,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f285,f302,f306,f316,f318,f432,f466,f551,f929,f933,f949,f1050,f1051,f1301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:49:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.44 % Refutation found
% 0.09/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.46 % Elapsed time: 0.089236 seconds
% 0.09/0.46 % CPU time: 0.562105 seconds
% 0.09/0.46 % Total memory used: 111.160 MB
% 0.09/0.46 % Net memory used: 109.869 MB
%------------------------------------------------------------------------------