%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU119+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 : n017.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 7 unt; 9 def)
% Number of atoms : 253 ( 34 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 292 ( 116 ~; 113 |; 50 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 123 ( 104 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/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/sandbox/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(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(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(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(f30,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f31,plain,
! [X0,X1,X2] :
( in(sK1_skl(X0,X2,X1),X2)
| in(sK1_skl(X0,X2,X1),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(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(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(f88,plain,
! [X0,X1] :
( ~ sP0_prd(X1,X0)
| set_intersection2(X0,X1) != empty_set ),
inference(resolution,[status(thm)],[f35,f56]) ).
fof(f92,plain,
( ~ sQ0_spl
| set_intersection2(sK4_skl,sK5_skl) != empty_set ),
inference(resolution,[status(thm)],[f88,f61]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( ~ in(sK1_skl(X0,X2,X1),X3)
| ~ sP0_prd(X3,X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(resolution,[status(thm)],[f30,f57]) ).
fof(f239,definition,
( sQ8_spl
<=> in(sK0_skl(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ8_spl
| in(sK0_skl(empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f262,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(resolution,[status(thm)],[f31,f118]) ).
fof(f273,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X1)
| in(sK1_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(duplicate_literals_removal,[status(thm)],[f262]) ).
fof(f332,plain,
! [X0] :
( ~ sQ0_spl
| in(sK1_skl(X0,sK5_skl,sK4_skl),X0)
| X0 = set_intersection2(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f273,f61]) ).
fof(f379,plain,
( ~ sQ0_spl
| empty_set = set_intersection2(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f332,f75]) ).
fof(f405,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f92]) ).
fof(f406,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f410,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK8_skl,X0)
| in(sK8_skl,set_intersection2(X0,sK7_skl)) ),
inference(resolution,[status(thm)],[f68,f78]) ).
fof(f413,plain,
( ~ sQ3_spl
| set_intersection2(sK6_skl,sK7_skl) = empty_set ),
inference(resolution,[status(thm)],[f72,f34]) ).
fof(f653,definition,
( sQ43_spl
<=> in(sK9_skl(sK7_skl,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( ~ sQ43_spl
| in(sK9_skl(sK7_skl,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f666,definition,
( sQ46_spl
<=> in(sK9_skl(sK6_skl,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( ~ sQ46_spl
| in(sK9_skl(sK6_skl,empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f698,definition,
( sQ48_spl
<=> in(sK9_skl(empty_set,sK7_skl),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ48_spl
| in(sK9_skl(empty_set,sK7_skl),empty_set) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f706,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f75]) ).
fof(f707,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f708,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f75]) ).
fof(f709,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f710,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f667,f75]) ).
fof(f711,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f710]) ).
fof(f712,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f654,f75]) ).
fof(f713,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f946,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| in(sK8_skl,set_intersection2(sK6_skl,sK7_skl)) ),
inference(resolution,[status(thm)],[f410,f64]) ).
fof(f948,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| in(sK8_skl,empty_set) ),
inference(forward_demodulation,[status(thm)],[f413,f946]) ).
fof(f949,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f948,f75]) ).
fof(f950,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f949]) ).
fof(f951,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f70,f74,f406,f707,f709,f711,f713,f950]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:46:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.080102 seconds
% 0.13/0.44 % CPU time: 0.280635 seconds
% 0.13/0.44 % Total memory used: 104.851 MB
% 0.13/0.44 % Net memory used: 104.191 MB
%------------------------------------------------------------------------------