%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:11:05 PM UTC 2026
% Result : Theorem 0.22s 0.80s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 36
% Syntax : Number of formulae : 167 ( 10 unt; 30 def)
% Number of atoms : 442 ( 111 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 477 ( 202 ~; 214 |; 22 &)
% ( 34 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 31 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 153 ( 145 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(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(f7,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f25,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f34,plain,
! [A,B] :
( ( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f35,plain,
( ! [A,B] :
( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ! [A,B] :
( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( X0 != empty_set
| cartesian_product2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X0,X1] :
( X1 != empty_set
| cartesian_product2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
? [A,B,C,D] :
( ( B != D
| A != C )
& B != empty_set
& A != empty_set
& cartesian_product2(A,B) = cartesian_product2(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
( ( sK4_skl != sK6_skl
| sK3_skl != sK5_skl )
& sK4_skl != empty_set
& sK3_skl != empty_set
& cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(sK5_skl,sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl),skolemize(D,sK6_skl)],[f39]) ).
fof(f41,plain,
cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
sK4_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
( sK4_skl != sK6_skl
| sK3_skl != sK5_skl ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK7_skl(B,A),B)
| ~ in(sK7_skl(B,A),A) )
& ( in(sK7_skl(B,A),B)
| in(sK7_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(C,sK7_skl(B,A))],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( X1 = X0
| in(sK7_skl(X0,X1),X0)
| in(sK7_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( X1 = X0
| ~ in(sK7_skl(X0,X1),X0)
| ~ in(sK7_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ0_spl
<=> sK3_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,definition,
( sQ1_spl
<=> sK4_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f50,f53]) ).
fof(f57,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0] : cartesian_product2(empty_set,X0) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f37]) ).
fof(f59,plain,
! [X0] : cartesian_product2(X0,empty_set) = empty_set,
inference(destructive_equality_resolution,[status(thm)],[f38]) ).
fof(f60,plain,
( sK6_skl = empty_set
| sK5_skl = empty_set
| cartesian_product2(sK3_skl,sK4_skl) != empty_set ),
inference(paramodulation,[status(thm)],[f41,f36]) ).
fof(f61,definition,
( sQ2_spl
<=> cartesian_product2(sK3_skl,sK4_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f64,definition,
( sQ3_spl
<=> sK5_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ3_spl
| sK5_skl = empty_set ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f66,plain,
( sQ3_spl
| sK5_skl != empty_set ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,definition,
( sQ4_spl
<=> sK6_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| sK6_skl = empty_set ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ4_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f60,f61,f64,f67]) ).
fof(f71,plain,
( ~ sQ4_spl
| cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(sK5_skl,empty_set) ),
inference(backward_demodulation,[status(thm)],[f68,f41]) ).
fof(f79,plain,
( ~ sQ3_spl
| cartesian_product2(sK3_skl,sK4_skl) = cartesian_product2(empty_set,sK6_skl) ),
inference(backward_demodulation,[status(thm)],[f65,f41]) ).
fof(f81,plain,
( ~ sQ3_spl
| sK4_skl = empty_set
| sK3_skl = empty_set
| cartesian_product2(empty_set,sK6_skl) != empty_set ),
inference(paramodulation,[status(thm)],[f79,f36]) ).
fof(f82,definition,
( sQ6_spl
<=> cartesian_product2(empty_set,sK6_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ6_spl
| cartesian_product2(empty_set,sK6_skl) != empty_set ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ7_spl
<=> sK3_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| sK3_skl = empty_set ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ8_spl
<=> sK4_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ8_spl
| sK4_skl = empty_set ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ3_spl
| sQ8_spl
| sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f81,f82,f85,f88,f64]) ).
fof(f92,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f43]) ).
fof(f93,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f92]) ).
fof(f94,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f86,f42]) ).
fof(f95,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f98,plain,
( sQ6_spl
| empty_set != empty_set ),
inference(backward_demodulation,[status(thm)],[f58,f84]) ).
fof(f101,plain,
( sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f98]) ).
fof(f102,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f101]) ).
fof(f157,plain,
! [X0,X1] :
( in(X0,sK5_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f41,f27]) ).
fof(f160,plain,
! [X0,X1] :
( in(X1,sK6_skl)
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f41,f28]) ).
fof(f162,plain,
! [X0,X1] :
( in(X1,sK6_skl)
| ~ in(X1,sK4_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f29,f160]) ).
fof(f163,plain,
! [X0,X1] :
( in(X0,sK5_skl)
| ~ in(X1,sK4_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f29,f157]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( in(X2,X3)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f29,f28]) ).
fof(f168,plain,
! [X0,X1] :
( ~ in(X1,sK6_skl)
| ~ in(X0,sK5_skl)
| in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f41,f29]) ).
fof(f170,definition,
! [X0] :
( sQ10_spl
<=> ~ in(X0,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f171,plain,
! [X0] :
( ~ sQ10_spl
| ~ in(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
! [X1] :
( sQ11_spl
<=> ( in(X1,sK6_skl)
| ~ in(X1,sK4_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
! [X0] :
( ~ sQ11_spl
| in(X0,sK6_skl)
| ~ in(X0,sK4_skl) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f162,f170,f173]) ).
fof(f177,definition,
! [X0] :
( sQ12_spl
<=> ( in(X0,sK5_skl)
| ~ in(X0,sK3_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f178,plain,
! [X0] :
( ~ sQ12_spl
| in(X0,sK5_skl)
| ~ in(X0,sK3_skl) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
! [X1] :
( sQ13_spl
<=> ~ in(X1,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f181,plain,
! [X0] :
( ~ sQ13_spl
| ~ in(X0,sK4_skl) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f163,f177,f180]) ).
fof(f184,definition,
! [X0,X1] :
( sQ14_spl
<=> ~ in(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ in(X0,X1) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X2,X3] :
( sQ15_spl
<=> ( in(X2,X3)
| ~ in(X2,X3) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f164,f184,f187]) ).
fof(f192,plain,
( ~ sQ10_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f171,f21]) ).
fof(f193,plain,
( ~ sQ10_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f192,f85,f170]) ).
fof(f194,plain,
! [X0] :
( ~ sQ12_spl
| ~ in(sK5_skl,X0)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f178,f15]) ).
fof(f195,plain,
! [X0] :
( ~ sQ11_spl
| ~ in(sK6_skl,X0)
| ~ in(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f174,f15]) ).
fof(f197,plain,
( ~ sQ12_spl
| ~ in(sK5_skl,sK3_skl)
| ~ in(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f194,f178]) ).
fof(f205,definition,
( sQ18_spl
<=> in(sK5_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ12_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f197,f205,f177]) ).
fof(f209,plain,
( ~ sQ11_spl
| ~ in(sK6_skl,sK4_skl)
| ~ in(sK6_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f195,f174]) ).
fof(f211,definition,
( sQ19_spl
<=> in(sK6_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ11_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f209,f211,f173]) ).
fof(f216,plain,
! [X0,X1] :
( in(X1,sK6_skl)
| ~ in(X1,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f168,f160]) ).
fof(f217,plain,
! [X0,X1] :
( in(X0,sK5_skl)
| ~ in(X1,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f168,f157]) ).
fof(f218,plain,
! [X0,X1] :
( in(X1,sK4_skl)
| ~ in(X1,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f168,f28]) ).
fof(f219,plain,
! [X0,X1] :
( in(X0,sK3_skl)
| ~ in(X1,sK6_skl)
| ~ in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f168,f27]) ).
fof(f221,definition,
! [X0] :
( sQ20_spl
<=> ~ in(X0,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f222,plain,
! [X0] :
( ~ sQ20_spl
| ~ in(X0,sK5_skl) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
! [X1] :
( sQ21_spl
<=> ( in(X1,sK6_skl)
| ~ in(X1,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f216,f221,f224]) ).
fof(f228,definition,
! [X0] :
( sQ22_spl
<=> ( in(X0,sK5_skl)
| ~ in(X0,sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f231,definition,
! [X1] :
( sQ23_spl
<=> ~ in(X1,sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f232,plain,
! [X0] :
( ~ sQ23_spl
| ~ in(X0,sK6_skl) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f217,f228,f231]) ).
fof(f235,definition,
! [X1] :
( sQ24_spl
<=> ( in(X1,sK4_skl)
| ~ in(X1,sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f236,plain,
! [X0] :
( ~ sQ24_spl
| in(X0,sK4_skl)
| ~ in(X0,sK6_skl) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( sQ24_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f218,f221,f235]) ).
fof(f239,definition,
! [X0] :
( sQ25_spl
<=> ( in(X0,sK3_skl)
| ~ in(X0,sK5_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f240,plain,
! [X0] :
( ~ sQ25_spl
| in(X0,sK3_skl)
| ~ in(X0,sK5_skl) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( sQ23_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f219,f239,f231]) ).
fof(f243,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ in(ordered_pair(X0,X1),cartesian_product2(sK3_skl,sK4_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f160,f232]) ).
fof(f246,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ in(X1,sK4_skl)
| ~ in(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f243,f29]) ).
fof(f247,plain,
( ~ sQ23_spl
| sQ13_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f246,f170,f180,f231]) ).
fof(f250,plain,
! [X0] :
( ~ sQ14_spl
| X0 = empty_set ),
inference(backward_subsumption_resolution,[status(thm)],[f21,f185]) ).
fof(f251,plain,
( sQ3_spl
| ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f66,f250]) ).
fof(f257,plain,
( sQ3_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f259,plain,
( ~ sQ13_spl
| sK4_skl = empty_set ),
inference(resolution,[status(thm)],[f21,f181]) ).
fof(f260,plain,
( ~ sQ20_spl
| sK5_skl = empty_set ),
inference(resolution,[status(thm)],[f21,f222]) ).
fof(f262,plain,
( ~ sQ13_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f259,f88,f180]) ).
fof(f263,plain,
( ~ sQ20_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f260,f64,f221]) ).
fof(f264,plain,
( ~ sQ25_spl
| sK5_skl = empty_set
| in(sK0_skl(sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f240,f21]) ).
fof(f265,definition,
( sQ26_spl
<=> in(sK0_skl(sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ25_spl
| sQ3_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f264,f265,f64,f239]) ).
fof(f270,plain,
! [X0] :
( ~ sQ25_spl
| in(sK7_skl(X0,sK5_skl),sK3_skl)
| sK5_skl = X0
| in(sK7_skl(X0,sK5_skl),X0) ),
inference(resolution,[status(thm)],[f48,f240]) ).
fof(f271,plain,
! [X0] :
( empty_set = X0
| in(sK7_skl(X0,empty_set),X0) ),
inference(resolution,[status(thm)],[f48,f57]) ).
fof(f276,plain,
! [X0] :
( ~ sQ11_spl
| sK6_skl = X0
| ~ in(sK7_skl(X0,sK6_skl),X0)
| ~ in(sK7_skl(X0,sK6_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f174,f49]) ).
fof(f280,plain,
! [X0] :
( ~ sQ24_spl
| sK6_skl = X0
| in(sK7_skl(X0,sK6_skl),X0)
| in(sK7_skl(X0,sK6_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f236,f48]) ).
fof(f281,plain,
( ~ sQ24_spl
| sK6_skl = empty_set
| in(sK0_skl(sK6_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f236,f21]) ).
fof(f283,definition,
( sQ27_spl
<=> in(sK0_skl(sK6_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ24_spl
| sQ4_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f281,f283,f67,f235]) ).
fof(f288,plain,
! [X0] :
( ~ sQ12_spl
| sK5_skl = X0
| ~ in(sK7_skl(X0,sK5_skl),X0)
| ~ in(sK7_skl(X0,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f178,f49]) ).
fof(f298,plain,
( ~ sQ24_spl
| in(sK7_skl(sK6_skl,empty_set),sK4_skl)
| empty_set = sK6_skl ),
inference(resolution,[status(thm)],[f271,f236]) ).
fof(f299,plain,
( ~ sQ25_spl
| in(sK7_skl(sK5_skl,empty_set),sK3_skl)
| empty_set = sK5_skl ),
inference(resolution,[status(thm)],[f271,f240]) ).
fof(f306,definition,
( sQ29_spl
<=> in(sK7_skl(sK6_skl,empty_set),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ sQ24_spl
| sQ29_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f298,f67,f306,f235]) ).
fof(f310,definition,
( sQ30_spl
<=> in(sK7_skl(sK5_skl,empty_set),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ25_spl
| sQ30_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f299,f64,f310,f239]) ).
fof(f317,plain,
! [X0] :
( ~ sQ25_spl
| ~ in(sK3_skl,sK7_skl(X0,sK5_skl))
| sK5_skl = X0
| in(sK7_skl(X0,sK5_skl),X0) ),
inference(resolution,[status(thm)],[f270,f15]) ).
fof(f318,plain,
! [X0] :
( ~ sQ24_spl
| ~ in(sK4_skl,sK7_skl(X0,sK6_skl))
| sK6_skl = X0
| in(sK7_skl(X0,sK6_skl),X0) ),
inference(resolution,[status(thm)],[f280,f15]) ).
fof(f323,plain,
( ~ sQ4_spl
| cartesian_product2(sK3_skl,sK4_skl) = empty_set ),
inference(backward_demodulation,[status(thm)],[f59,f71]) ).
fof(f331,plain,
( ~ sQ4_spl
| sK4_skl = empty_set
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f323,f36]) ).
fof(f333,plain,
( ~ sQ4_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f331,f85,f88,f67]) ).
fof(f428,plain,
( ~ sQ25_spl
| ~ in(sK3_skl,sK7_skl(empty_set,sK5_skl))
| sK5_skl = empty_set ),
inference(resolution,[status(thm)],[f317,f57]) ).
fof(f433,definition,
( sQ32_spl
<=> in(sK7_skl(sK3_skl,sK5_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( ~ sQ32_spl
| in(sK7_skl(sK3_skl,sK5_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f435,plain,
( sQ32_spl
| ~ in(sK7_skl(sK3_skl,sK5_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f461,definition,
( sQ40_spl
<=> in(sK3_skl,sK7_skl(empty_set,sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ25_spl
| ~ sQ40_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f64,f461,f239]) ).
fof(f619,plain,
( ~ sQ25_spl
| sQ32_spl
| sK5_skl = sK3_skl
| in(sK7_skl(sK3_skl,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f435,f270]) ).
fof(f622,plain,
( ~ sQ25_spl
| sQ0_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f619,f433,f50,f239]) ).
fof(f841,plain,
( ~ sQ24_spl
| ~ in(sK4_skl,sK7_skl(empty_set,sK6_skl))
| sK6_skl = empty_set ),
inference(resolution,[status(thm)],[f318,f57]) ).
fof(f857,definition,
( sQ48_spl
<=> in(sK4_skl,sK7_skl(empty_set,sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ24_spl
| ~ sQ48_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f841,f67,f857,f235]) ).
fof(f892,definition,
( sQ50_spl
<=> in(sK7_skl(sK4_skl,sK6_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f893,plain,
( ~ sQ50_spl
| in(sK7_skl(sK4_skl,sK6_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f892]) ).
fof(f894,plain,
( sQ50_spl
| ~ in(sK7_skl(sK4_skl,sK6_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f892]) ).
fof(f903,plain,
( ~ sQ24_spl
| sQ50_spl
| sK6_skl = sK4_skl
| in(sK7_skl(sK4_skl,sK6_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f894,f280]) ).
fof(f906,plain,
( ~ sQ24_spl
| sQ1_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f903,f892,f53,f235]) ).
fof(f909,plain,
( ~ sQ11_spl
| ~ sQ50_spl
| sK6_skl = sK4_skl
| ~ in(sK7_skl(sK4_skl,sK6_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f893,f276]) ).
fof(f911,plain,
( ~ sQ11_spl
| sQ1_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f909,f892,f53,f173]) ).
fof(f1070,plain,
( ~ sQ32_spl
| ~ sQ12_spl
| sK5_skl = sK3_skl
| ~ in(sK7_skl(sK3_skl,sK5_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f288,f434]) ).
fof(f1075,plain,
( ~ sQ12_spl
| sQ0_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f1070,f433,f50,f177]) ).
fof(f1079,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f70,f91,f93,f95,f102,f176,f183,f190,f193,f208,f214,f227,f234,f238,f242,f247,f257,f262,f263,f268,f286,f309,f313,f333,f464,f622,f860,f906,f911,f1075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:47:58 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.22/0.80 % Refutation found
% 0.22/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.38/0.84 % Elapsed time: 0.383311 seconds
% 1.38/0.84 % CPU time: 2.697136 seconds
% 1.38/0.84 % Total memory used: 136.528 MB
% 1.38/0.84 % Net memory used: 132.644 MB
%------------------------------------------------------------------------------