%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU166+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:19:30 PM UTC 2026
% Result : Theorem 8.71s 1.57s
% Output : CNFRefutation 8.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 4 unt; 1 def)
% Number of atoms : 227 ( 60 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 302 ( 132 ~; 130 |; 30 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-5 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 240 ( 217 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f19,definition,
! [A,B,D,E,F] :
( sP0_prd(F,E,D,B,A)
<=> ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f20,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : sP0_prd(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f3,f19]) ).
fof(f21,plain,
! [A,B,C] :
( ( ? [D] :
( ( ? [E,F] : sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C = cartesian_product2(A,B) )
& ( ! [D] :
( ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ? [E,F] : sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [A,B,C] :
( ? [D] :
( ( ? [E,F] : sP0_prd(F,E,D,B,A)
| in(D,C) )
& ( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C = cartesian_product2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ! [D] :
( ? [E,F] : sP0_prd(F,E,D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [A,B,C] :
( ( ( sP0_prd(sK4_skl(C,B,A),sK3_skl(C,B,A),sK2_skl(C,B,A),B,A)
| in(sK2_skl(C,B,A),C) )
& ( ! [E,F] : ~ sP0_prd(F,E,sK2_skl(C,B,A),B,A)
| ~ in(sK2_skl(C,B,A),C) ) )
| C = cartesian_product2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ! [E,F] : ~ sP0_prd(F,E,D,B,A)
| in(D,C) )
& ! [D] :
( sP0_prd(sK1_skl(D,C,B,A),sK0_skl(D,C,B,A),D,B,A)
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(F,sK1_skl(D,C,B,A)),skolemize(D,sK2_skl(C,B,A)),skolemize(E,sK3_skl(C,B,A)),skolemize(F,sK4_skl(C,B,A))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( sP0_prd(sK1_skl(X3,X0,X2,X1),sK0_skl(X3,X0,X2,X1),X3,X2,X1)
| ~ in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X4,X5,X3,X2,X1)
| in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f28,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [A,B] :
( ( ~ in(sK5_skl(B,A),B)
& in(sK5_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(C,sK5_skl(B,A))],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( in(sK5_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in(sK5_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f43,plain,
? [A,B,C] :
( ( ~ subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ~ subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
? [A,B] :
( ( ? [C] : ~ subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ? [C] : ~ subset(cartesian_product2(A,C),cartesian_product2(B,C)) )
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ( ~ subset(cartesian_product2(sK11_skl,sK8_skl),cartesian_product2(sK11_skl,sK9_skl))
| ~ subset(cartesian_product2(sK8_skl,sK10_skl),cartesian_product2(sK9_skl,sK10_skl)) )
& subset(sK8_skl,sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(C,sK11_skl)],[f44]) ).
fof(f46,plain,
subset(sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ subset(cartesian_product2(sK11_skl,sK8_skl),cartesian_product2(sK11_skl,sK9_skl))
| ~ subset(cartesian_product2(sK8_skl,sK10_skl),cartesian_product2(sK9_skl,sK10_skl)) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [A,B,D,E,F] :
( ( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| sP0_prd(F,E,D,B,A) )
& ( ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f49,plain,
( ! [A,B,D,E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| sP0_prd(F,E,D,B,A) )
& ! [A,B,D,E,F] :
( ( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ sP0_prd(F,E,D,B,A) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( in(X1,X4)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X3)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( X2 != ordered_pair(X1,X0)
| ~ in(X0,X3)
| ~ in(X1,X4)
| sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X0] :
( in(X0,sK9_skl)
| ~ in(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f32,f46]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( in(sK1_skl(X3,X0,X2,X1),X2)
| ~ in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(resolution,[status(thm)],[f24,f51]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( in(sK0_skl(X3,X0,X2,X1),X1)
| ~ in(X3,X0)
| X0 != cartesian_product2(X1,X2) ),
inference(resolution,[status(thm)],[f24,f50]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| X0 = ordered_pair(sK0_skl(X0,X1,X2,X3),sK1_skl(X0,X1,X2,X3)) ),
inference(resolution,[status(thm)],[f52,f24]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4,X5] :
( in(X4,X5)
| X5 != cartesian_product2(X1,X3)
| X4 != ordered_pair(X0,X2)
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f53,f25]) ).
fof(f185,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| in(X0,X6)
| X6 != cartesian_product2(X4,X5)
| ~ in(sK1_skl(X0,X1,X2,X3),X5)
| ~ in(sK0_skl(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[f95,f73]) ).
fof(f230,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| in(X0,X5)
| X5 != cartesian_product2(X4,X2)
| ~ in(sK0_skl(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[f185,f69]) ).
fof(f234,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(sK1_skl(X0,X1,X2,X3),sK8_skl)
| ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| in(X0,X5)
| X5 != cartesian_product2(X4,sK9_skl)
| ~ in(sK0_skl(X0,X1,X2,X3),X4) ),
inference(resolution,[status(thm)],[f185,f54]) ).
fof(f235,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X3,X2)
| in(X0,X5)
| X5 != cartesian_product2(X4,X2)
| ~ in(sK0_skl(X0,X1,X2,X3),X4) ),
inference(duplicate_literals_removal,[status(thm)],[f230]) ).
fof(f552,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(sK0_skl(X2,X3,X1,X4),sK8_skl)
| ~ in(X2,X3)
| X3 != cartesian_product2(X4,X1)
| in(X2,X0)
| X0 != cartesian_product2(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f235,f54]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| X3 != cartesian_product2(sK8_skl,X1)
| ~ in(X2,X3)
| X3 != cartesian_product2(sK8_skl,X1)
| in(X2,X0)
| X0 != cartesian_product2(sK9_skl,X1) ),
inference(resolution,[status(thm)],[f552,f70]) ).
fof(f555,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| X3 != cartesian_product2(sK8_skl,X1)
| in(X2,X0)
| X0 != cartesian_product2(sK9_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f554]) ).
fof(f557,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| X2 != cartesian_product2(sK8_skl,X1)
| in(X0,cartesian_product2(sK9_skl,X1)) ),
inference(equality_resolution,[status(thm)],[f555]) ).
fof(f565,plain,
! [X0,X1,X2] :
( subset(X2,cartesian_product2(sK9_skl,X1))
| ~ in(sK5_skl(cartesian_product2(sK9_skl,X1),X2),X0)
| X0 != cartesian_product2(sK8_skl,X1) ),
inference(resolution,[status(thm)],[f557,f34]) ).
fof(f573,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(sK9_skl,X1))
| subset(X0,cartesian_product2(sK9_skl,X1))
| X0 != cartesian_product2(sK8_skl,X1) ),
inference(resolution,[status(thm)],[f565,f33]) ).
fof(f579,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(sK9_skl,X1))
| X0 != cartesian_product2(sK8_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f573]) ).
fof(f774,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X2,sK8_skl)
| ~ in(X0,X1)
| X1 != cartesian_product2(X2,sK8_skl)
| in(X0,X4)
| X4 != cartesian_product2(X3,sK9_skl)
| ~ in(sK0_skl(X0,X1,sK8_skl,X2),X3) ),
inference(resolution,[status(thm)],[f234,f69]) ).
fof(f775,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,X1)
| X1 != cartesian_product2(X2,sK8_skl)
| in(X0,X4)
| X4 != cartesian_product2(X3,sK9_skl)
| ~ in(sK0_skl(X0,X1,sK8_skl,X2),X3) ),
inference(duplicate_literals_removal,[status(thm)],[f774]) ).
fof(f1620,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| X3 != cartesian_product2(X1,sK8_skl)
| ~ in(X2,X3)
| X3 != cartesian_product2(X1,sK8_skl)
| in(X2,X0)
| X0 != cartesian_product2(X1,sK9_skl) ),
inference(resolution,[status(thm)],[f775,f70]) ).
fof(f1627,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| X3 != cartesian_product2(X1,sK8_skl)
| in(X2,X0)
| X0 != cartesian_product2(X1,sK9_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1620]) ).
fof(f1629,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| X2 != cartesian_product2(X1,sK8_skl)
| in(X0,cartesian_product2(X1,sK9_skl)) ),
inference(equality_resolution,[status(thm)],[f1627]) ).
fof(f1649,plain,
! [X0,X1,X2] :
( subset(X2,cartesian_product2(X1,sK9_skl))
| ~ in(sK5_skl(cartesian_product2(X1,sK9_skl),X2),X0)
| X0 != cartesian_product2(X1,sK8_skl) ),
inference(resolution,[status(thm)],[f1629,f34]) ).
fof(f1997,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(X1,sK9_skl))
| subset(X0,cartesian_product2(X1,sK9_skl))
| X0 != cartesian_product2(X1,sK8_skl) ),
inference(resolution,[status(thm)],[f1649,f33]) ).
fof(f2005,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(X1,sK9_skl))
| X0 != cartesian_product2(X1,sK8_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1997]) ).
fof(f2006,plain,
( ~ subset(cartesian_product2(sK8_skl,sK10_skl),cartesian_product2(sK9_skl,sK10_skl))
| cartesian_product2(sK11_skl,sK8_skl) != cartesian_product2(sK11_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f2005,f47]) ).
fof(f2008,plain,
~ subset(cartesian_product2(sK8_skl,sK10_skl),cartesian_product2(sK9_skl,sK10_skl)),
inference(trivial_equality_resolution,[status(thm)],[f2006]) ).
fof(f2009,plain,
cartesian_product2(sK8_skl,sK10_skl) != cartesian_product2(sK8_skl,sK10_skl),
inference(resolution,[status(thm)],[f2008,f579]) ).
fof(f2011,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU166+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/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 05:51:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 8.71/1.57 % Refutation found
% 8.71/1.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.71/1.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.57/1.60 % Elapsed time: 1.222103 seconds
% 9.57/1.60 % CPU time: 9.366654 seconds
% 9.57/1.60 % Total memory used: 207.644 MB
% 9.57/1.60 % Net memory used: 193.314 MB
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