%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.42s 1.04s
% Output : CNFRefutation 0.42s
% 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(f10,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(f11,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)],[f10]) ).
fof(f15,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(f16,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,f15]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,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)],[f19]) ).
fof(f21,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)],[f19]) ).
fof(f24,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( in(sK5_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ in(sK5_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f39,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)],[f11]) ).
fof(f40,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)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f42,plain,
subset(sK8_skl,sK9_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,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)],[f41]) ).
fof(f44,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)],[f15]) ).
fof(f45,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)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( in(X1,X4)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X3)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,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)],[f45]) ).
fof(f50,plain,
! [X0] :
( in(X0,sK9_skl)
| ~ in(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f65,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)],[f20,f47]) ).
fof(f66,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)],[f20,f46]) ).
fof(f69,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)],[f48,f20]) ).
fof(f91,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)],[f49,f21]) ).
fof(f181,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)],[f91,f69]) ).
fof(f226,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)],[f181,f65]) ).
fof(f230,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)],[f181,f50]) ).
fof(f231,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)],[f226]) ).
fof(f548,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)],[f231,f50]) ).
fof(f550,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)],[f548,f66]) ).
fof(f551,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)],[f550]) ).
fof(f553,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)],[f551]) ).
fof(f561,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)],[f553,f30]) ).
fof(f569,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)],[f561,f29]) ).
fof(f575,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(sK9_skl,X1))
| X0 != cartesian_product2(sK8_skl,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f569]) ).
fof(f770,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)],[f230,f65]) ).
fof(f771,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)],[f770]) ).
fof(f1616,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)],[f771,f66]) ).
fof(f1623,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)],[f1616]) ).
fof(f1625,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)],[f1623]) ).
fof(f1645,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)],[f1625,f30]) ).
fof(f1993,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)],[f1645,f29]) ).
fof(f2001,plain,
! [X0,X1] :
( subset(X0,cartesian_product2(X1,sK9_skl))
| X0 != cartesian_product2(X1,sK8_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1993]) ).
fof(f2002,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)],[f2001,f43]) ).
fof(f2004,plain,
~ subset(cartesian_product2(sK8_skl,sK10_skl),cartesian_product2(sK9_skl,sK10_skl)),
inference(trivial_equality_resolution,[status(thm)],[f2002]) ).
fof(f2005,plain,
cartesian_product2(sK8_skl,sK10_skl) != cartesian_product2(sK8_skl,sK10_skl),
inference(resolution,[status(thm)],[f2004,f575]) ).
fof(f2007,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU166+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n020.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:55:17 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.42/1.04 % Refutation found
% 0.42/1.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.42/1.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.42/1.09 % Elapsed time: 0.632475 seconds
% 0.42/1.09 % CPU time: 4.540567 seconds
% 0.42/1.09 % Total memory used: 140.087 MB
% 0.42/1.09 % Net memory used: 135.013 MB
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