%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:11:02 PM UTC 2026
% Result : Theorem 0.13s 5.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 4 unt; 1 def)
% Number of atoms : 81 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 98 ( 38 ~; 31 |; 24 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 115 ( 95 !; 20 ?)
% 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(f8,conjecture,
! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
~ ( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,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(f14,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,f13]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,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)],[f17]) ).
fof(f28,plain,
? [A,B,C] :
( ! [D,E] : ordered_pair(D,E) != A
& in(A,cartesian_product2(B,C)) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
? [A] :
( ! [D,E] : ordered_pair(D,E) != A
& ? [B,C] : in(A,cartesian_product2(B,C)) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [D,E] : ordered_pair(D,E) != sK7_skl
& in(sK7_skl,cartesian_product2(sK8_skl,sK9_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f29]) ).
fof(f31,plain,
in(sK7_skl,cartesian_product2(sK8_skl,sK9_skl)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] : ordered_pair(X0,X1) != sK7_skl,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,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)],[f13]) ).
fof(f34,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)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( sP0_prd(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f70,plain,
! [X0,X1,X2] :
( X0 = ordered_pair(sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),sK1_skl(X0,cartesian_product2(X1,X2),X2,X1))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f71,plain,
! [X0,X1] : ~ in(sK7_skl,cartesian_product2(X0,X1)),
inference(resolution,[status(thm)],[f70,f32]) ).
fof(f73,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f31,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.58 % Computer : n008.cluster.edu
% 0.13/5.58 % Model : x86_64 x86_64
% 0.13/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.58 % Memory : 8046.5625MB
% 0.13/5.58 % OS : Linux 6.8.0-71-generic
% 0.13/5.58 % CPULimit : 300
% 0.13/5.58 % WCLimit : 300
% 0.13/5.58 % DateTime : Mon Sep 21 05:45:44 UTC 2026
% 0.13/5.58 % CPUTime :
% 0.13/5.59 % Drodi V4.1.1
% 0.13/5.59 % Refutation found
% 0.13/5.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/5.66 % Elapsed time: 0.072418 seconds
% 0.17/5.66 % CPU time: 0.089378 seconds
% 0.17/5.66 % Total memory used: 3.209 MB
% 0.17/5.66 % Net memory used: 3.207 MB
%------------------------------------------------------------------------------