%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:19:26 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 1 unt; 4 def)
% Number of atoms : 178 ( 31 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 199 ( 77 ~; 82 |; 28 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 152 ( 130 !; 22 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [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(f11,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f14,axiom,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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(f19,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,f18]) ).
fof(f20,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)],[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) )
& ! [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)],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,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)],[f22]) ).
fof(f24,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)],[f22]) ).
fof(f29,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<~> ( in(B,D)
& in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f30,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)],[f29]) ).
fof(f31,plain,
( ( ~ in(sK6_skl,sK8_skl)
| ~ in(sK5_skl,sK7_skl)
| ~ in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) )
& ( ( in(sK6_skl,sK8_skl)
& in(sK5_skl,sK7_skl) )
| in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl),skolemize(D,sK8_skl)],[f30]) ).
fof(f32,plain,
( in(sK5_skl,sK7_skl)
| in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( in(sK6_skl,sK8_skl)
| in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ in(sK6_skl,sK8_skl)
| ~ in(sK5_skl,sK7_skl)
| ~ in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,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)],[f18]) ).
fof(f43,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)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( in(X1,X4)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X3)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( X2 = ordered_pair(X1,X0)
| ~ sP0_prd(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,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)],[f43]) ).
fof(f48,definition,
( sQ0_spl
<=> in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ0_spl
| in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f50,plain,
( sQ0_spl
| ~ in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,definition,
( sQ1_spl
<=> in(sK5_skl,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ1_spl
| in(sK5_skl,sK7_skl) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f48,f51]) ).
fof(f55,definition,
( sQ2_spl
<=> in(sK6_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( sQ2_spl
| ~ in(sK6_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f48,f55]) ).
fof(f59,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f48,f51,f55]) ).
fof(f60,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)],[f23]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( ~ sP0_prd(X3,X4,X0,X2,X1)
| in(X0,cartesian_product2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,X2)
| ~ in(X1,X3)
| sP0_prd(X0,X1,ordered_pair(X1,X0),X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f70,plain,
( ~ sQ0_spl
| sP0_prd(sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),ordered_pair(sK5_skl,sK6_skl),sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f60,f49]) ).
fof(f77,plain,
( ~ sQ0_spl
| in(sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK8_skl) ),
inference(resolution,[status(thm)],[f45,f70]) ).
fof(f79,plain,
( ~ sQ0_spl
| ordered_pair(sK5_skl,sK6_skl) = ordered_pair(sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl)) ),
inference(resolution,[status(thm)],[f46,f70]) ).
fof(f102,plain,
( ~ sQ0_spl
| sK6_skl = sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f79,f41]) ).
fof(f103,plain,
( ~ sQ0_spl
| sK5_skl = sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f79,f40]) ).
fof(f125,plain,
( ~ sQ0_spl
| in(sK6_skl,sK8_skl) ),
inference(backward_demodulation,[status(thm)],[f102,f77]) ).
fof(f126,plain,
( ~ sQ0_spl
| sP0_prd(sK6_skl,sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),ordered_pair(sK5_skl,sK6_skl),sK8_skl,sK7_skl) ),
inference(backward_demodulation,[status(thm)],[f102,f70]) ).
fof(f161,plain,
( sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f125]) ).
fof(f162,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f165,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ in(X0,X1)
| sP0_prd(X0,sK5_skl,ordered_pair(sK5_skl,X0),X1,sK7_skl) ),
inference(resolution,[status(thm)],[f52,f62]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sQ1_spl
| in(ordered_pair(sK5_skl,X0),cartesian_product2(sK7_skl,X1))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f165,f61]) ).
fof(f180,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ in(sK6_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f175,f50]) ).
fof(f184,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f180,f55,f51,f48]) ).
fof(f202,plain,
( ~ sQ0_spl
| sP0_prd(sK6_skl,sK5_skl,ordered_pair(sK5_skl,sK6_skl),sK8_skl,sK7_skl) ),
inference(backward_demodulation,[status(thm)],[f103,f126]) ).
fof(f205,plain,
( ~ sQ0_spl
| in(sK5_skl,sK7_skl) ),
inference(resolution,[status(thm)],[f202,f44]) ).
fof(f207,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f205,f51,f48]) ).
fof(f208,plain,
$false,
inference(sat_refutation,[status(thm)],[f54,f58,f59,f162,f184,f207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 05:48:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.080020 seconds
% 0.14/0.45 % CPU time: 0.218285 seconds
% 0.14/0.45 % Total memory used: 104.129 MB
% 0.14/0.45 % Net memory used: 103.631 MB
%------------------------------------------------------------------------------