%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU251+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 : n010.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 02:19:54 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 7 unt; 6 def)
% Number of atoms : 213 ( 31 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 246 ( 98 ~; 96 |; 32 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 100 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f52,plain,
! [A] :
( ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ( in(ordered_pair(D,B),A)
& D != B )
| in(D,C) )
& ( ~ in(ordered_pair(D,B),A)
| D = B
| ~ in(D,C) ) )
| C = fiber(A,B) )
& ( ! [D] :
( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ( in(ordered_pair(D,B),A)
& D != B )
| in(D,C) )
& ( ~ in(ordered_pair(D,B),A)
| D = B
| ~ in(D,C) ) )
| C = fiber(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ! [D] :
( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(ordered_pair(sK0_skl(C,B,A),B),A)
& sK0_skl(C,B,A) != B )
| in(sK0_skl(C,B,A),C) )
& ( ~ in(ordered_pair(sK0_skl(C,B,A),B),A)
| sK0_skl(C,B,A) = B
| ~ in(sK0_skl(C,B,A),C) ) )
| C = fiber(A,B) )
& ! [B,C] :
( ( ! [D] :
( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ! [D] :
( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| ~ in(X3,X1)
| X1 != fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,X2),X0)
| ~ in(X3,X1)
| X1 != fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| X3 = X2
| in(X3,X1)
| X1 != fiber(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f62,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f63,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)],[f62]) ).
fof(f64,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)],[f63]) ).
fof(f65,plain,
( ! [A,B] :
( ( ~ in(sK1_skl(B,A),B)
& in(sK1_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,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f64]) ).
fof(f67,plain,
! [X0,X1] :
( in(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0,X1] :
( ~ in(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f72,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f73,plain,
! [A] :
( ! [B] : relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f98,plain,
! [A,B,C] :
( ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f99,plain,
! [A,B,C] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ! [A,B] :
( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( in(X1,X0)
| ~ in(X1,relation_restriction(X0,X2))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f106,plain,
? [A,B,C] :
( ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B))
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f107,plain,
? [C] :
( ? [A,B] : ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B))
& relation(C) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ subset(fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl),fiber(sK8_skl,sK10_skl))
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(C,sK8_skl),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f107]) ).
fof(f109,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
~ subset(fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl),fiber(sK8_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X1,fiber(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f134,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| ~ in(X1,fiber(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X1 = X2
| in(X1,fiber(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f176,plain,
in(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),
inference(resolution,[status(thm)],[f67,f110]) ).
fof(f177,plain,
( in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),relation_restriction(sK8_skl,sK9_skl))
| ~ relation(relation_restriction(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f176,f134]) ).
fof(f181,definition,
( sQ0_spl
<=> relation(relation_restriction(sK8_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ0_spl
| ~ relation(relation_restriction(sK8_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
( sQ1_spl
<=> in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),relation_restriction(sK8_skl,sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ1_spl
| in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),relation_restriction(sK8_skl,sK9_skl)) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f177,f181,f184]) ).
fof(f188,plain,
( sQ0_spl
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f183,f74]) ).
fof(f189,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f109]) ).
fof(f190,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ1_spl
| in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f185,f101]) ).
fof(f199,definition,
( sQ3_spl
<=> sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)) = sK10_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ3_spl
| sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)) = sK10_skl ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f203,definition,
( sQ4_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( sQ4_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ5_spl
<=> in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ5_spl
| in(ordered_pair(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),sK10_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f192,f203,f206,f184]) ).
fof(f210,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f109]) ).
fof(f211,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f212,plain,
( ~ sQ5_spl
| sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)) = sK10_skl
| in(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),fiber(sK8_skl,sK10_skl))
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f207,f135]) ).
fof(f216,definition,
( sQ6_spl
<=> in(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),fiber(sK8_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ6_spl
| in(sK1_skl(fiber(sK8_skl,sK10_skl),fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)),fiber(sK8_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ5_spl
| sQ3_spl
| sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f212,f203,f216,f199,f206]) ).
fof(f223,plain,
( ~ sQ3_spl
| in(sK10_skl,fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl)) ),
inference(backward_demodulation,[status(thm)],[f200,f176]) ).
fof(f230,plain,
( ~ sQ3_spl
| ~ relation(relation_restriction(sK8_skl,sK9_skl)) ),
inference(resolution,[status(thm)],[f223,f133]) ).
fof(f238,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f230,f181,f199]) ).
fof(f323,plain,
( ~ sQ6_spl
| subset(fiber(relation_restriction(sK8_skl,sK9_skl),sK10_skl),fiber(sK8_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f217,f68]) ).
fof(f328,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f110]) ).
fof(f329,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
$false,
inference(sat_refutation,[status(thm)],[f187,f190,f209,f211,f219,f238,f329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU251+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 : n010.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 06:03:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.089252 seconds
% 0.13/0.46 % CPU time: 0.310691 seconds
% 0.13/0.46 % Total memory used: 106.630 MB
% 0.13/0.46 % Net memory used: 106.178 MB
%------------------------------------------------------------------------------