%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU248+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 : n013.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 02:19:53 PM UTC 2026
% Result : Theorem 0.22s 1.10s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 4 unt; 0 def)
% Number of atoms : 196 ( 19 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 247 ( 96 ~; 99 |; 35 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 154 ( 136 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f46,plain,
! [A,B] :
( ! [C] :
( ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( ( ( in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),B)
& in(sK1_skl(A,C,B),A) )
| in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),C) )
& ( ~ in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),B)
| ~ in(sK1_skl(A,C,B),A)
| ~ in(ordered_pair(sK0_skl(A,C,B),sK1_skl(A,C,B)),C) ) )
| C = relation_rng_restriction(A,B) )
& ! [A] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),B)
| ~ in(E,A)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(A,C,B)),skolemize(E,sK1_skl(A,C,B))],[f48]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_rng_restriction(X2,X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,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)],[f56]) ).
fof(f58,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)],[f57]) ).
fof(f59,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f64,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK4_skl(B,A),sK5_skl(B,A)),A)
| in(sK4_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK4_skl(B,A),D),A)
| ~ in(sK4_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK3_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(D,sK3_skl(C,B,A)),skolemize(C,sK4_skl(B,A)),skolemize(D,sK5_skl(B,A))],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK3_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f72,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f73,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f83,plain,
? [A,B] :
( ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f84,plain,
? [B] :
( ? [A] : ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
& relation(B) ),
inference(miniscoping,[status(thm)],[f83]) ).
fof(f85,plain,
( ~ subset(relation_dom(relation_rng_restriction(sK8_skl,sK7_skl)),relation_dom(sK7_skl))
& relation(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(B,sK7_skl),skolemize(A,sK8_skl)],[f84]) ).
fof(f86,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
~ subset(relation_dom(relation_rng_restriction(sK8_skl,sK7_skl)),relation_dom(sK7_skl)),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f130,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK3_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f67]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f74]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(relation_dom(X1),X0),X2),X1)
| ~ relation(X1)
| subset(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f62,f131]) ).
fof(f256,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2_skl(relation_dom(sK7_skl),X0),X1),sK7_skl)
| subset(X0,relation_dom(sK7_skl)) ),
inference(resolution,[status(thm)],[f239,f86]) ).
fof(f295,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| in(ordered_pair(X0,sK3_skl(X0,relation_dom(relation_rng_restriction(X1,X2)),relation_rng_restriction(X1,X2))),relation_rng_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_rng_restriction(X1,X2))) ),
inference(resolution,[status(thm)],[f130,f74]) ).
fof(f306,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(relation_dom(sK7_skl),X0),X1),relation_rng_restriction(X2,sK7_skl))
| ~ relation(sK7_skl)
| subset(X0,relation_dom(sK7_skl)) ),
inference(resolution,[status(thm)],[f256,f133]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK2_skl(relation_dom(sK7_skl),X0),X1),relation_rng_restriction(X2,sK7_skl))
| subset(X0,relation_dom(sK7_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f86]) ).
fof(f343,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK3_skl(X0,relation_dom(relation_rng_restriction(X1,sK7_skl)),relation_rng_restriction(X1,sK7_skl))),relation_rng_restriction(X1,sK7_skl))
| ~ in(X0,relation_dom(relation_rng_restriction(X1,sK7_skl))) ),
inference(resolution,[status(thm)],[f295,f86]) ).
fof(f1148,plain,
! [X0,X1] :
( ~ in(sK2_skl(relation_dom(sK7_skl),X0),relation_dom(relation_rng_restriction(X1,sK7_skl)))
| subset(X0,relation_dom(sK7_skl)) ),
inference(resolution,[status(thm)],[f309,f343]) ).
fof(f1313,plain,
! [X0] :
( subset(relation_dom(relation_rng_restriction(X0,sK7_skl)),relation_dom(sK7_skl))
| subset(relation_dom(relation_rng_restriction(X0,sK7_skl)),relation_dom(sK7_skl)) ),
inference(resolution,[status(thm)],[f1148,f61]) ).
fof(f1318,plain,
! [X0] : subset(relation_dom(relation_rng_restriction(X0,sK7_skl)),relation_dom(sK7_skl)),
inference(duplicate_literals_removal,[status(thm)],[f1313]) ).
fof(f1320,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f87,f1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU248+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n013.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 06:03:06 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.50 % Drodi V4.1.1
% 0.22/1.10 % Refutation found
% 0.22/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.88/1.14 % Elapsed time: 0.654523 seconds
% 2.88/1.14 % CPU time: 4.592574 seconds
% 2.88/1.14 % Total memory used: 150.265 MB
% 2.88/1.14 % Net memory used: 143.424 MB
%------------------------------------------------------------------------------