%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU187+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 02:19:35 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 161 ( 56 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 187 ( 80 ~; 73 |; 23 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 74 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,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)],[f4]) ).
fof(f40,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)],[f39]) ).
fof(f41,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)],[f40]) ).
fof(f42,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK1_skl(B,A),sK2_skl(B,A)),A)
| in(sK1_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK1_skl(B,A),D),A)
| ~ in(sK1_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,sK0_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f41]) ).
fof(f46,plain,
! [X0,X1] :
( in(ordered_pair(sK1_skl(X1,X0),sK2_skl(X1,X0)),X0)
| in(sK1_skl(X1,X0),X1)
| X1 = relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK5_skl(B,A),sK4_skl(B,A)),A)
| in(sK4_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK4_skl(B,A)),A)
| ~ in(sK4_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK3_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(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))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK3_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f68,plain,
( relation(sK7_skl)
& empty(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f22]) ).
fof(f69,plain,
empty(sK7_skl),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f71,plain,
empty(sK8_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f23]) ).
fof(f72,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f87,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f88,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f90,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f92,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f99,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f103,plain,
sK7_skl = empty_set,
inference(resolution,[status(thm)],[f69,f90]) ).
fof(f105,plain,
sK8_skl = empty_set,
inference(resolution,[status(thm)],[f72,f90]) ).
fof(f116,plain,
( relation_rng(empty_set) != sK7_skl
| relation_dom(empty_set) != empty_set ),
inference(backward_demodulation,[status(thm)],[f103,f88]) ).
fof(f117,plain,
( relation_rng(empty_set) != sK7_skl
| relation_dom(sK7_skl) != empty_set ),
inference(forward_demodulation,[status(thm)],[f103,f116]) ).
fof(f118,plain,
( relation_rng(empty_set) != sK7_skl
| relation_dom(sK7_skl) != sK7_skl ),
inference(forward_demodulation,[status(thm)],[f103,f117]) ).
fof(f119,plain,
( relation_rng(sK7_skl) != sK7_skl
| relation_dom(sK7_skl) != sK7_skl ),
inference(forward_demodulation,[status(thm)],[f103,f118]) ).
fof(f123,plain,
( relation_rng(sK7_skl) != sK8_skl
| relation_dom(sK7_skl) != sK7_skl ),
inference(backward_demodulation,[status(thm)],[f127,f119]) ).
fof(f125,plain,
relation(sK8_skl),
inference(backward_demodulation,[status(thm)],[f127,f70]) ).
fof(f127,plain,
sK8_skl = sK7_skl,
inference(forward_demodulation,[status(thm)],[f103,f105]) ).
fof(f128,plain,
( relation_rng(sK7_skl) != sK8_skl
| relation_dom(sK8_skl) != sK7_skl ),
inference(forward_demodulation,[status(thm)],[f127,f123]) ).
fof(f129,plain,
( relation_rng(sK7_skl) != sK8_skl
| relation_dom(sK8_skl) != sK8_skl ),
inference(forward_demodulation,[status(thm)],[f127,f128]) ).
fof(f130,plain,
( relation_rng(sK8_skl) != sK8_skl
| relation_dom(sK8_skl) != sK8_skl ),
inference(forward_demodulation,[status(thm)],[f127,f129]) ).
fof(f135,plain,
! [X0] : ~ in(X0,sK8_skl),
inference(resolution,[status(thm)],[f93,f72]) ).
fof(f137,plain,
! [X0] :
( in(ordered_pair(sK1_skl(X0,sK8_skl),sK2_skl(X0,sK8_skl)),sK8_skl)
| in(sK1_skl(X0,sK8_skl),X0)
| X0 = relation_dom(sK8_skl) ),
inference(resolution,[status(thm)],[f46,f125]) ).
fof(f140,plain,
! [X0] :
( in(sK1_skl(X0,sK8_skl),X0)
| X0 = relation_dom(sK8_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f135]) ).
fof(f144,plain,
sK8_skl = relation_dom(sK8_skl),
inference(resolution,[status(thm)],[f140,f135]) ).
fof(f147,plain,
! [X0] :
( in(sK1_skl(X0,sK8_skl),X0)
| X0 = sK8_skl ),
inference(backward_demodulation,[status(thm)],[f144,f140]) ).
fof(f148,plain,
( relation_rng(sK8_skl) != sK8_skl
| sK8_skl != sK8_skl ),
inference(backward_demodulation,[status(thm)],[f144,f130]) ).
fof(f151,plain,
relation_rng(sK8_skl) != sK8_skl,
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f177,plain,
! [X0] :
( in(ordered_pair(sK3_skl(X0,relation_rng(sK8_skl),sK8_skl),X0),sK8_skl)
| ~ in(X0,relation_rng(sK8_skl)) ),
inference(resolution,[status(thm)],[f99,f125]) ).
fof(f180,plain,
! [X0] : ~ in(X0,relation_rng(sK8_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f177,f135]) ).
fof(f189,plain,
relation_rng(sK8_skl) = sK8_skl,
inference(resolution,[status(thm)],[f180,f147]) ).
fof(f191,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f189,f151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 05:55:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.066510 seconds
% 0.13/0.44 % CPU time: 0.187956 seconds
% 0.13/0.44 % Total memory used: 102.489 MB
% 0.13/0.44 % Net memory used: 102.297 MB
%------------------------------------------------------------------------------