%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 : Fri Sep 25 02:51:17 PM UTC 2026
% Result : Theorem 23.46s 9.09s
% Output : Proof 23.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 198 ( 21 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 242 ( 99 ~; 100 |; 31 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 123 ( 14 sgn 39 !; 9 ?)
% 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',d4_relat_1) ).
fof(f4_nnf,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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk3(A,B),sk4(A,B)),A)
& ~ in(sk3(A,B),B) )
| ( ~ in(ordered_pair(sk3(A,B),D),A)
& in(sk3(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk2(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f4_nnf]) ).
cnf(c12,plain,
( in(ordered_pair(X2,sk2(X0,X1,X2)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p119,plain,
( in(ordered_pair(X1,sk2(X0,relation_dom(X0),X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[status(thm)],[c12]) ).
fof(f11,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f11_nnf,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c24,plain,
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f29,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A,B,C] :
( ( ( in(A,relation_dom(C))
& in(A,B)
& ~ in(A,relation_dom(relation_dom_restriction(C,B))) )
| ( ( ~ in(A,relation_dom(C))
| ~ in(A,B) )
& in(A,relation_dom(relation_dom_restriction(C,B))) ) )
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( ( ( in(sk10,relation_dom(sk12))
& in(sk10,sk11)
& ~ in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))) )
| ( ( ~ in(sk10,relation_dom(sk12))
| ~ in(sk10,sk11) )
& in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))) ) )
& relation(sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12])],[f29_nnf]) ).
cnf(c46,plain,
relation(sk12),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p166,plain,
relation(relation_dom_restriction(sk12,X0)),
inference(resolution,[status(thm)],[c24,c46]) ).
cnf(p1003,plain,
( in(ordered_pair(X0,sk2(relation_dom_restriction(sk12,X1),relation_dom(relation_dom_restriction(sk12,X1)),X0)),relation_dom_restriction(sk12,X1))
| ~ in(X0,relation_dom(relation_dom_restriction(sk12,X1))) ),
inference(resolution,[status(thm)],[p119,p166]) ).
cnf(c49,plain,
( in(sk10,relation_dom(sk12))
| in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p1120,plain,
( in(sk10,relation_dom(sk12))
| in(ordered_pair(sk10,sk2(relation_dom_restriction(sk12,sk11),relation_dom(relation_dom_restriction(sk12,sk11)),sk10)),relation_dom_restriction(sk12,sk11)) ),
inference(resolution,[status(thm)],[p1003,c49]) ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f3_nnf,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B)
& ~ in(ordered_pair(D,E),C) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,C,B,D,E] :
( ( ( ( in(ordered_pair(sk0(A,B,C),sk1(A,B,C)),A)
& in(sk0(A,B,C),B)
& ~ in(ordered_pair(sk0(A,B,C),sk1(A,B,C)),C) )
| ( ( ~ in(ordered_pair(sk0(A,B,C),sk1(A,B,C)),A)
| ~ in(sk0(A,B,C),B) )
& in(ordered_pair(sk0(A,B,C),sk1(A,B,C)),C) )
| C = relation_dom_restriction(A,B) )
& ( ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C)
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f3_nnf]) ).
cnf(c4,plain,
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_dom_restriction(X0,X1)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p63,plain,
( in(ordered_pair(X2,X3),sk12)
| ~ in(ordered_pair(X2,X3),X0)
| X0 != relation_dom_restriction(sk12,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c4,c46]) ).
cnf(p64,plain,
( in(ordered_pair(X1,X2),sk12)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(sk12,X0))
| ~ relation(relation_dom_restriction(sk12,X0)) ),
inference(equality_resolution,[status(thm)],[p63]) ).
cnf(p175,plain,
( in(ordered_pair(X0,X1),sk12)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(sk12,X2)) ),
inference(resolution,[status(thm)],[p166,p64]) ).
cnf(p1155,plain,
( in(ordered_pair(sk10,sk2(relation_dom_restriction(sk12,sk11),relation_dom(relation_dom_restriction(sk12,sk11)),sk10)),sk12)
| in(sk10,relation_dom(sk12)) ),
inference(resolution,[status(thm)],[p1120,p175]) ).
cnf(c13,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p127,plain,
( ~ in(ordered_pair(X1,X2),sk12)
| in(X1,X0)
| X0 != relation_dom(sk12) ),
inference(resolution,[status(thm)],[c13,c46]) ).
cnf(p131,plain,
( ~ in(ordered_pair(X0,X1),sk12)
| in(X0,relation_dom(sk12)) ),
inference(equality_resolution,[status(thm)],[p127]) ).
cnf(p1160,plain,
( in(sk10,relation_dom(sk12))
| in(sk10,relation_dom(sk12)) ),
inference(resolution,[status(thm)],[p1155,p131]) ).
cnf(p1164,plain,
in(sk10,relation_dom(sk12)),
inference(factoring,[status(thm)],[p1160]) ).
cnf(p120,plain,
( in(ordered_pair(X1,sk2(sk12,X0,X1)),sk12)
| ~ in(X1,X0)
| X0 != relation_dom(sk12) ),
inference(resolution,[status(thm)],[c12,c46]) ).
cnf(p124,plain,
( in(ordered_pair(X0,sk2(sk12,relation_dom(sk12),X0)),sk12)
| ~ in(X0,relation_dom(sk12)) ),
inference(equality_resolution,[status(thm)],[p120]) ).
cnf(p1166,plain,
in(ordered_pair(sk10,sk2(sk12,relation_dom(sk12),sk10)),sk12),
inference(resolution,[status(thm)],[p1164,p124]) ).
cnf(c48,plain,
( in(sk10,sk11)
| in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p1119,plain,
( in(sk10,sk11)
| in(ordered_pair(sk10,sk2(relation_dom_restriction(sk12,sk11),relation_dom(relation_dom_restriction(sk12,sk11)),sk10)),relation_dom_restriction(sk12,sk11)) ),
inference(resolution,[status(thm)],[p1003,c48]) ).
cnf(c3,plain,
( in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2)
| X2 != relation_dom_restriction(X0,X1)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p59,plain,
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0)
| X0 != relation_dom_restriction(sk12,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c3,c46]) ).
cnf(p60,plain,
( in(X1,X0)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(sk12,X0))
| ~ relation(relation_dom_restriction(sk12,X0)) ),
inference(equality_resolution,[status(thm)],[p59]) ).
cnf(p172,plain,
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_dom_restriction(sk12,X2)) ),
inference(resolution,[status(thm)],[p166,p60]) ).
cnf(p1126,plain,
( in(sk10,sk11)
| in(sk10,sk11) ),
inference(resolution,[status(thm)],[p1119,p172]) ).
cnf(p1131,plain,
in(sk10,sk11),
inference(factoring,[status(thm)],[p1126]) ).
cnf(c5,plain,
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| in(ordered_pair(X3,X4),X2)
| X2 != relation_dom_restriction(X0,X1)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p70,plain,
( ~ in(ordered_pair(X2,X3),sk12)
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),X0)
| X0 != relation_dom_restriction(sk12,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[c5,c46]) ).
cnf(p72,plain,
( ~ in(ordered_pair(X1,X2),sk12)
| ~ in(X1,X0)
| in(ordered_pair(X1,X2),relation_dom_restriction(sk12,X0))
| ~ relation(relation_dom_restriction(sk12,X0)) ),
inference(equality_resolution,[status(thm)],[p70]) ).
cnf(p180,plain,
( ~ in(ordered_pair(X0,X1),sk12)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),relation_dom_restriction(sk12,X2)) ),
inference(resolution,[status(thm)],[p166,p72]) ).
cnf(p1151,plain,
( ~ in(ordered_pair(sk10,X0),sk12)
| in(ordered_pair(sk10,X0),relation_dom_restriction(sk12,sk11)) ),
inference(resolution,[status(thm)],[p1131,p180]) ).
cnf(p1187,plain,
in(ordered_pair(sk10,sk2(sk12,relation_dom(sk12),sk10)),relation_dom_restriction(sk12,sk11)),
inference(resolution,[status(thm)],[p1166,p1151]) ).
cnf(p185,plain,
( ~ in(ordered_pair(X2,X3),relation_dom_restriction(sk12,X1))
| in(X2,X0)
| X0 != relation_dom(relation_dom_restriction(sk12,X1)) ),
inference(resolution,[status(thm)],[p166,c13]) ).
cnf(p308,plain,
( ~ in(ordered_pair(X0,X2),relation_dom_restriction(sk12,X1))
| in(X0,relation_dom(relation_dom_restriction(sk12,X1))) ),
inference(equality_resolution,[status(thm)],[p185]) ).
cnf(p1190,plain,
in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))),
inference(resolution,[status(thm)],[p1187,p308]) ).
cnf(c50,plain,
( ~ in(sk10,relation_dom(relation_dom_restriction(sk12,sk11)))
| ~ in(sk10,relation_dom(sk12))
| ~ in(sk10,sk11) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p1150,plain,
( ~ in(sk10,relation_dom(relation_dom_restriction(sk12,sk11)))
| ~ in(sk10,relation_dom(sk12)) ),
inference(resolution,[status(thm)],[p1131,c50]) ).
cnf(p1170,plain,
~ in(sk10,relation_dom(relation_dom_restriction(sk12,sk11))),
inference(resolution,[status(thm)],[p1164,p1150]) ).
cnf(p1198,plain,
$false,
inference(resolution,[status(thm)],[p1190,p1170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.61 % Computer : n004.cluster.edu
% 0.11/5.61 % Model : x86_64 x86_64
% 0.11/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.61 % Memory : 8046.5625MB
% 0.11/5.61 % OS : Linux 6.8.0-71-generic
% 0.11/5.61 % CPULimit : 300
% 0.11/5.61 % WCLimit : 300
% 0.11/5.61 % DateTime : Thu Sep 24 13:07:42 UTC 2026
% 0.11/5.61 % CPUTime :
% 0.11/5.61 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.46/9.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.46/9.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------