%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU179+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:51:14 PM UTC 2026
% Result : Theorem 7.86s 1.55s
% Output : Proof 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 157 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 178 ( 66 ~; 70 |; 28 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 92 ( 6 sgn 37 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f4_nnf,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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk6(A,B),sk5(A,B)),A)
& ~ in(sk5(A,B),B) )
| ( ~ in(ordered_pair(D,sk5(A,B)),A)
& in(sk5(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk4(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f4_nnf]) ).
cnf(c11,plain,
( in(ordered_pair(sk4(X0,X1,X2),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f27,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f27_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A] :
( ? [B] :
( ( ~ subset(relation_rng(A),relation_rng(B))
| ~ subset(relation_dom(A),relation_dom(B)) )
& subset(A,B)
& relation(B) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( ( ~ subset(relation_rng(sk13),relation_rng(sk14))
| ~ subset(relation_dom(sk13),relation_dom(sk14)) )
& subset(sk13,sk14)
& relation(sk14)
& relation(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f27_nnf]) ).
cnf(c42,plain,
relation(sk13),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p103,plain,
( in(ordered_pair(sk4(sk13,X0,X1),X1),sk13)
| ~ in(X1,X0)
| X0 != relation_rng(sk13) ),
inference(resolution,[status(thm)],[c11,c42]) ).
cnf(p134,plain,
( in(ordered_pair(sk4(sk13,relation_rng(sk13),X0),X0),sk13)
| ~ in(X0,relation_rng(sk13)) ),
inference(equality_resolution,[status(thm)],[p103]) ).
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_nnf,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)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p135,plain,
( subset(relation_rng(sk13),X0)
| in(ordered_pair(sk4(sk13,relation_rng(sk13),sk0(relation_rng(sk13),X0)),sk0(relation_rng(sk13),X0)),sk13) ),
inference(resolution,[status(thm)],[p134,c3]) ).
cnf(c2,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c44,plain,
subset(sk13,sk14),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p55,plain,
( in(X0,sk14)
| ~ in(X0,sk13) ),
inference(resolution,[status(thm)],[c2,c44]) ).
cnf(p461,plain,
( in(ordered_pair(sk4(sk13,relation_rng(sk13),sk0(relation_rng(sk13),X0)),sk0(relation_rng(sk13),X0)),sk14)
| subset(relation_rng(sk13),X0) ),
inference(resolution,[status(thm)],[p135,p55]) ).
cnf(c12,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c43,plain,
relation(sk14),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p115,plain,
( ~ in(ordered_pair(X2,X1),sk14)
| in(X1,X0)
| X0 != relation_rng(sk14) ),
inference(resolution,[status(thm)],[c12,c43]) ).
cnf(p122,plain,
( ~ in(ordered_pair(X1,X0),sk14)
| in(X0,relation_rng(sk14)) ),
inference(equality_resolution,[status(thm)],[p115]) ).
cnf(p2350,plain,
( in(sk0(relation_rng(sk13),X0),relation_rng(sk14))
| subset(relation_rng(sk13),X0) ),
inference(resolution,[status(thm)],[p461,p122]) ).
cnf(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p2355,plain,
( subset(relation_rng(sk13),relation_rng(sk14))
| subset(relation_rng(sk13),relation_rng(sk14)) ),
inference(resolution,[status(thm)],[p2350,c4]) ).
cnf(p2361,plain,
subset(relation_rng(sk13),relation_rng(sk14)),
inference(factoring,[status(thm)],[p2355]) ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk2(A,B),sk3(A,B)),A)
& ~ in(sk2(A,B),B) )
| ( ~ in(ordered_pair(sk2(A,B),D),A)
& in(sk2(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk1(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f3_nnf]) ).
cnf(c5,plain,
( in(ordered_pair(X2,sk1(X0,X1,X2)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p60,plain,
( in(ordered_pair(X1,sk1(sk13,X0,X1)),sk13)
| ~ in(X1,X0)
| X0 != relation_dom(sk13) ),
inference(resolution,[status(thm)],[c5,c42]) ).
cnf(p63,plain,
( in(ordered_pair(X0,sk1(sk13,relation_dom(sk13),X0)),sk13)
| ~ in(X0,relation_dom(sk13)) ),
inference(equality_resolution,[status(thm)],[p60]) ).
cnf(p64,plain,
( subset(relation_dom(sk13),X0)
| in(ordered_pair(sk0(relation_dom(sk13),X0),sk1(sk13,relation_dom(sk13),sk0(relation_dom(sk13),X0))),sk13) ),
inference(resolution,[status(thm)],[p63,c3]) ).
cnf(p74,plain,
( in(ordered_pair(sk0(relation_dom(sk13),X0),sk1(sk13,relation_dom(sk13),sk0(relation_dom(sk13),X0))),sk14)
| subset(relation_dom(sk13),X0) ),
inference(resolution,[status(thm)],[p64,p55]) ).
cnf(c6,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p69,plain,
( ~ in(ordered_pair(X1,X2),sk14)
| in(X1,X0)
| X0 != relation_dom(sk14) ),
inference(resolution,[status(thm)],[c6,c43]) ).
cnf(p72,plain,
( ~ in(ordered_pair(X0,X1),sk14)
| in(X0,relation_dom(sk14)) ),
inference(equality_resolution,[status(thm)],[p69]) ).
cnf(p77,plain,
( in(sk0(relation_dom(sk13),X0),relation_dom(sk14))
| subset(relation_dom(sk13),X0) ),
inference(resolution,[status(thm)],[p74,p72]) ).
cnf(p82,plain,
( subset(relation_dom(sk13),relation_dom(sk14))
| subset(relation_dom(sk13),relation_dom(sk14)) ),
inference(resolution,[status(thm)],[p77,c4]) ).
cnf(p84,plain,
subset(relation_dom(sk13),relation_dom(sk14)),
inference(factoring,[status(thm)],[p82]) ).
cnf(c45,plain,
( ~ subset(relation_rng(sk13),relation_rng(sk14))
| ~ subset(relation_dom(sk13),relation_dom(sk14)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p85,plain,
~ subset(relation_rng(sk13),relation_rng(sk14)),
inference(resolution,[status(thm)],[p84,c45]) ).
cnf(p2363,plain,
$false,
inference(resolution,[status(thm)],[p2361,p85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU179+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.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 : Thu Sep 24 13:07:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.86/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.86/1.55 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------