%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU206+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 : n008.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 02:51:19 PM UTC 2026
% Result : Theorem 29.57s 4.62s
% Output : Proof 29.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 7 unt; 0 def)
% Number of atoms : 209 ( 39 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 250 ( 95 ~; 101 |; 40 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 1 con; 0-4 aty)
% Number of variables : 134 ( 7 sgn 56 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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',d5_relat_1) ).
fof(f7_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)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk9(A,B),sk8(A,B)),A)
& ~ in(sk8(A,B),B) )
| ( ~ in(ordered_pair(D,sk8(A,B)),A)
& in(sk8(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk7(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f7_nnf]) ).
cnf(c24,plain,
( in(ordered_pair(sk7(X0,X1,X2),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f37,conjecture,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f37_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f37_nnf,plain,
? [A] :
( relation_image(A,relation_dom(A)) != relation_rng(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f37_neg]) ).
fof(f37_sk,plain,
( relation_image(sk17,relation_dom(sk17)) != relation_rng(sk17)
& relation(sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f37_nnf]) ).
cnf(c66,plain,
relation(sk17),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p324,plain,
( in(ordered_pair(sk7(sk17,X0,X1),X1),sk17)
| ~ in(X1,X0)
| X0 != relation_rng(sk17) ),
inference(resolution,[status(thm)],[c24,c66]) ).
cnf(p333,plain,
( in(ordered_pair(sk7(sk17,relation_rng(sk17),X0),X0),sk17)
| ~ in(X0,relation_rng(sk17)) ),
inference(equality_resolution,[status(thm)],[p324]) ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5_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)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk3(A,B),B)
& in(sk3(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f5_nnf]) ).
cnf(c16,plain,
( in(sk3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p343,plain,
( subset(relation_rng(sk17),X0)
| in(ordered_pair(sk7(sk17,relation_rng(sk17),sk3(relation_rng(sk17),X0)),sk3(relation_rng(sk17),X0)),sk17) ),
inference(resolution,[status(thm)],[p333,c16]) ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f4_nnf,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
& ~ in(D,C) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,C,B,D,E] :
( ( ( ( in(sk2(A,B,C),B)
& in(ordered_pair(sk2(A,B,C),sk1(A,B,C)),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(E,B)
| ~ in(ordered_pair(E,sk1(A,B,C)),A) )
& in(sk1(A,B,C),C) )
| C = relation_image(A,B) )
& ( ( ( ~ in(E,B)
| ~ in(ordered_pair(E,D),A)
| in(D,C) )
& ( ( in(sk0(A,B,C,D),B)
& in(ordered_pair(sk0(A,B,C,D),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f4_nnf]) ).
cnf(c8,plain,
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X2)
| X2 != relation_image(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p102,plain,
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X2),sk17)
| in(X2,X0)
| X0 != relation_image(sk17,X1) ),
inference(resolution,[status(thm)],[c8,c66]) ).
cnf(p108,plain,
( ~ in(X2,X1)
| ~ in(ordered_pair(X2,X0),sk17)
| in(X0,relation_image(sk17,X1)) ),
inference(equality_resolution,[status(thm)],[p102]) ).
cnf(p348,plain,
( ~ in(sk7(sk17,relation_rng(sk17),sk3(relation_rng(sk17),X0)),X1)
| in(sk3(relation_rng(sk17),X0),relation_image(sk17,X1))
| subset(relation_rng(sk17),X0) ),
inference(resolution,[status(thm)],[p343,p108]) ).
fof(f6,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(f6_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)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk5(A,B),sk6(A,B)),A)
& ~ in(sk5(A,B),B) )
| ( ~ in(ordered_pair(sk5(A,B),D),A)
& in(sk5(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk4(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f6_nnf]) ).
cnf(c19,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p243,plain,
( ~ in(ordered_pair(X1,X2),sk17)
| in(X1,X0)
| X0 != relation_dom(sk17) ),
inference(resolution,[status(thm)],[c19,c66]) ).
cnf(p252,plain,
( ~ in(ordered_pair(X0,X1),sk17)
| in(X0,relation_dom(sk17)) ),
inference(equality_resolution,[status(thm)],[p243]) ).
cnf(p349,plain,
( in(sk7(sk17,relation_rng(sk17),sk3(relation_rng(sk17),X0)),relation_dom(sk17))
| subset(relation_rng(sk17),X0) ),
inference(resolution,[status(thm)],[p343,p252]) ).
cnf(p528,plain,
( subset(relation_rng(sk17),X0)
| in(sk3(relation_rng(sk17),X0),relation_image(sk17,relation_dom(sk17)))
| subset(relation_rng(sk17),X0) ),
inference(resolution,[status(thm)],[p348,p349]) ).
cnf(p6836,plain,
( in(sk3(relation_rng(sk17),X0),relation_image(sk17,relation_dom(sk17)))
| subset(relation_rng(sk17),X0) ),
inference(factoring,[status(thm)],[p528]) ).
cnf(c17,plain,
( ~ in(sk3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p6846,plain,
( subset(relation_rng(sk17),relation_image(sk17,relation_dom(sk17)))
| subset(relation_rng(sk17),relation_image(sk17,relation_dom(sk17))) ),
inference(resolution,[status(thm)],[p6836,c17]) ).
cnf(p6855,plain,
subset(relation_rng(sk17),relation_image(sk17,relation_dom(sk17))),
inference(factoring,[status(thm)],[p6846]) ).
cnf(c25,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p353,plain,
( ~ in(ordered_pair(X2,X1),sk17)
| in(X1,X0)
| X0 != relation_rng(sk17) ),
inference(resolution,[status(thm)],[c25,c66]) ).
cnf(p362,plain,
( ~ in(ordered_pair(X1,X0),sk17)
| in(X0,relation_rng(sk17)) ),
inference(equality_resolution,[status(thm)],[p353]) ).
cnf(c6,plain,
( in(ordered_pair(sk0(X0,X1,X2,X3),X3),X0)
| ~ in(X3,X2)
| X2 != relation_image(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p82,plain,
( in(ordered_pair(sk0(sk17,X1,X0,X2),X2),sk17)
| ~ in(X2,X0)
| X0 != relation_image(sk17,X1) ),
inference(resolution,[status(thm)],[c6,c66]) ).
cnf(p88,plain,
( in(ordered_pair(sk0(sk17,X1,relation_image(sk17,X1),X0),X0),sk17)
| ~ in(X0,relation_image(sk17,X1)) ),
inference(equality_resolution,[status(thm)],[p82]) ).
cnf(p209,plain,
( in(ordered_pair(sk0(sk17,X0,relation_image(sk17,X0),sk3(relation_image(sk17,X0),X1)),sk3(relation_image(sk17,X0),X1)),sk17)
| subset(relation_image(sk17,X0),X1) ),
inference(resolution,[status(thm)],[c16,p88]) ).
cnf(p364,plain,
( subset(relation_image(sk17,X0),X1)
| in(sk3(relation_image(sk17,X0),X1),relation_rng(sk17)) ),
inference(resolution,[status(thm)],[p362,p209]) ).
cnf(p368,plain,
( subset(relation_image(sk17,X0),relation_rng(sk17))
| subset(relation_image(sk17,X0),relation_rng(sk17)) ),
inference(resolution,[status(thm)],[p364,c17]) ).
cnf(p370,plain,
subset(relation_image(sk17,X0),relation_rng(sk17)),
inference(factoring,[status(thm)],[p368]) ).
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p371,plain,
( ~ subset(relation_rng(sk17),relation_image(sk17,X0))
| relation_image(sk17,X0) = relation_rng(sk17) ),
inference(resolution,[status(thm)],[p370,c5]) ).
cnf(p6858,plain,
relation_image(sk17,relation_dom(sk17)) = relation_rng(sk17),
inference(resolution,[status(thm)],[p6855,p371]) ).
cnf(c67,plain,
relation_image(sk17,relation_dom(sk17)) != relation_rng(sk17),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p6859,plain,
relation_rng(sk17) != relation_rng(sk17),
inference(demodulation,[status(thm)],[p6858,c67]) ).
cnf(p7051,plain,
$false,
inference(equality_resolution,[status(thm)],[p6859]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU206+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.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 13:11:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.57/4.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.57/4.62 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------