%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 08:44:58 AM UTC 2026
% Result : Theorem 130.61s 18.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 93 ( 22 unt; 0 def)
% Number of atoms : 296 ( 93 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 330 ( 127 ~; 153 |; 36 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 207 ( 12 sgn 83 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d14_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('theBenchmark.p',d14_relat_1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t142_funct_1,conjecture,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('theBenchmark.p',t142_funct_1) ).
fof(t142_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
inference(assume_negation,[status(cth)],[t142_funct_1]) ).
fof(nnf_39,plain,
? [A,B] :
( ( relation_inverse_image(B,singleton(A)) = empty_set
| ~ in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| in(A,relation_rng(B)) )
& relation(B) ),
inference(fof_nnf,[status(thm)],[t142_funct_1_neg]) ).
fof(sk_t142_funct_1_neg,plain,
( ( relation_inverse_image(sK0,singleton(sK5)) = empty_set
| ~ in(sK5,relation_rng(sK0)) )
& ( relation_inverse_image(sK0,singleton(sK5)) != empty_set
| in(sK5,relation_rng(sK0)) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK5]),skolemize(A,sK5),skolemize(B,sK0)],[nnf_39]) ).
cnf(c_45,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t142_funct_1_neg]) ).
fof(nnf_20,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(sk_rc1_funct_1,plain,
( function(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_20]) ).
cnf(c_52,plain,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_rc1_funct_1]) ).
fof(nnf_9,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) )
& ( ? [X3] : in(ordered_pair(X3,C),A)
| in(C,B) ) )
| relation_rng(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X2,X0),A)
| in(X0,B) )
& ( ? [X1] : in(ordered_pair(X1,X0),A)
| ~ in(X0,B) ) )
| relation_rng(A) != B ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(sk_d5_relat_1_sk,plain,
! [A] :
( ! [B] :
( ( ( ( ! [D] : ~ in(ordered_pair(D,sK7(A,B)),A)
| ~ in(sK7(A,B),B) )
& ( in(ordered_pair(sK8(A,B),sK7(A,B)),A)
| in(sK7(A,B),B) ) )
| relation_rng(A) = B )
& ( ! [X0] :
( ( ! [X2] : ~ in(ordered_pair(X2,X0),A)
| in(X0,B) )
& ( in(ordered_pair(sK2(A,B,X0),X0),A)
| ~ in(X0,B) ) )
| relation_rng(A) != B ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK7,sK8]),skolemize(X1,sK2(A,B,X0)),skolemize(C,sK7(A,B)),skolemize(X3,sK8(A,B))],[nnf_9]) ).
fof(sk_d5_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(ordered_pair(VAR_2,sK7(VAR_0,VAR_1)),VAR_0)
| ~ in(sK7(VAR_0,VAR_1),VAR_1)
| relation_rng(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK8(VAR_0,VAR_1),sK7(VAR_0,VAR_1)),VAR_0)
| in(sK7(VAR_0,VAR_1),VAR_1)
| relation_rng(VAR_0) = VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(ordered_pair(VAR_3,VAR_2),VAR_0)
| in(VAR_2,VAR_1)
| relation_rng(VAR_0) != VAR_1
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK2(VAR_0,VAR_1,VAR_2),VAR_2),VAR_0)
| ~ in(VAR_2,VAR_1)
| relation_rng(VAR_0) != VAR_1
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d5_relat_1_sk]) ).
cnf(c_59,plain,
( ~ in(ordered_pair(D,C),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d5_relat_1]) ).
cnf(c_60,plain,
( in(ordered_pair(sK2(A,B,C),C),A)
| ~ in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d5_relat_1]) ).
fof(nnf_6,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) )
& ( ? [X3] :
( in(X3,B)
& in(ordered_pair(D,X3),A) )
| in(D,C) ) )
| relation_inverse_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X0,X2),A) )
| in(X0,C) )
& ( ? [X1] :
( in(X1,B)
& in(ordered_pair(X0,X1),A) )
| ~ in(X0,C) ) )
| relation_inverse_image(A,B) != C ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_1]) ).
fof(sk_d14_relat_1_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK3(A,B,C),E),A) )
| ~ in(sK3(A,B,C),C) )
& ( ( in(sK4(A,B,C),B)
& in(ordered_pair(sK3(A,B,C),sK4(A,B,C)),A) )
| in(sK3(A,B,C),C) ) )
| relation_inverse_image(A,B) = C )
& ( ! [X0] :
( ( ! [X2] :
( ~ in(X2,B)
| ~ in(ordered_pair(X0,X2),A) )
| in(X0,C) )
& ( ( in(sK9(A,B,C,X0),B)
& in(ordered_pair(X0,sK9(A,B,C,X0)),A) )
| ~ in(X0,C) ) )
| relation_inverse_image(A,B) != C ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK3,sK4]),skolemize(X1,sK9(A,B,C,X0)),skolemize(D,sK3(A,B,C)),skolemize(X3,sK4(A,B,C))],[nnf_6]) ).
fof(sk_d14_relat_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| ~ in(ordered_pair(sK3(VAR_0,VAR_1,VAR_2),VAR_3),VAR_0)
| ~ in(sK3(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_inverse_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK4(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK3(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_inverse_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(ordered_pair(sK3(VAR_0,VAR_1,VAR_2),sK4(VAR_0,VAR_1,VAR_2)),VAR_0)
| in(sK3(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_inverse_image(VAR_0,VAR_1) = VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ in(VAR_4,VAR_1)
| ~ in(ordered_pair(VAR_3,VAR_4),VAR_0)
| in(VAR_3,VAR_2)
| relation_inverse_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK9(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| relation_inverse_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(ordered_pair(VAR_3,sK9(VAR_0,VAR_1,VAR_2,VAR_3)),VAR_0)
| ~ in(VAR_3,VAR_2)
| relation_inverse_image(VAR_0,VAR_1) != VAR_2
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d14_relat_1_sk]) ).
cnf(c_62,plain,
( in(sK4(A,B,C),B)
| in(sK3(A,B,C),C)
| relation_inverse_image(A,B) = C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_63,plain,
( in(ordered_pair(sK3(A,B,C),sK4(A,B,C)),A)
| in(sK3(A,B,C),C)
| relation_inverse_image(A,B) = C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_64,plain,
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A)
| in(D,C)
| relation_inverse_image(A,B) != C
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d14_relat_1]) ).
cnf(c_72,negated_conjecture,
( relation_inverse_image(sK0,singleton(sK5)) = empty_set
| ~ in(sK5,relation_rng(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t142_funct_1_neg]) ).
cnf(c_73,negated_conjecture,
( relation_inverse_image(sK0,singleton(sK5)) != empty_set
| in(sK5,relation_rng(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t142_funct_1_neg]) ).
cnf(c_75,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_76,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_26,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(sk_rc2_subset_1,plain,
! [A] :
( empty(sK6(A))
& element(sK6(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(B,sK6(A))],[nnf_26]) ).
cnf(c_82,plain,
empty(sK6(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
cnf(c_97,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_99,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_102,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_103,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_104,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_164,negated_conjecture,
( ~ in(ordered_pair(C,B),sK0)
| in(B,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_59,c_45]) ).
cnf(c_8577,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(C,B),singleton(C)),sK0)
| in(B,A)
| relation_rng(sK0) != A ),
inference(paramod,[status(thm)],[c_97,c_164]) ).
cnf(c_165,negated_conjecture,
( ~ in(unordered_pair(singleton(C),unordered_pair(C,B)),sK0)
| in(B,A)
| relation_rng(sK0) != A ),
inference(paramod,[status(thm)],[c_104,c_8577]) ).
cnf(c_182,negated_conjecture,
( in(ordered_pair(sK2(sK0,A,B),B),sK0)
| ~ in(B,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_60,c_45]) ).
cnf(c_8578,negated_conjecture,
( in(unordered_pair(unordered_pair(sK2(sK0,A,B),B),singleton(sK2(sK0,A,B))),sK0)
| ~ in(B,A)
| relation_rng(sK0) != A ),
inference(paramod,[status(thm)],[c_97,c_182]) ).
cnf(c_8579,negated_conjecture,
( in(unordered_pair(unordered_pair(B,sK2(sK0,A,B)),singleton(sK2(sK0,A,B))),sK0)
| ~ in(B,A)
| relation_rng(sK0) != A ),
inference(paramod,[status(thm)],[c_104,c_8578]) ).
cnf(c_183,negated_conjecture,
( in(unordered_pair(singleton(sK2(sK0,A,B)),unordered_pair(B,sK2(sK0,A,B))),sK0)
| ~ in(B,A)
| relation_rng(sK0) != A ),
inference(paramod,[status(thm)],[c_104,c_8579]) ).
cnf(c_204,plain,
( in(sK4(sK1,A,B),A)
| in(sK3(sK1,A,B),B)
| relation_inverse_image(sK1,A) = B ),
inference(resolve,[status(thm)],[c_62,c_52]) ).
cnf(c_210,negated_conjecture,
( in(sK4(sK0,A,B),A)
| in(sK3(sK0,A,B),B)
| relation_inverse_image(sK0,A) = B ),
inference(resolve,[status(thm)],[c_62,c_45]) ).
cnf(c_227,negated_conjecture,
( in(ordered_pair(sK3(sK0,A,B),sK4(sK0,A,B)),sK0)
| in(sK3(sK0,A,B),B)
| relation_inverse_image(sK0,A) = B ),
inference(resolve,[status(thm)],[c_63,c_45]) ).
cnf(c_8580,negated_conjecture,
( in(unordered_pair(unordered_pair(sK3(sK0,A,B),sK4(sK0,A,B)),singleton(sK3(sK0,A,B))),sK0)
| in(sK3(sK0,A,B),B)
| relation_inverse_image(sK0,A) = B ),
inference(paramod,[status(thm)],[c_97,c_227]) ).
cnf(c_228,negated_conjecture,
( in(unordered_pair(singleton(sK3(sK0,A,B)),unordered_pair(sK3(sK0,A,B),sK4(sK0,A,B))),sK0)
| in(sK3(sK0,A,B),B)
| relation_inverse_image(sK0,A) = B ),
inference(paramod,[status(thm)],[c_104,c_8580]) ).
cnf(c_245,negated_conjecture,
( ~ in(D,A)
| ~ in(ordered_pair(C,D),sK0)
| in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(resolve,[status(thm)],[c_64,c_45]) ).
cnf(c_8581,negated_conjecture,
( ~ in(D,A)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),sK0)
| in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(paramod,[status(thm)],[c_97,c_245]) ).
cnf(c_246,negated_conjecture,
( ~ in(D,A)
| ~ in(unordered_pair(singleton(C),unordered_pair(C,D)),sK0)
| in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(paramod,[status(thm)],[c_104,c_8581]) ).
cnf(c_8582,plain,
empty_set = sK6(A),
inference(resolve,[status(thm)],[c_82,c_76]) ).
cnf(c_302,plain,
sK6(A) = empty_set,
inference(copy,[status(thm)],[c_8582]) ).
cnf(c_8583,plain,
~ in(A,sK6(B)),
inference(resolve,[status(thm)],[c_82,c_75]) ).
cnf(c_303,plain,
~ in(A,empty_set),
inference(paramod,[status(thm)],[c_302,c_8583]) ).
cnf(c_330,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_102]) ).
cnf(c_332,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_103]) ).
cnf(c_391,plain,
( ~ in(unordered_pair(singleton(B),unordered_pair(B,A)),sK0)
| in(A,relation_rng(sK0)) ),
inference(xxres,[status(thm)],[c_165]) ).
cnf(c_429,plain,
( in(unordered_pair(singleton(sK2(sK0,relation_rng(sK0),A)),unordered_pair(A,sK2(sK0,relation_rng(sK0),A))),sK0)
| ~ in(A,relation_rng(sK0)) ),
inference(xxres,[status(thm)],[c_183]) ).
cnf(c_1374,plain,
( in(sK4(sK0,A,empty_set),A)
| relation_inverse_image(sK0,A) = empty_set ),
inference(resolve,[status(thm)],[c_303,c_210]) ).
cnf(c_1381,plain,
( in(sK3(sK1,empty_set,A),A)
| relation_inverse_image(sK1,empty_set) = A ),
inference(resolve,[status(thm)],[c_303,c_204]) ).
cnf(c_1603,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_330]) ).
cnf(c_8584,plain,
empty_set != singleton(A),
inference(resolve,[status(thm)],[c_1603,c_99]) ).
cnf(c_1640,plain,
singleton(A) != empty_set,
inference(copy,[status(thm)],[c_8584]) ).
cnf(c_1912,plain,
( sK4(sK0,singleton(A),empty_set) = A
| relation_inverse_image(sK0,singleton(A)) = empty_set ),
inference(resolve,[status(thm)],[c_1374,c_332]) ).
cnf(c_8585,plain,
( sK3(sK1,empty_set,singleton(A)) = A
| relation_inverse_image(sK1,empty_set) = singleton(A) ),
inference(resolve,[status(thm)],[c_1381,c_332]) ).
cnf(c_2360,plain,
( sK3(sK1,empty_set,singleton(A)) = A
| singleton(A) = relation_inverse_image(sK1,empty_set) ),
inference(copy,[status(thm)],[c_8585]) ).
cnf(c_2365,plain,
relation_inverse_image(sK1,empty_set) = empty_set,
inference(resolve,[status(thm)],[c_1381,c_303]) ).
cnf(c_8586,plain,
( sK3(sK1,empty_set,singleton(A)) = A
| singleton(A) = empty_set ),
inference(paramod,[status(thm)],[c_2365,c_2360]) ).
cnf(c_2405,plain,
sK3(sK1,empty_set,singleton(A)) = A,
inference(resolve,[status(thm)],[c_1640,c_8586]) ).
cnf(c_2406,plain,
( in(sK3(sK1,empty_set,A),A)
| empty_set = A ),
inference(paramod,[status(thm)],[c_2365,c_1381]) ).
cnf(c_3435,plain,
( in(sK3(sK0,A,B),B)
| relation_inverse_image(sK0,A) = B
| in(sK4(sK0,A,B),relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_391,c_228]) ).
cnf(c_8587,plain,
( in(sK3(sK0,singleton(A),empty_set),empty_set)
| relation_inverse_image(sK0,singleton(A)) = empty_set
| in(A,relation_rng(sK0))
| relation_inverse_image(sK0,singleton(A)) = empty_set ),
inference(paramod,[status(thm)],[c_1912,c_3435]) ).
cnf(c_8588,plain,
( in(sK3(sK0,singleton(A),empty_set),empty_set)
| in(A,relation_rng(sK0))
| relation_inverse_image(sK0,singleton(A)) = empty_set ),
inference(copy,[status(thm)],[c_8587]) ).
cnf(c_8249,plain,
( in(A,relation_rng(sK0))
| relation_inverse_image(sK0,singleton(A)) = empty_set ),
inference(resolve,[status(thm)],[c_303,c_8588]) ).
cnf(c_8589,negated_conjecture,
( relation_inverse_image(sK0,singleton(sK5)) = empty_set
| relation_inverse_image(sK0,singleton(sK5)) = empty_set ),
inference(resolve,[status(thm)],[c_8249,c_72]) ).
cnf(c_8443,negated_conjecture,
relation_inverse_image(sK0,singleton(sK5)) = empty_set,
inference(copy,[status(thm)],[c_8589]) ).
cnf(c_8590,negated_conjecture,
( empty_set != empty_set
| in(sK5,relation_rng(sK0)) ),
inference(paramod,[status(thm)],[c_8443,c_73]) ).
cnf(c_8444,negated_conjecture,
in(sK5,relation_rng(sK0)),
inference(copy,[status(thm)],[c_8590]) ).
cnf(c_8446,plain,
in(unordered_pair(singleton(sK2(sK0,relation_rng(sK0),sK5)),unordered_pair(sK5,sK2(sK0,relation_rng(sK0),sK5))),sK0),
inference(resolve,[status(thm)],[c_8444,c_429]) ).
cnf(c_8591,negated_conjecture,
( ~ in(B,singleton(sK5))
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK0)
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_8443,c_246]) ).
cnf(c_8540,negated_conjecture,
( ~ in(B,singleton(sK5))
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK0) ),
inference(resolve,[status(thm)],[c_303,c_8591]) ).
cnf(c_8592,plain,
( empty_set = singleton(sK5)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,sK3(sK1,empty_set,singleton(sK5)))),sK0) ),
inference(resolve,[status(thm)],[c_8540,c_2406]) ).
cnf(c_8593,plain,
( empty_set = singleton(sK5)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,sK5)),sK0) ),
inference(paramod,[status(thm)],[c_2405,c_8592]) ).
cnf(c_8594,plain,
( singleton(sK5) = empty_set
| ~ in(unordered_pair(singleton(A),unordered_pair(A,sK5)),sK0) ),
inference(copy,[status(thm)],[c_8593]) ).
cnf(c_8558,plain,
~ in(unordered_pair(singleton(A),unordered_pair(A,sK5)),sK0),
inference(resolve,[status(thm)],[c_1640,c_8594]) ).
cnf(c_8575,plain,
~ in(unordered_pair(singleton(A),unordered_pair(sK5,A)),sK0),
inference(paramod,[status(thm)],[c_104,c_8558]) ).
cnf(c_8576,plain,
$false,
inference(resolve,[status(thm)],[c_8575,c_8446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU061+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 : Sat Sep 26 08:39:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 1389985 was started by sandbox2 on n001,
% 0.13/0.37 % Sat Sep 26 08:39:58 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 130.61/18.40
% 130.61/18.40 % given #500 (W,wt=27): 681 relation_inverse_image(c10,A) = B | in(f2(c10,A,B),B) | -element(A,powerset(C)) | -empty(C). [resolve(210,c,77,a)].
% 130.61/18.40
% 130.61/18.40 % SZS status Theorem for theBenchmark
% 130.61/18.40
% 130.61/18.40 % Proof 1 at 1.41 (+ 0.42) seconds.
% 130.61/18.40 % Length of proof is 62.
% 130.61/18.40 % Level of proof is 11.
% 130.61/18.40 % Maximum clause weight is 48.000.
% 130.61/18.40 % Given clauses 811.
% 130.61/18.40
% 130.61/18.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------