%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU048+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 : n014.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 08:44:57 AM UTC 2026
% Result : Theorem 53.93s 8.18s
% Output : CNFRefutation 53.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 76 ( 14 unt; 0 def)
% Number of atoms : 284 ( 75 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 354 ( 146 ~; 165 |; 29 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 25 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(t85_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('theBenchmark.p',t85_funct_1) ).
fof(t99_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( one_to_one(B)
=> one_to_one(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',t99_funct_1) ).
fof(t99_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( one_to_one(B)
=> one_to_one(relation_rng_restriction(A,B)) ) ),
inference(assume_negation,[status(cth)],[t99_funct_1]) ).
fof(nnf_5,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& apply(A,C) = apply(A,B)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(sk_d8_funct_1_sk,plain,
! [A] :
( ( ( ( sK1(A) != sK0(A)
& apply(A,sK1(A)) = apply(A,sK0(A))
& in(sK1(A),relation_dom(A))
& in(sK0(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0(A)),skolemize(C,sK1(A))],[nnf_5]) ).
fof(sk_d8_funct_1,plain,
( ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( apply(VAR_0,sK1(VAR_0)) = apply(VAR_0,sK0(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK0(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| apply(VAR_0,VAR_2) != apply(VAR_0,VAR_1)
| ~ in(VAR_2,relation_dom(VAR_0))
| ~ in(VAR_1,relation_dom(VAR_0))
| ~ one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_funct_1_sk]) ).
cnf(c_43,plain,
( C = B
| apply(A,C) != apply(A,B)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_44,plain,
( in(sK0(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_45,plain,
( in(sK1(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_46,plain,
( apply(A,sK1(A)) = apply(A,sK0(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_47,plain,
( sK1(A) != sK0(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_48,plain,
( relation(relation_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
cnf(c_53,plain,
( function(relation_rng_restriction(B,A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc5_funct_1]) ).
cnf(c_82,plain,
( in(D,relation_dom(B))
| ~ in(D,relation_dom(A))
| relation_rng_restriction(C,B) != A
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t85_funct_1]) ).
cnf(c_85,plain,
( apply(B,D) = apply(A,D)
| ~ in(D,relation_dom(A))
| relation_rng_restriction(C,B) != A
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t85_funct_1]) ).
fof(nnf_34,plain,
? [A,B] :
( ~ one_to_one(relation_rng_restriction(A,B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t99_funct_1_neg]) ).
fof(sk_t99_funct_1_neg,plain,
( ~ one_to_one(relation_rng_restriction(sK3,sK2))
& one_to_one(sK2)
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK3),skolemize(B,sK2)],[nnf_34]) ).
cnf(c_93,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t99_funct_1_neg]) ).
cnf(c_94,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t99_funct_1_neg]) ).
cnf(c_95,negated_conjecture,
one_to_one(sK2),
inference(split_conjunct,[status(thm)],[sk_t99_funct_1_neg]) ).
cnf(c_96,negated_conjecture,
~ one_to_one(relation_rng_restriction(sK3,sK2)),
inference(split_conjunct,[status(thm)],[sk_t99_funct_1_neg]) ).
cnf(c_201,plain,
relation(relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_93,c_48]) ).
cnf(c_7425,negated_conjecture,
( function(relation_rng_restriction(A,sK2))
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_94,c_53]) ).
cnf(c_210,negated_conjecture,
function(relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_93,c_7425]) ).
cnf(c_7426,plain,
( apply(relation_rng_restriction(A,sK2),sK1(relation_rng_restriction(A,sK2))) = apply(relation_rng_restriction(A,sK2),sK0(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2))
| ~ relation(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_210,c_46]) ).
cnf(c_381,plain,
( apply(relation_rng_restriction(A,sK2),sK1(relation_rng_restriction(A,sK2))) = apply(relation_rng_restriction(A,sK2),sK0(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_201,c_7426]) ).
cnf(c_7427,plain,
( in(sK1(relation_rng_restriction(A,sK2)),relation_dom(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2))
| ~ relation(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_210,c_45]) ).
cnf(c_382,plain,
( in(sK1(relation_rng_restriction(A,sK2)),relation_dom(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_201,c_7427]) ).
cnf(c_7428,plain,
( in(sK0(relation_rng_restriction(A,sK2)),relation_dom(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2))
| ~ relation(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_210,c_44]) ).
cnf(c_383,plain,
( in(sK0(relation_rng_restriction(A,sK2)),relation_dom(relation_rng_restriction(A,sK2)))
| one_to_one(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_201,c_7428]) ).
cnf(c_7429,plain,
( sK1(relation_rng_restriction(A,sK2)) != sK0(relation_rng_restriction(A,sK2))
| one_to_one(relation_rng_restriction(A,sK2))
| ~ function(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_47,c_201]) ).
cnf(c_7430,plain,
( sK1(relation_rng_restriction(A,sK2)) != sK0(relation_rng_restriction(A,sK2))
| one_to_one(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_7429,c_210]) ).
cnf(c_414,negated_conjecture,
sK1(relation_rng_restriction(sK3,sK2)) != sK0(relation_rng_restriction(sK3,sK2)),
inference(resolve,[status(thm)],[c_7430,c_96]) ).
cnf(c_7431,plain,
( apply(B,D) = apply(relation_rng_restriction(A,sK2),D)
| ~ in(D,relation_dom(relation_rng_restriction(A,sK2)))
| relation_rng_restriction(C,B) != relation_rng_restriction(A,sK2)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_85,c_201]) ).
cnf(c_7432,plain,
( apply(A,D) = apply(relation_rng_restriction(C,sK2),D)
| ~ in(D,relation_dom(relation_rng_restriction(C,sK2)))
| relation_rng_restriction(B,A) != relation_rng_restriction(C,sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_7431,c_210]) ).
cnf(c_7433,negated_conjecture,
( apply(sK2,C) = apply(relation_rng_restriction(B,sK2),C)
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_7432,c_93]) ).
cnf(c_7434,negated_conjecture,
( apply(sK2,C) = apply(relation_rng_restriction(B,sK2),C)
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2) ),
inference(resolve,[status(thm)],[c_7433,c_94]) ).
cnf(c_7435,plain,
( apply(sK2,A) = apply(relation_rng_restriction(B,sK2),A)
| ~ in(A,relation_dom(relation_rng_restriction(B,sK2))) ),
inference(xxres,[status(thm)],[c_7434]) ).
cnf(c_7436,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| apply(sK2,sK1(relation_rng_restriction(A,sK2))) = apply(relation_rng_restriction(A,sK2),sK1(relation_rng_restriction(A,sK2))) ),
inference(resolve,[status(thm)],[c_7435,c_382]) ).
cnf(c_1279,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| apply(relation_rng_restriction(A,sK2),sK1(relation_rng_restriction(A,sK2))) = apply(sK2,sK1(relation_rng_restriction(A,sK2))) ),
inference(copy,[status(thm)],[c_7436]) ).
cnf(c_7437,plain,
( in(D,relation_dom(B))
| ~ in(D,relation_dom(relation_rng_restriction(A,sK2)))
| relation_rng_restriction(C,B) != relation_rng_restriction(A,sK2)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_82,c_201]) ).
cnf(c_7438,plain,
( in(D,relation_dom(A))
| ~ in(D,relation_dom(relation_rng_restriction(C,sK2)))
| relation_rng_restriction(B,A) != relation_rng_restriction(C,sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_7437,c_210]) ).
cnf(c_7439,negated_conjecture,
( in(C,relation_dom(sK2))
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_7438,c_93]) ).
cnf(c_7440,negated_conjecture,
( in(C,relation_dom(sK2))
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2) ),
inference(resolve,[status(thm)],[c_7439,c_94]) ).
cnf(c_7441,plain,
( in(A,relation_dom(sK2))
| ~ in(A,relation_dom(relation_rng_restriction(B,sK2))) ),
inference(xxres,[status(thm)],[c_7440]) ).
cnf(c_1282,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| in(sK1(relation_rng_restriction(A,sK2)),relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_7441,c_382]) ).
cnf(c_7442,plain,
( apply(B,D) = apply(relation_rng_restriction(A,sK2),D)
| ~ in(D,relation_dom(relation_rng_restriction(A,sK2)))
| relation_rng_restriction(C,B) != relation_rng_restriction(A,sK2)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_85,c_201]) ).
cnf(c_7443,plain,
( apply(A,D) = apply(relation_rng_restriction(C,sK2),D)
| ~ in(D,relation_dom(relation_rng_restriction(C,sK2)))
| relation_rng_restriction(B,A) != relation_rng_restriction(C,sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_7442,c_210]) ).
cnf(c_7444,negated_conjecture,
( apply(sK2,C) = apply(relation_rng_restriction(B,sK2),C)
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_7443,c_93]) ).
cnf(c_7445,negated_conjecture,
( apply(sK2,C) = apply(relation_rng_restriction(B,sK2),C)
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2) ),
inference(resolve,[status(thm)],[c_7444,c_94]) ).
cnf(c_7446,plain,
( apply(sK2,A) = apply(relation_rng_restriction(B,sK2),A)
| ~ in(A,relation_dom(relation_rng_restriction(B,sK2))) ),
inference(xxres,[status(thm)],[c_7445]) ).
cnf(c_7447,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| apply(sK2,sK0(relation_rng_restriction(A,sK2))) = apply(relation_rng_restriction(A,sK2),sK0(relation_rng_restriction(A,sK2))) ),
inference(resolve,[status(thm)],[c_7446,c_383]) ).
cnf(c_1325,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| apply(relation_rng_restriction(A,sK2),sK0(relation_rng_restriction(A,sK2))) = apply(sK2,sK0(relation_rng_restriction(A,sK2))) ),
inference(copy,[status(thm)],[c_7447]) ).
cnf(c_7448,plain,
( in(D,relation_dom(B))
| ~ in(D,relation_dom(relation_rng_restriction(A,sK2)))
| relation_rng_restriction(C,B) != relation_rng_restriction(A,sK2)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_rng_restriction(A,sK2)) ),
inference(resolve,[status(thm)],[c_82,c_201]) ).
cnf(c_7449,plain,
( in(D,relation_dom(A))
| ~ in(D,relation_dom(relation_rng_restriction(C,sK2)))
| relation_rng_restriction(B,A) != relation_rng_restriction(C,sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_7448,c_210]) ).
cnf(c_7450,negated_conjecture,
( in(C,relation_dom(sK2))
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_7449,c_93]) ).
cnf(c_7451,negated_conjecture,
( in(C,relation_dom(sK2))
| ~ in(C,relation_dom(relation_rng_restriction(B,sK2)))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2) ),
inference(resolve,[status(thm)],[c_7450,c_94]) ).
cnf(c_7452,plain,
( in(A,relation_dom(sK2))
| ~ in(A,relation_dom(relation_rng_restriction(B,sK2))) ),
inference(xxres,[status(thm)],[c_7451]) ).
cnf(c_1328,plain,
( one_to_one(relation_rng_restriction(A,sK2))
| in(sK0(relation_rng_restriction(A,sK2)),relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_7452,c_383]) ).
cnf(c_6402,plain,
apply(relation_rng_restriction(sK3,sK2),sK1(relation_rng_restriction(sK3,sK2))) = apply(relation_rng_restriction(sK3,sK2),sK0(relation_rng_restriction(sK3,sK2))),
inference(resolve,[status(thm)],[c_381,c_96]) ).
cnf(c_7453,negated_conjecture,
apply(relation_rng_restriction(sK3,sK2),sK1(relation_rng_restriction(sK3,sK2))) = apply(sK2,sK1(relation_rng_restriction(sK3,sK2))),
inference(resolve,[status(thm)],[c_1279,c_96]) ).
cnf(c_7193,negated_conjecture,
apply(relation_rng_restriction(sK3,sK2),sK0(relation_rng_restriction(sK3,sK2))) = apply(sK2,sK1(relation_rng_restriction(sK3,sK2))),
inference(paramod,[status(thm)],[c_6402,c_7453]) ).
cnf(c_7454,negated_conjecture,
apply(relation_rng_restriction(sK3,sK2),sK0(relation_rng_restriction(sK3,sK2))) = apply(sK2,sK0(relation_rng_restriction(sK3,sK2))),
inference(resolve,[status(thm)],[c_1325,c_96]) ).
cnf(c_7419,negated_conjecture,
apply(sK2,sK1(relation_rng_restriction(sK3,sK2))) = apply(sK2,sK0(relation_rng_restriction(sK3,sK2))),
inference(paramod,[status(thm)],[c_7193,c_7454]) ).
cnf(c_7455,negated_conjecture,
( B = A
| apply(sK2,B) != apply(sK2,A)
| ~ in(B,relation_dom(sK2))
| ~ in(A,relation_dom(sK2))
| ~ one_to_one(sK2)
| ~ function(sK2) ),
inference(resolve,[status(thm)],[c_43,c_93]) ).
cnf(c_7456,negated_conjecture,
( B = A
| apply(sK2,B) != apply(sK2,A)
| ~ in(B,relation_dom(sK2))
| ~ in(A,relation_dom(sK2))
| ~ one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_7455,c_94]) ).
cnf(c_7457,negated_conjecture,
( B = A
| apply(sK2,B) != apply(sK2,A)
| ~ in(B,relation_dom(sK2))
| ~ in(A,relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_7456,c_95]) ).
cnf(c_7458,negated_conjecture,
( one_to_one(relation_rng_restriction(B,sK2))
| A = sK0(relation_rng_restriction(B,sK2))
| apply(sK2,A) != apply(sK2,sK0(relation_rng_restriction(B,sK2)))
| ~ in(A,relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_7457,c_1328]) ).
cnf(c_7459,negated_conjecture,
( one_to_one(relation_rng_restriction(A,sK2))
| one_to_one(relation_rng_restriction(B,sK2))
| sK1(relation_rng_restriction(A,sK2)) = sK0(relation_rng_restriction(B,sK2))
| apply(sK2,sK1(relation_rng_restriction(A,sK2))) != apply(sK2,sK0(relation_rng_restriction(B,sK2))) ),
inference(resolve,[status(thm)],[c_7458,c_1282]) ).
cnf(c_7460,negated_conjecture,
( one_to_one(relation_rng_restriction(sK3,sK2))
| one_to_one(relation_rng_restriction(sK3,sK2))
| sK1(relation_rng_restriction(sK3,sK2)) = sK0(relation_rng_restriction(sK3,sK2)) ),
inference(resolve,[status(thm)],[c_7459,c_7419]) ).
cnf(c_7461,negated_conjecture,
( one_to_one(relation_rng_restriction(sK3,sK2))
| sK1(relation_rng_restriction(sK3,sK2)) = sK0(relation_rng_restriction(sK3,sK2)) ),
inference(copy,[status(thm)],[c_7460]) ).
cnf(c_7462,negated_conjecture,
one_to_one(relation_rng_restriction(sK3,sK2)),
inference(resolve,[status(thm)],[c_414,c_7461]) ).
cnf(c_7424,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_96,c_7462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU048+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:32:31 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.34 % Process 2656220 was started by sandbox2 on n014,
% 0.08/0.34 % Sat Sep 26 08:32:31 2026
% 0.08/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 53.93/8.18
% 53.93/8.18 % given #500 (T,wt=27): 1754 c10 = empty_set | in(f6(empty_set,c10,c1),relation_dom(c10)) | -in(relation_dom(c10),f7(empty_set,c10,c1)). [resolve(1703,c,39,b)].
% 53.93/8.18
% 53.93/8.18 % given #1000 (F,wt=23): 4293 -in(c9,apply(c10,f6(c9,empty_set,c10))). [ur(1013,a,4288,a)].
% 53.93/8.18
% 53.93/8.18 % SZS status Theorem for theBenchmark
% 53.93/8.18
% 53.93/8.18 % Proof 1 at 7.28 (+ 0.46) seconds.
% 53.93/8.18 % Length of proof is 32.
% 53.93/8.18 % Level of proof is 7.
% 53.93/8.18 % Maximum clause weight is 41.000.
% 53.93/8.18 % Given clauses 1413.
% 53.93/8.18
% 53.93/8.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------