%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:45:29 AM UTC 2026
% Result : Theorem 3.04s 0.81s
% Output : CNFRefutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 136 ( 40 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 153 ( 61 ~; 58 |; 17 &)
% ( 4 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 10 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(l82_funct_1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(t68_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t72_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_1) ).
fof(t72_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
cnf(c_57,plain,
( empty_set = C
| apply(A,B) != C
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_funct_1]) ).
cnf(c_58,plain,
( empty_set != C
| apply(A,B) = C
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_funct_1]) ).
cnf(c_61,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_73,plain,
( function(relation_dom_restriction(A,B))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc4_funct_1]) ).
cnf(c_80,plain,
( ~ in(B,C)
| ~ in(B,relation_dom(A))
| in(B,relation_dom(relation_dom_restriction(A,C)))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[l82_funct_1]) ).
cnf(c_106,plain,
( apply(B,D) = apply(A,D)
| ~ in(D,relation_dom(A))
| relation_dom_restriction(B,C) != A
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t68_funct_1]) ).
fof(nnf_45,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t72_funct_1_neg]) ).
fof(sk_t72_funct_1_neg,plain,
( apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1)
& in(sK1,sK2)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1),skolemize(C,sK0)],[nnf_45]) ).
cnf(c_112,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_113,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_114,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_115,negated_conjecture,
apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_1568,plain,
( empty_set = apply(A,B)
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(xxres,[status(thm)],[c_57]) ).
cnf(c_123,plain,
( apply(A,B) = empty_set
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_1568]) ).
cnf(c_1569,negated_conjecture,
( function(relation_dom_restriction(sK0,A))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_112,c_73]) ).
cnf(c_339,negated_conjecture,
function(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_113,c_1569]) ).
cnf(c_343,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_112,c_61]) ).
cnf(c_1570,negated_conjecture,
( apply(sK0,A) = empty_set
| in(A,relation_dom(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_123,c_112]) ).
cnf(c_388,negated_conjecture,
( apply(sK0,A) = empty_set
| in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_113,c_1570]) ).
cnf(c_1571,plain,
( apply(B,D) = apply(relation_dom_restriction(sK0,A),D)
| ~ in(D,relation_dom(relation_dom_restriction(sK0,A)))
| relation_dom_restriction(B,C) != relation_dom_restriction(sK0,A)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_106,c_343]) ).
cnf(c_1572,plain,
( apply(A,D) = apply(relation_dom_restriction(sK0,C),D)
| ~ in(D,relation_dom(relation_dom_restriction(sK0,C)))
| relation_dom_restriction(A,B) != relation_dom_restriction(sK0,C)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_1571,c_339]) ).
cnf(c_1573,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,B),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,B)))
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_1572,c_112]) ).
cnf(c_1574,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,B),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,B)))
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B) ),
inference(resolve,[status(thm)],[c_1573,c_113]) ).
cnf(c_1575,plain,
( apply(sK0,A) = apply(relation_dom_restriction(sK0,B),A)
| ~ in(A,relation_dom(relation_dom_restriction(sK0,B))) ),
inference(xxres,[status(thm)],[c_1574]) ).
cnf(c_1576,negated_conjecture,
apply(sK0,sK1) != apply(relation_dom_restriction(sK0,sK2),sK1),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_638,negated_conjecture,
~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))),
inference(resolve,[status(thm)],[c_1575,c_1576]) ).
cnf(c_1577,negated_conjecture,
( ~ in(A,B)
| ~ in(A,relation_dom(sK0))
| in(A,relation_dom(relation_dom_restriction(sK0,B)))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_80,c_112]) ).
cnf(c_1578,negated_conjecture,
( ~ in(A,B)
| ~ in(A,relation_dom(sK0))
| in(A,relation_dom(relation_dom_restriction(sK0,B))) ),
inference(resolve,[status(thm)],[c_1577,c_113]) ).
cnf(c_1579,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_1578,c_638]) ).
cnf(c_1560,negated_conjecture,
~ in(sK1,relation_dom(sK0)),
inference(resolve,[status(thm)],[c_1579,c_114]) ).
cnf(c_1580,plain,
( empty_set != C
| apply(relation_dom_restriction(sK0,A),B) = C
| in(B,relation_dom(relation_dom_restriction(sK0,A)))
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_58,c_343]) ).
cnf(c_1581,plain,
( empty_set != C
| apply(relation_dom_restriction(sK0,B),A) = C
| in(A,relation_dom(relation_dom_restriction(sK0,B))) ),
inference(resolve,[status(thm)],[c_1580,c_339]) ).
cnf(c_1582,plain,
( empty_set != A
| apply(relation_dom_restriction(sK0,sK2),sK1) = A ),
inference(resolve,[status(thm)],[c_1581,c_638]) ).
cnf(c_1583,negated_conjecture,
empty_set != apply(sK0,sK1),
inference(resolve,[status(thm)],[c_1582,c_115]) ).
cnf(c_1566,negated_conjecture,
apply(sK0,sK1) != empty_set,
inference(copy,[status(thm)],[c_1583]) ).
cnf(c_1584,plain,
apply(sK0,sK1) = empty_set,
inference(resolve,[status(thm)],[c_1560,c_388]) ).
cnf(c_1567,plain,
$false,
inference(resolve,[status(thm)],[c_1566,c_1584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:49:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 313177 was started by sandbox on n017,
% 0.11/0.37 % Sat Sep 26 08:49:18 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 3.04/0.81
% 3.04/0.81 % SZS status Theorem for theBenchmark
% 3.04/0.81
% 3.04/0.81 % Proof 1 at 0.32 (+ 0.10) seconds.
% 3.04/0.81 % Length of proof is 24.
% 3.04/0.81 % Level of proof is 5.
% 3.04/0.81 % Maximum clause weight is 34.000.
% 3.04/0.81 % Given clauses 280.
% 3.04/0.81
% 3.04/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------