%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 0.24s 0.67s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 136 ( 39 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 155 ( 63 ~; 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 : 75 ( 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_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_59,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_62,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_72,plain,
( function(relation_dom_restriction(A,B))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc4_funct_1]) ).
cnf(c_79,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_97,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_46,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_46]) ).
cnf(c_103,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_104,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_105,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_106,negated_conjecture,
apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t72_funct_1_neg]) ).
cnf(c_788,plain,
( empty_set = apply(A,B)
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(xxres,[status(thm)],[c_58]) ).
cnf(c_115,plain,
( apply(A,B) = empty_set
| in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_788]) ).
cnf(c_789,negated_conjecture,
( function(relation_dom_restriction(sK0,A))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_103,c_72]) ).
cnf(c_296,negated_conjecture,
function(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_104,c_789]) ).
cnf(c_300,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_103,c_62]) ).
cnf(c_790,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_97,c_300]) ).
cnf(c_791,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_790,c_296]) ).
cnf(c_792,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_791,c_103]) ).
cnf(c_793,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_792,c_104]) ).
cnf(c_794,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_793]) ).
cnf(c_795,negated_conjecture,
apply(sK0,sK1) != apply(relation_dom_restriction(sK0,sK2),sK1),
inference(copy,[status(thm)],[c_106]) ).
cnf(c_567,negated_conjecture,
~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))),
inference(resolve,[status(thm)],[c_794,c_795]) ).
cnf(c_796,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_79,c_103]) ).
cnf(c_797,negated_conjecture,
( ~ in(A,B)
| ~ in(A,relation_dom(sK0))
| in(A,relation_dom(relation_dom_restriction(sK0,B))) ),
inference(resolve,[status(thm)],[c_796,c_104]) ).
cnf(c_798,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_797,c_567]) ).
cnf(c_683,negated_conjecture,
~ in(sK1,relation_dom(sK0)),
inference(resolve,[status(thm)],[c_798,c_105]) ).
cnf(c_799,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_59,c_300]) ).
cnf(c_800,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_799,c_296]) ).
cnf(c_801,plain,
( empty_set != A
| apply(relation_dom_restriction(sK0,sK2),sK1) = A ),
inference(resolve,[status(thm)],[c_800,c_567]) ).
cnf(c_802,negated_conjecture,
empty_set != apply(sK0,sK1),
inference(resolve,[status(thm)],[c_801,c_106]) ).
cnf(c_691,negated_conjecture,
apply(sK0,sK1) != empty_set,
inference(copy,[status(thm)],[c_802]) ).
cnf(c_803,negated_conjecture,
( apply(sK0,A) = empty_set
| in(A,relation_dom(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_115,c_104]) ).
cnf(c_804,negated_conjecture,
( apply(sK0,sK1) = empty_set
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_803,c_683]) ).
cnf(c_805,negated_conjecture,
~ relation(sK0),
inference(resolve,[status(thm)],[c_804,c_691]) ).
cnf(c_787,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_103,c_805]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:53:47 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1752471 was started by sandbox on n005,
% 0.17/0.44 % Sat Sep 26 08:53:47 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.24/0.67
% 0.24/0.67 % SZS status Theorem for theBenchmark
% 0.24/0.67
% 0.24/0.67 % Proof 1 at 0.16 (+ 0.04) seconds.
% 0.24/0.67 % Length of proof is 23.
% 0.24/0.67 % Level of proof is 5.
% 0.24/0.67 % Maximum clause weight is 34.000.
% 0.24/0.67 % Given clauses 112.
% 0.24/0.67
% 0.24/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------