%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU223+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 : n020.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 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 73 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 25 |; 13 &)
% ( 1 <=>; 9 =>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 9 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t70_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t70_funct_1) ).
fof(t70_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(assume_negation,[status(cth)],[t70_funct_1]) ).
cnf(c_63,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_64,plain,
( function(relation_dom_restriction(A,B))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc4_funct_1]) ).
cnf(c_88,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_38,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A)))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t70_funct_1_neg]) ).
fof(sk_t70_funct_1_neg,plain,
( apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1)
& in(sK1,relation_dom(relation_dom_restriction(sK0,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_38]) ).
cnf(c_91,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t70_funct_1_neg]) ).
cnf(c_92,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t70_funct_1_neg]) ).
cnf(c_93,negated_conjecture,
in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))),
inference(split_conjunct,[status(thm)],[sk_t70_funct_1_neg]) ).
cnf(c_94,negated_conjecture,
apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t70_funct_1_neg]) ).
cnf(c_156,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_91,c_63]) ).
cnf(c_269,negated_conjecture,
( function(relation_dom_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_92,c_64]) ).
cnf(c_163,negated_conjecture,
function(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_91,c_269]) ).
cnf(c_270,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_88,c_156]) ).
cnf(c_271,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,A),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,A)))
| relation_dom_restriction(sK0,B) != relation_dom_restriction(sK0,A)
| ~ function(sK0)
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_270,c_91]) ).
cnf(c_272,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,A),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,A)))
| relation_dom_restriction(sK0,B) != relation_dom_restriction(sK0,A)
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_271,c_92]) ).
cnf(c_273,plain,
( apply(sK0,B) = apply(relation_dom_restriction(sK0,A),B)
| ~ in(B,relation_dom(relation_dom_restriction(sK0,A)))
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(xxres,[status(thm)],[c_272]) ).
cnf(c_274,negated_conjecture,
( apply(sK0,sK1) = apply(relation_dom_restriction(sK0,sK2),sK1)
| ~ function(relation_dom_restriction(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_273,c_93]) ).
cnf(c_275,negated_conjecture,
apply(sK0,sK1) != apply(relation_dom_restriction(sK0,sK2),sK1),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_276,negated_conjecture,
~ function(relation_dom_restriction(sK0,sK2)),
inference(resolve,[status(thm)],[c_274,c_275]) ).
cnf(c_268,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_163,c_276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:54:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1148006 was started by sandbox on n020,
% 0.09/0.37 % Sat Sep 26 08:54:35 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 14.
% 0.09/0.43 % Level of proof is 3.
% 0.09/0.43 % Maximum clause weight is 24.000.
% 0.09/0.43 % Given clauses 89.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------