%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU044+1 : 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 08:44:56 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 9 unt; 0 def)
% Number of atoms : 201 ( 15 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 268 ( 115 ~; 120 |; 22 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 9 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(t86_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',t86_funct_1) ).
fof(t86_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
<=> ( in(apply(C,B),A)
& in(B,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[t86_funct_1]) ).
fof(nnf_33,plain,
? [A,B,C] :
( ( ~ in(apply(C,B),A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_rng_restriction(A,C))) )
& ( ( in(apply(C,B),A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_rng_restriction(A,C))) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t86_funct_1_neg]) ).
fof(sk_t86_funct_1_neg_sk,plain,
( ( ~ in(apply(sK2,sK0),sK1)
| ~ in(sK0,relation_dom(sK2))
| ~ in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) )
& ( ( in(apply(sK2,sK0),sK1)
& in(sK0,relation_dom(sK2)) )
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) )
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_33]) ).
fof(sk_t86_funct_1_neg,plain,
( ( ~ in(apply(sK2,sK0),sK1)
| ~ in(sK0,relation_dom(sK2))
| ~ in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) )
& ( in(apply(sK2,sK0),sK1)
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) )
& ( in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) )
& function(sK2)
& relation(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_t86_funct_1_neg_sk]) ).
cnf(c_38,negated_conjecture,
( ~ in(apply(sK2,sK0),sK1)
| ~ in(sK0,relation_dom(sK2))
| ~ in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t86_funct_1_neg]) ).
cnf(c_39,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t86_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
( in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t86_funct_1_neg]) ).
cnf(c_41,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t86_funct_1_neg]) ).
cnf(c_42,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t86_funct_1_neg]) ).
cnf(c_50,plain,
( ~ in(apply(B,D),C)
| ~ 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_51,plain,
( in(apply(B,D),C)
| ~ 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_52,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_73,plain,
( function(relation_rng_restriction(B,A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc5_funct_1]) ).
cnf(c_75,plain,
( relation(relation_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
cnf(c_188,negated_conjecture,
( in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(A))
| relation_rng_restriction(sK1,sK2) != A
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_50,c_39]) ).
cnf(c_189,negated_conjecture,
( in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(A))
| relation_rng_restriction(sK1,sK2) != A
| ~ function(sK2)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_42,c_188]) ).
cnf(c_108,negated_conjecture,
( in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(A))
| relation_rng_restriction(sK1,sK2) != A
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_41,c_189]) ).
cnf(c_190,plain,
( ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| relation_rng_restriction(sK1,sK2) != relation_rng_restriction(sK1,sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(factor,[status(thm)],[c_108]) ).
cnf(c_109,plain,
( ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(copy,[status(thm)],[c_190]) ).
cnf(c_191,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| in(apply(A,sK0),B)
| relation_rng_restriction(B,A) != relation_rng_restriction(sK1,sK2)
| ~ function(A)
| ~ relation(A)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_51,c_39]) ).
cnf(c_112,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| in(apply(A,sK0),B)
| relation_rng_restriction(sK1,sK2) != relation_rng_restriction(B,A)
| ~ function(A)
| ~ relation(A)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_192,plain,
( in(apply(sK2,sK0),sK1)
| relation_rng_restriction(sK1,sK2) != relation_rng_restriction(sK1,sK2)
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(factor,[status(thm)],[c_112]) ).
cnf(c_193,plain,
( in(apply(sK2,sK0),sK1)
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(copy,[status(thm)],[c_192]) ).
cnf(c_194,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| ~ function(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_42,c_193]) ).
cnf(c_115,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_41,c_194]) ).
cnf(c_195,negated_conjecture,
( in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(A))
| relation_rng_restriction(B,A) != relation_rng_restriction(sK1,sK2)
| ~ function(A)
| ~ relation(A)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_52,c_40]) ).
cnf(c_117,negated_conjecture,
( in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(A))
| relation_rng_restriction(sK1,sK2) != relation_rng_restriction(B,A)
| ~ function(A)
| ~ relation(A)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(copy,[status(thm)],[c_195]) ).
cnf(c_196,plain,
( in(sK0,relation_dom(sK2))
| relation_rng_restriction(sK1,sK2) != relation_rng_restriction(A,sK2)
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(factor,[status(thm)],[c_117]) ).
cnf(c_197,plain,
( in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
( in(sK0,relation_dom(sK2))
| ~ function(sK2)
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_42,c_197]) ).
cnf(c_119,negated_conjecture,
( in(sK0,relation_dom(sK2))
| ~ function(relation_rng_restriction(sK1,sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_41,c_198]) ).
cnf(c_199,negated_conjecture,
( function(relation_rng_restriction(A,sK2))
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_73,c_41]) ).
cnf(c_170,negated_conjecture,
function(relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_42,c_199]) ).
cnf(c_171,negated_conjecture,
( in(sK0,relation_dom(sK2))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_170,c_119]) ).
cnf(c_173,negated_conjecture,
( in(apply(sK2,sK0),sK1)
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_170,c_115]) ).
cnf(c_174,plain,
( ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2)))
| ~ relation(relation_rng_restriction(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_170,c_109]) ).
cnf(c_181,plain,
relation(relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_75,c_42]) ).
cnf(c_182,plain,
( ~ in(sK0,relation_dom(sK2))
| in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) ),
inference(resolve,[status(thm)],[c_181,c_174]) ).
cnf(c_183,negated_conjecture,
in(apply(sK2,sK0),sK1),
inference(resolve,[status(thm)],[c_181,c_173]) ).
cnf(c_185,negated_conjecture,
in(sK0,relation_dom(sK2)),
inference(resolve,[status(thm)],[c_181,c_171]) ).
cnf(c_200,negated_conjecture,
( ~ in(apply(sK2,sK0),sK1)
| ~ in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))) ),
inference(resolve,[status(thm)],[c_185,c_38]) ).
cnf(c_186,negated_conjecture,
~ in(sK0,relation_dom(relation_rng_restriction(sK1,sK2))),
inference(resolve,[status(thm)],[c_183,c_200]) ).
cnf(c_201,negated_conjecture,
~ in(sK0,relation_dom(sK2)),
inference(resolve,[status(thm)],[c_186,c_182]) ).
cnf(c_187,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_185,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU044+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 08:33:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1095985 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 08:33:19 2026
% 0.09/0.36 % 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).
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.40 % Length of proof is 30.
% 0.13/0.40 % Level of proof is 7.
% 0.13/0.40 % Maximum clause weight is 39.000.
% 0.13/0.40 % Given clauses 38.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------