%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU045+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 : n008.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 75 ( 18 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 81 ( 31 ~; 25 |; 14 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 41 ( 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(t87_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
file('theBenchmark.p',t87_funct_1) ).
fof(t87_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
inference(assume_negation,[status(cth)],[t87_funct_1]) ).
fof(nnf_33,plain,
? [A,B,C] :
( apply(relation_rng_restriction(A,C),B) != apply(C,B)
& in(B,relation_dom(relation_rng_restriction(A,C)))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t87_funct_1_neg]) ).
fof(sk_t87_funct_1_neg,plain,
( apply(relation_rng_restriction(sK0,sK1),sK2) != apply(sK1,sK2)
& in(sK2,relation_dom(relation_rng_restriction(sK0,sK1)))
& function(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK1)],[nnf_33]) ).
cnf(c_38,negated_conjecture,
apply(relation_rng_restriction(sK0,sK1),sK2) != apply(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t87_funct_1_neg]) ).
cnf(c_39,negated_conjecture,
in(sK2,relation_dom(relation_rng_restriction(sK0,sK1))),
inference(split_conjunct,[status(thm)],[sk_t87_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t87_funct_1_neg]) ).
cnf(c_41,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t87_funct_1_neg]) ).
cnf(c_48,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]) ).
cnf(c_72,plain,
( function(relation_rng_restriction(B,A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc5_funct_1]) ).
cnf(c_74,plain,
( relation(relation_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
cnf(c_271,negated_conjecture,
( function(relation_rng_restriction(A,sK1))
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_72,c_40]) ).
cnf(c_149,negated_conjecture,
function(relation_rng_restriction(A,sK1)),
inference(resolve,[status(thm)],[c_41,c_271]) ).
cnf(c_160,plain,
relation(relation_rng_restriction(A,sK1)),
inference(resolve,[status(thm)],[c_74,c_41]) ).
cnf(c_272,plain,
( apply(B,D) = apply(relation_rng_restriction(A,sK1),D)
| ~ in(D,relation_dom(relation_rng_restriction(A,sK1)))
| relation_rng_restriction(C,B) != relation_rng_restriction(A,sK1)
| ~ function(B)
| ~ relation(B)
| ~ relation(relation_rng_restriction(A,sK1)) ),
inference(resolve,[status(thm)],[c_48,c_149]) ).
cnf(c_273,negated_conjecture,
( apply(sK1,C) = apply(relation_rng_restriction(A,sK1),C)
| ~ in(C,relation_dom(relation_rng_restriction(A,sK1)))
| relation_rng_restriction(B,sK1) != relation_rng_restriction(A,sK1)
| ~ function(sK1)
| ~ relation(relation_rng_restriction(A,sK1)) ),
inference(resolve,[status(thm)],[c_272,c_41]) ).
cnf(c_274,negated_conjecture,
( apply(sK1,C) = apply(relation_rng_restriction(A,sK1),C)
| ~ in(C,relation_dom(relation_rng_restriction(A,sK1)))
| relation_rng_restriction(B,sK1) != relation_rng_restriction(A,sK1)
| ~ relation(relation_rng_restriction(A,sK1)) ),
inference(resolve,[status(thm)],[c_273,c_40]) ).
cnf(c_275,plain,
( apply(sK1,B) = apply(relation_rng_restriction(A,sK1),B)
| ~ in(B,relation_dom(relation_rng_restriction(A,sK1)))
| ~ relation(relation_rng_restriction(A,sK1)) ),
inference(xxres,[status(thm)],[c_274]) ).
cnf(c_276,negated_conjecture,
( apply(sK1,sK2) = apply(relation_rng_restriction(sK0,sK1),sK2)
| ~ relation(relation_rng_restriction(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_275,c_39]) ).
cnf(c_277,negated_conjecture,
apply(sK1,sK2) != apply(relation_rng_restriction(sK0,sK1),sK2),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_278,negated_conjecture,
~ relation(relation_rng_restriction(sK0,sK1)),
inference(resolve,[status(thm)],[c_276,c_277]) ).
cnf(c_270,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_160,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n008.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 08:33:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.39 % Process 3214203 was started by sandbox2 on n008,
% 0.12/0.39 % Sat Sep 26 08:33:09 2026
% 0.12/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.16/0.46 % Length of proof is 14.
% 0.16/0.46 % Level of proof is 3.
% 0.16/0.46 % Maximum clause weight is 24.000.
% 0.16/0.46 % Given clauses 74.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------