%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU217+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 08:45:27 AM UTC 2026
% Result : Theorem 0.08s 0.49s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 36 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 35 ( 15 ~; 10 |; 5 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t35_funct_1,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('theBenchmark.p',t35_funct_1) ).
fof(t35_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(assume_negation,[status(cth)],[t35_funct_1]) ).
cnf(c_36,plain,
( apply(A,C) = C
| ~ in(C,B)
| identity_relation(B) != A
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t34_funct_1]) ).
cnf(c_42,plain,
relation(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
fof(nnf_30,plain,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(fof_nnf,[status(thm)],[t35_funct_1_neg]) ).
fof(sk_t35_funct_1_neg,plain,
( apply(identity_relation(sK0),sK1) != sK1
& in(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_30]) ).
cnf(c_50,negated_conjecture,
apply(identity_relation(sK0),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_t35_funct_1_neg]) ).
cnf(c_51,negated_conjecture,
in(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t35_funct_1_neg]) ).
cnf(c_63,plain,
function(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_97,plain,
( apply(identity_relation(A),C) = C
| ~ in(C,B)
| identity_relation(B) != identity_relation(A)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_42,c_36]) ).
cnf(c_98,plain,
( apply(identity_relation(B),C) = C
| ~ in(C,A)
| identity_relation(A) != identity_relation(B) ),
inference(resolve,[status(thm)],[c_63,c_97]) ).
cnf(c_164,negated_conjecture,
( apply(identity_relation(A),sK1) = sK1
| identity_relation(sK0) != identity_relation(A) ),
inference(resolve,[status(thm)],[c_98,c_51]) ).
cnf(c_165,negated_conjecture,
identity_relation(sK0) != identity_relation(sK0),
inference(resolve,[status(thm)],[c_164,c_50]) ).
cnf(c_163,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n017.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Sat Sep 26 08:48:04 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.42 % Process 309061 was started by sandbox on n017,
% 0.08/0.42 % Sat Sep 26 08:48:04 2026
% 0.08/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.43
% 0.08/0.43 % From the command line: assign(max_seconds, 300).
% 0.08/0.49
% 0.08/0.49 % SZS status Theorem for theBenchmark
% 0.08/0.49
% 0.08/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.49 % Length of proof is 11.
% 0.08/0.49 % Level of proof is 4.
% 0.08/0.49 % Maximum clause weight is 14.000.
% 0.08/0.49 % Given clauses 40.
% 0.08/0.49
% 0.08/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------