%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU247+2 : 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 : n010.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 08:45:34 AM UTC 2026
% Result : Theorem 27.89s 4.57s
% Output : CNFRefutation 27.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 25 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t140_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)) ),
file('theBenchmark.p',t140_relat_1) ).
fof(t17_wellord1,axiom,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
file('theBenchmark.p',t17_wellord1) ).
fof(t18_wellord1,conjecture,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
file('theBenchmark.p',t18_wellord1) ).
fof(t18_wellord1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_rng_restriction(A,relation_dom_restriction(B,A)) ),
inference(assume_negation,[status(cth)],[t18_wellord1]) ).
cnf(c_772,plain,
( relation_rng_restriction(B,relation_dom_restriction(A,C)) = relation_dom_restriction(relation_rng_restriction(B,A),C)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t140_relat_1]) ).
cnf(c_796,plain,
( relation_restriction(A,B) = relation_dom_restriction(relation_rng_restriction(B,A),B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t17_wellord1]) ).
cnf(c_797,plain,
( relation_dom_restriction(relation_rng_restriction(B,A),B) = relation_restriction(A,B)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_796]) ).
fof(nnf_303,plain,
? [A,B] :
( relation_restriction(B,A) != relation_rng_restriction(A,relation_dom_restriction(B,A))
& relation(B) ),
inference(fof_nnf,[status(thm)],[t18_wellord1_neg]) ).
fof(sk_t18_wellord1_neg,plain,
( relation_restriction(sK0,sK1) != relation_rng_restriction(sK1,relation_dom_restriction(sK0,sK1))
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_303]) ).
cnf(c_941,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t18_wellord1_neg]) ).
cnf(c_942,negated_conjecture,
relation_restriction(sK0,sK1) != relation_rng_restriction(sK1,relation_dom_restriction(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t18_wellord1_neg]) ).
cnf(c_943,negated_conjecture,
relation_rng_restriction(sK1,relation_dom_restriction(sK0,sK1)) != relation_restriction(sK0,sK1),
inference(copy,[status(thm)],[c_942]) ).
cnf(c_16943,plain,
relation_rng_restriction(A,relation_dom_restriction(sK0,B)) = relation_dom_restriction(relation_rng_restriction(A,sK0),B),
inference(resolve,[status(thm)],[c_772,c_941]) ).
cnf(c_16956,negated_conjecture,
relation_dom_restriction(relation_rng_restriction(sK1,sK0),sK1) != relation_restriction(sK0,sK1),
inference(paramod,[status(thm)],[c_16943,c_943]) ).
cnf(c_17627,plain,
relation_dom_restriction(relation_rng_restriction(A,sK0),A) = relation_restriction(sK0,A),
inference(resolve,[status(thm)],[c_797,c_941]) ).
cnf(c_17628,plain,
$false,
inference(resolve,[status(thm)],[c_17627,c_16956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU247+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:58:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2966287 was started by sandbox on n010,
% 0.11/0.38 % Sat Sep 26 08:58:45 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.46
% 0.11/0.46 % From the command line: assign(max_seconds, 300).
% 0.11/0.46
% 0.11/0.46 % SInE: 240 to sos, 64 to usable, of 304 axioms (tolerance 2.00, depth 0 fixpoint).
% 27.89/4.57
% 27.89/4.57 % given #500 (F,wt=26): 5943 relation_rng_restriction(powerset(empty_set),c11) != empty_set | -in(ordered_pair(A,empty_set),c11). [resolve(5939,a,5636,b)].
% 27.89/4.57
% 27.89/4.57 % given #1000 (W,wt=16): 12300 -well_ordering(identity_relation(A)) | reflexive(identity_relation(A)). [resolve(647,a,347,a)].
% 27.89/4.57
% 27.89/4.57 % SZS status Theorem for theBenchmark
% 27.89/4.57
% 27.89/4.57 % Proof 1 at 3.27 (+ 0.61) seconds.
% 27.89/4.57 % Length of proof is 13.
% 27.89/4.57 % Level of proof is 4.
% 27.89/4.57 % Maximum clause weight is 28.000.
% 27.89/4.57 % Given clauses 1290.
% 27.89/4.57
% 27.89/4.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------