%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU248+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 : n014.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 08:45:35 AM UTC 2026
% Result : Theorem 27.48s 9.55s
% Output : CNFRefutation 27.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 30 ( 12 ~; 8 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 6 sgn 10 !; 2 ?)
% 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(t117_relat_1,axiom,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t25_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('theBenchmark.p',t25_relat_1) ).
fof(l29_wellord1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
file('theBenchmark.p',l29_wellord1) ).
fof(l29_wellord1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ),
inference(assume_negation,[status(cth)],[l29_wellord1]) ).
cnf(c_670,plain,
( relation(relation_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
cnf(c_772,plain,
( subset(relation_rng_restriction(B,A),A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t117_relat_1]) ).
cnf(c_814,plain,
( subset(relation_dom(A),relation_dom(B))
| ~ subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t25_relat_1]) ).
fof(nnf_304,plain,
? [A,B] :
( ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[l29_wellord1_neg]) ).
fof(sk_l29_wellord1_neg,plain,
( ~ subset(relation_dom(relation_rng_restriction(sK1,sK0)),relation_dom(sK0))
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_304]) ).
cnf(c_931,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_l29_wellord1_neg]) ).
cnf(c_932,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(sK1,sK0)),relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_l29_wellord1_neg]) ).
cnf(c_1527,plain,
relation(relation_rng_restriction(A,sK0)),
inference(resolve,[status(thm)],[c_670,c_931]) ).
cnf(c_2674,plain,
subset(relation_rng_restriction(A,sK0),sK0),
inference(resolve,[status(thm)],[c_772,c_931]) ).
cnf(c_16092,plain,
( subset(relation_dom(relation_rng_restriction(A,sK0)),relation_dom(sK0))
| ~ relation(sK0)
| ~ relation(relation_rng_restriction(A,sK0)) ),
inference(resolve,[status(thm)],[c_814,c_2674]) ).
cnf(c_16093,plain,
( subset(relation_dom(relation_rng_restriction(A,sK0)),relation_dom(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_1527,c_16092]) ).
cnf(c_16090,negated_conjecture,
subset(relation_dom(relation_rng_restriction(A,sK0)),relation_dom(sK0)),
inference(resolve,[status(thm)],[c_931,c_16093]) ).
cnf(c_16091,plain,
$false,
inference(resolve,[status(thm)],[c_16090,c_932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU248+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n014.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sat Sep 26 08:58:22 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 2710099 was started by sandbox on n014,
% 0.17/5.45 % Sat Sep 26 08:58:22 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/5.56
% 0.21/5.56 % From the command line: assign(max_seconds, 300).
% 0.21/5.56
% 0.21/5.56 % SInE: 229 to sos, 76 to usable, of 305 axioms (tolerance 2.00, depth 0 fixpoint).
% 27.48/9.55
% 27.48/9.55 % given #500 (F,wt=22): 4342 set_difference(A,singleton(B)) != f106(B). [resolve(4336,a,3059,b),flip(a)].
% 27.48/9.55
% 27.48/9.55 % given #1000 (W,wt=8): 12610 element(c3,empty_set). [resolve(732,a,5062,b)].
% 27.48/9.55
% 27.48/9.55 % SZS status Theorem for theBenchmark
% 27.48/9.55
% 27.48/9.55 % Proof 1 at 3.01 (+ 0.63) seconds.
% 27.48/9.55 % Length of proof is 13.
% 27.48/9.55 % Level of proof is 4.
% 27.48/9.55 % Maximum clause weight is 22.000.
% 27.48/9.55 % Given clauses 1264.
% 27.48/9.55
% 27.48/9.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------