%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU200+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:45:23 AM UTC 2026
% Result : Theorem 12.86s 2.30s
% Output : CNFRefutation 12.86s
% 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(t118_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('theBenchmark.p',t118_relat_1) ).
fof(t118_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
inference(assume_negation,[status(cth)],[t118_relat_1]) ).
cnf(c_374,plain,
( relation(relation_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
cnf(c_433,plain,
( subset(relation_rng_restriction(B,A),A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t117_relat_1]) ).
cnf(c_445,plain,
( subset(relation_rng(A),relation_rng(B))
| ~ subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t25_relat_1]) ).
fof(nnf_191,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[t118_relat_1_neg]) ).
fof(sk_t118_relat_1_neg,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK1,sK0)),relation_rng(sK0))
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_191]) ).
cnf(c_517,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t118_relat_1_neg]) ).
cnf(c_518,negated_conjecture,
~ subset(relation_rng(relation_rng_restriction(sK1,sK0)),relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t118_relat_1_neg]) ).
cnf(c_1012,plain,
relation(relation_rng_restriction(A,sK0)),
inference(resolve,[status(thm)],[c_374,c_517]) ).
cnf(c_1616,plain,
subset(relation_rng_restriction(A,sK0),sK0),
inference(resolve,[status(thm)],[c_433,c_517]) ).
cnf(c_9860,plain,
( subset(relation_rng(relation_rng_restriction(A,sK0)),relation_rng(sK0))
| ~ relation(sK0)
| ~ relation(relation_rng_restriction(A,sK0)) ),
inference(resolve,[status(thm)],[c_445,c_1616]) ).
cnf(c_9861,plain,
( subset(relation_rng(relation_rng_restriction(A,sK0)),relation_rng(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_1012,c_9860]) ).
cnf(c_9858,negated_conjecture,
subset(relation_rng(relation_rng_restriction(A,sK0)),relation_rng(sK0)),
inference(resolve,[status(thm)],[c_517,c_9861]) ).
cnf(c_9859,plain,
$false,
inference(resolve,[status(thm)],[c_9858,c_518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:46:39 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3338799 was started by sandbox2 on n007,
% 0.12/0.38 % Sat Sep 26 08:46:39 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.42
% 0.12/0.42 % From the command line: assign(max_seconds, 300).
% 0.12/0.42
% 0.12/0.42 % SInE: 149 to sos, 43 to usable, of 192 axioms (tolerance 2.00, depth 0 fixpoint).
% 12.86/2.30
% 12.86/2.30 % given #500 (F,wt=19): 6492 set_difference(A,B) != singleton(c1) | -in(empty_set,B). [para(6474(a,1),5972(b,1))].
% 12.86/2.30
% 12.86/2.30 % SZS status Theorem for theBenchmark
% 12.86/2.30
% 12.86/2.30 % Proof 1 at 1.50 (+ 0.31) seconds.
% 12.86/2.30 % Length of proof is 13.
% 12.86/2.30 % Level of proof is 4.
% 12.86/2.30 % Maximum clause weight is 22.000.
% 12.86/2.30 % Given clauses 692.
% 12.86/2.30
% 12.86/2.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------