%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU196+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 : n016.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 7.16s 11.44s
% Output : CNFRefutation 7.16s
% 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_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_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(t88_relat_1,axiom,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t99_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
file('theBenchmark.p',t99_relat_1) ).
fof(t99_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)) ),
inference(assume_negation,[status(cth)],[t99_relat_1]) ).
cnf(c_360,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_427,plain,
( subset(relation_rng(A),relation_rng(B))
| ~ subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t25_relat_1]) ).
cnf(c_491,plain,
( subset(relation_dom_restriction(A,B),A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t88_relat_1]) ).
fof(nnf_185,plain,
? [A,B] :
( ~ subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B))
& relation(B) ),
inference(fof_nnf,[status(thm)],[t99_relat_1_neg]) ).
fof(sk_t99_relat_1_neg,plain,
( ~ subset(relation_rng(relation_dom_restriction(sK0,sK1)),relation_rng(sK0))
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_185]) ).
cnf(c_498,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t99_relat_1_neg]) ).
cnf(c_499,negated_conjecture,
~ subset(relation_rng(relation_dom_restriction(sK0,sK1)),relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t99_relat_1_neg]) ).
cnf(c_989,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_360,c_498]) ).
cnf(c_1579,plain,
subset(relation_dom_restriction(sK0,A),sK0),
inference(resolve,[status(thm)],[c_491,c_498]) ).
cnf(c_9431,plain,
( subset(relation_rng(relation_dom_restriction(sK0,A)),relation_rng(sK0))
| ~ relation(sK0)
| ~ relation(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_427,c_1579]) ).
cnf(c_9432,plain,
( subset(relation_rng(relation_dom_restriction(sK0,A)),relation_rng(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_989,c_9431]) ).
cnf(c_9429,negated_conjecture,
subset(relation_rng(relation_dom_restriction(sK0,A)),relation_rng(sK0)),
inference(resolve,[status(thm)],[c_498,c_9432]) ).
cnf(c_9430,plain,
$false,
inference(resolve,[status(thm)],[c_9429,c_499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU196+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n016.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 26 08:52:41 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.39 % Process 473189 was started by sandbox2 on n016,
% 0.10/10.39 % Sat Sep 26 08:52:41 2026
% 0.10/10.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.43
% 0.15/10.43 % From the command line: assign(max_seconds, 300).
% 0.15/10.43
% 0.15/10.43 % SInE: 143 to sos, 43 to usable, of 186 axioms (tolerance 2.00, depth 0 fixpoint).
% 7.16/11.44
% 7.16/11.44 % given #500 (F,wt=22): 6445 f54(c1) != set_difference(A,singleton(empty_set)). [resolve(6012,a,1035,b)].
% 7.16/11.44
% 7.16/11.44 % SZS status Theorem for theBenchmark
% 7.16/11.44
% 7.16/11.44 % Proof 1 at 0.79 (+ 0.16) seconds.
% 7.16/11.44 % Length of proof is 13.
% 7.16/11.44 % Level of proof is 4.
% 7.16/11.44 % Maximum clause weight is 22.000.
% 7.16/11.44 % Given clauses 651.
% 7.16/11.44
% 7.16/11.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------