%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU177+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 : 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 08:45:19 AM UTC 2026
% Result : Theorem 2.98s 0.91s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 50 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 20 ~; 15 |; 6 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 2 sgn 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(t20_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t20_relat_1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[t20_relat_1]) ).
cnf(c_216,plain,
( ~ in(ordered_pair(C,D),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_relat_1]) ).
cnf(c_233,plain,
( ~ in(ordered_pair(D,C),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_relat_1]) ).
fof(nnf_140,plain,
? [A,B,C] :
( ( ~ in(B,relation_rng(C))
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1_neg]) ).
fof(sk_t20_relat_1_neg,plain,
( ( ~ in(sK2,relation_rng(sK0))
| ~ in(sK1,relation_dom(sK0)) )
& in(ordered_pair(sK1,sK2),sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_140]) ).
cnf(c_359,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_relat_1_neg]) ).
cnf(c_360,negated_conjecture,
in(ordered_pair(sK1,sK2),sK0),
inference(split_conjunct,[status(thm)],[sk_t20_relat_1_neg]) ).
cnf(c_361,negated_conjecture,
( ~ in(sK2,relation_rng(sK0))
| ~ in(sK1,relation_dom(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t20_relat_1_neg]) ).
cnf(c_3684,negated_conjecture,
( in(sK1,A)
| relation_dom(sK0) != A
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_216,c_360]) ).
cnf(c_2374,negated_conjecture,
( in(sK1,A)
| relation_dom(sK0) != A ),
inference(resolve,[status(thm)],[c_359,c_3684]) ).
cnf(c_2405,plain,
in(sK1,relation_dom(sK0)),
inference(xxres,[status(thm)],[c_2374]) ).
cnf(c_2406,negated_conjecture,
~ in(sK2,relation_rng(sK0)),
inference(resolve,[status(thm)],[c_2405,c_361]) ).
cnf(c_3685,negated_conjecture,
( in(sK2,A)
| relation_rng(sK0) != A
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_233,c_360]) ).
cnf(c_3670,negated_conjecture,
( in(sK2,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_359,c_3685]) ).
cnf(c_3686,plain,
in(sK2,relation_rng(sK0)),
inference(xxres,[status(thm)],[c_3670]) ).
cnf(c_3683,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2406,c_3686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n017.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:40:34 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 299485 was started by sandbox2 on n017,
% 0.19/0.45 % Sat Sep 26 08:40:34 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.50
% 0.19/0.50 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % SInE: 121 to sos, 20 to usable, of 141 axioms (tolerance 2.00, depth 0 fixpoint).
% 2.98/0.91
% 2.98/0.91 % SZS status Theorem for theBenchmark
% 2.98/0.91
% 2.98/0.91 % Proof 1 at 0.30 (+ 0.07) seconds.
% 2.98/0.91 % Length of proof is 13.
% 2.98/0.91 % Level of proof is 5.
% 2.98/0.91 % Maximum clause weight is 24.000.
% 2.98/0.91 % Given clauses 308.
% 2.98/0.91
% 2.98/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------