%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:45:26 AM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 107 ( 31 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 122 ( 46 ~; 46 |; 18 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 1 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
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(t8_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(t8_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[t8_funct_1]) ).
cnf(c_35,plain,
( in(ordered_pair(B,C),A)
| apply(A,B) != C
| ~ in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_funct_1]) ).
cnf(c_37,plain,
( ~ in(ordered_pair(B,C),A)
| apply(A,B) = C
| ~ in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_funct_1]) ).
fof(nnf_34,plain,
? [A,B,C] :
( ( apply(C,A) != B
| ~ in(A,relation_dom(C))
| ~ in(ordered_pair(A,B),C) )
& ( ( apply(C,A) = B
& in(A,relation_dom(C)) )
| in(ordered_pair(A,B),C) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t8_funct_1_neg]) ).
fof(sk_t8_funct_1_neg_sk,plain,
( ( apply(sK0,sK1) != sK2
| ~ in(sK1,relation_dom(sK0))
| ~ in(ordered_pair(sK1,sK2),sK0) )
& ( ( apply(sK0,sK1) = sK2
& in(sK1,relation_dom(sK0)) )
| in(ordered_pair(sK1,sK2),sK0) )
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_34]) ).
fof(sk_t8_funct_1_neg,plain,
( ( apply(sK0,sK1) != sK2
| ~ in(sK1,relation_dom(sK0))
| ~ in(ordered_pair(sK1,sK2),sK0) )
& ( apply(sK0,sK1) = sK2
| in(ordered_pair(sK1,sK2),sK0) )
& ( in(sK1,relation_dom(sK0))
| in(ordered_pair(sK1,sK2),sK0) )
& function(sK0)
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t8_funct_1_neg_sk]) ).
cnf(c_41,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_46,negated_conjecture,
( in(ordered_pair(A,B),sK0)
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_47,negated_conjecture,
( ~ in(ordered_pair(A,B),sK0)
| apply(sK0,A) = B
| ~ in(A,relation_dom(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_41,c_37]) ).
cnf(c_57,negated_conjecture,
( apply(sK0,sK1) != sK2
| ~ in(sK1,relation_dom(sK0))
| ~ in(ordered_pair(sK1,sK2),sK0) ),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_58,negated_conjecture,
( apply(sK0,sK1) = sK2
| in(ordered_pair(sK1,sK2),sK0) ),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_59,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(ordered_pair(sK1,sK2),sK0) ),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_60,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_93,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_100,negated_conjecture,
( ~ in(ordered_pair(A,B),sK0)
| apply(sK0,A) = B
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_60,c_47]) ).
cnf(c_101,negated_conjecture,
( in(ordered_pair(A,B),sK0)
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_60,c_46]) ).
cnf(c_404,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(sK1,A)
| relation_dom(sK0) != A
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_93,c_59]) ).
cnf(c_165,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(sK1,A)
| relation_dom(sK0) != A ),
inference(resolve,[status(thm)],[c_60,c_404]) ).
cnf(c_405,plain,
( in(sK1,relation_dom(sK0))
| relation_dom(sK0) != relation_dom(sK0) ),
inference(factor,[status(thm)],[c_165]) ).
cnf(c_168,plain,
in(sK1,relation_dom(sK0)),
inference(copy,[status(thm)],[c_405]) ).
cnf(c_170,negated_conjecture,
( apply(sK0,sK1) != sK2
| ~ in(ordered_pair(sK1,sK2),sK0) ),
inference(resolve,[status(thm)],[c_168,c_57]) ).
cnf(c_406,negated_conjecture,
( apply(sK0,sK1) = sK2
| apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_100,c_58]) ).
cnf(c_407,negated_conjecture,
( apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0)) ),
inference(copy,[status(thm)],[c_406]) ).
cnf(c_182,negated_conjecture,
apply(sK0,sK1) = sK2,
inference(resolve,[status(thm)],[c_168,c_407]) ).
cnf(c_184,negated_conjecture,
~ in(ordered_pair(sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_182,c_170]) ).
cnf(c_408,negated_conjecture,
( in(ordered_pair(sK1,A),sK0)
| apply(sK0,sK1) != A ),
inference(resolve,[status(thm)],[c_101,c_168]) ).
cnf(c_409,negated_conjecture,
apply(sK0,sK1) != sK2,
inference(resolve,[status(thm)],[c_408,c_184]) ).
cnf(c_403,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_182,c_409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n020.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 08:51:48 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1142386 was started by sandbox on n020,
% 0.12/0.37 % Sat Sep 26 08:51:48 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.44
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44
% 0.12/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.44 % Length of proof is 21.
% 0.12/0.44 % Level of proof is 6.
% 0.12/0.44 % Maximum clause weight is 26.000.
% 0.12/0.44 % Given clauses 125.
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------