%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU212+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 : n002.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 08:45:25 AM UTC 2026
% Result : Theorem 9.66s 3.48s
% Output : CNFRefutation 9.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 106 ( 23 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 121 ( 46 ~; 45 |; 19 &)
% ( 4 <=>; 7 =>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 12 !; 3 ?)
% 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(t20_relat_1,axiom,
! [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(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_378,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_379,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_507,plain,
( in(B,relation_dom(A))
| ~ in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t20_relat_1]) ).
fof(nnf_213,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_213]) ).
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_585,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_586,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_587,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_588,negated_conjecture,
( apply(sK0,sK1) = sK2
| in(ordered_pair(sK1,sK2),sK0) ),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_589,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_6236,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_507,c_587]) ).
cnf(c_6237,negated_conjecture,
( in(sK1,relation_dom(sK0))
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_6236]) ).
cnf(c_3582,negated_conjecture,
in(sK1,relation_dom(sK0)),
inference(resolve,[status(thm)],[c_585,c_6237]) ).
cnf(c_3585,negated_conjecture,
( apply(sK0,sK1) != sK2
| ~ in(ordered_pair(sK1,sK2),sK0) ),
inference(resolve,[status(thm)],[c_3582,c_589]) ).
cnf(c_6238,negated_conjecture,
( apply(sK0,sK1) = sK2
| apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_379,c_588]) ).
cnf(c_6239,negated_conjecture,
( apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_6238]) ).
cnf(c_6240,negated_conjecture,
( apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_585,c_6239]) ).
cnf(c_6241,negated_conjecture,
( apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_586,c_6240]) ).
cnf(c_6225,negated_conjecture,
apply(sK0,sK1) = sK2,
inference(resolve,[status(thm)],[c_3582,c_6241]) ).
cnf(c_6242,negated_conjecture,
( sK2 != sK2
| ~ in(ordered_pair(sK1,sK2),sK0) ),
inference(paramod,[status(thm)],[c_6225,c_3585]) ).
cnf(c_6234,negated_conjecture,
~ in(ordered_pair(sK1,sK2),sK0),
inference(copy,[status(thm)],[c_6242]) ).
cnf(c_6243,plain,
( in(ordered_pair(sK1,sK2),sK0)
| ~ in(sK1,relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_6225,c_378]) ).
cnf(c_6244,negated_conjecture,
( in(ordered_pair(sK1,sK2),sK0)
| ~ in(sK1,relation_dom(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_585,c_6243]) ).
cnf(c_6245,negated_conjecture,
( in(ordered_pair(sK1,sK2),sK0)
| ~ in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_586,c_6244]) ).
cnf(c_6246,negated_conjecture,
in(ordered_pair(sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_3582,c_6245]) ).
cnf(c_6235,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6234,c_6246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 08:53:36 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1307605 was started by sandbox on n002,
% 0.11/0.36 % Sat Sep 26 08:53:36 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.42
% 0.11/0.42 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SInE: 161 to sos, 53 to usable, of 214 axioms (tolerance 2.00, depth 0 fixpoint).
% 9.66/3.48
% 9.66/3.48 % given #500 (F,wt=19): 4086 c9 != empty_set | -in(ordered_pair(A,B),relation_inverse(c9)). [back_rewrite(2673),rewrite([3876(2)]),flip(a)].
% 9.66/3.48
% 9.66/3.48 % SZS status Theorem for theBenchmark
% 9.66/3.48
% 9.66/3.48 % Proof 1 at 1.11 (+ 0.19) seconds.
% 9.66/3.48 % Length of proof is 16.
% 9.66/3.48 % Level of proof is 5.
% 9.66/3.48 % Maximum clause weight is 28.000.
% 9.66/3.48 % Given clauses 666.
% 9.66/3.48
% 9.66/3.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------