%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU212+1 : 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 : n012.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 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 131 ( 40 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 151 ( 61 ~; 60 |; 18 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 2 sgn 14 !; 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(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
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_45,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_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_37]) ).
cnf(c_56,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_57,negated_conjecture,
( apply(sK0,sK1) = sK2
| in(ordered_pair(sK1,sK2),sK0) ),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_58,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_59,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t8_funct_1_neg]) ).
cnf(c_79,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_84,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_85,plain,
( ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_79,c_84]) ).
cnf(c_158,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK0)
| apply(sK0,A) = B
| ~ in(A,relation_dom(sK0))
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_79,c_46]) ).
cnf(c_94,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK0)
| apply(sK0,A) = B
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_59,c_158]) ).
cnf(c_159,negated_conjecture,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK0)
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0))
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_79,c_45]) ).
cnf(c_95,negated_conjecture,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK0)
| apply(sK0,A) != B
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_59,c_159]) ).
cnf(c_100,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0) ),
inference(paramod,[status(thm)],[c_79,c_58]) ).
cnf(c_101,negated_conjecture,
( apply(sK0,sK1) = sK2
| in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0) ),
inference(paramod,[status(thm)],[c_79,c_57]) ).
cnf(c_102,negated_conjecture,
( apply(sK0,sK1) != sK2
| ~ in(sK1,relation_dom(sK0))
| ~ in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0) ),
inference(paramod,[status(thm)],[c_79,c_56]) ).
cnf(c_160,negated_conjecture,
( in(sK1,A)
| relation_dom(sK0) != A
| ~ relation(sK0)
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_100,c_85]) ).
cnf(c_133,negated_conjecture,
( in(sK1,A)
| relation_dom(sK0) != A
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_59,c_160]) ).
cnf(c_161,plain,
( relation_dom(sK0) != relation_dom(sK0)
| in(sK1,relation_dom(sK0)) ),
inference(factor,[status(thm)],[c_133]) ).
cnf(c_135,plain,
in(sK1,relation_dom(sK0)),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_136,negated_conjecture,
( apply(sK0,sK1) != sK2
| ~ in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0) ),
inference(resolve,[status(thm)],[c_135,c_102]) ).
cnf(c_162,negated_conjecture,
( apply(sK0,sK1) = sK2
| ~ in(sK1,relation_dom(sK0))
| apply(sK0,sK1) = sK2 ),
inference(resolve,[status(thm)],[c_101,c_94]) ).
cnf(c_163,negated_conjecture,
( ~ in(sK1,relation_dom(sK0))
| apply(sK0,sK1) = sK2 ),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_137,negated_conjecture,
apply(sK0,sK1) = sK2,
inference(resolve,[status(thm)],[c_135,c_163]) ).
cnf(c_164,negated_conjecture,
( sK2 != sK2
| ~ in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0) ),
inference(paramod,[status(thm)],[c_137,c_136]) ).
cnf(c_138,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK1,sK2),singleton(sK1)),sK0),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,negated_conjecture,
( in(unordered_pair(unordered_pair(sK1,A),singleton(sK1)),sK0)
| apply(sK0,sK1) != A ),
inference(resolve,[status(thm)],[c_95,c_135]) ).
cnf(c_166,negated_conjecture,
apply(sK0,sK1) != sK2,
inference(resolve,[status(thm)],[c_165,c_138]) ).
cnf(c_167,negated_conjecture,
sK2 != sK2,
inference(paramod,[status(thm)],[c_137,c_166]) ).
cnf(c_157,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU212+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n012.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 08:50:13 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 190779 was started by sandbox on n012,
% 0.09/5.36 % Sat Sep 26 08:50:13 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.09/5.39 % Length of proof is 27.
% 0.09/5.39 % Level of proof is 7.
% 0.09/5.39 % Maximum clause weight is 17.000.
% 0.09/5.39 % Given clauses 50.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------