%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU251+1 : 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 : 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 08:45:35 AM UTC 2026
% Result : Theorem 100.21s 13.78s
% Output : CNFRefutation 100.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 109 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 45 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 5 sgn 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('theBenchmark.p',d1_wellord1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t21_wellord1,conjecture,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('theBenchmark.p',t21_wellord1) ).
fof(t21_wellord1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(assume_negation,[status(cth)],[t21_wellord1]) ).
cnf(c_46,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_48,plain,
( D != B
| ~ in(D,C)
| fiber(A,B) != C
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord1]) ).
cnf(c_49,plain,
( in(ordered_pair(D,B),A)
| ~ in(D,C)
| fiber(A,B) != C
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord1]) ).
cnf(c_50,plain,
( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C)
| fiber(A,B) != C
| ~ relation(A) ),
inference(clausify,[status(thm)],[d1_wellord1]) ).
fof(nnf_7,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_7]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_55,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_56,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_57,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_60,plain,
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_wellord1]) ).
cnf(c_73,plain,
( in(B,A)
| ~ in(B,relation_restriction(A,C))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t16_wellord1]) ).
fof(nnf_39,plain,
? [A,B,C] :
( ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B))
& relation(C) ),
inference(fof_nnf,[status(thm)],[t21_wellord1_neg]) ).
fof(sk_t21_wellord1_neg,plain,
( ~ subset(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3))
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK1)],[nnf_39]) ).
cnf(c_86,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t21_wellord1_neg]) ).
cnf(c_87,negated_conjecture,
~ subset(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),
inference(split_conjunct,[status(thm)],[sk_t21_wellord1_neg]) ).
cnf(c_92,plain,
( ~ in(unordered_pair(unordered_pair(D,B),singleton(D)),A)
| D = B
| in(D,C)
| fiber(A,B) != C
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_57,c_50]) ).
cnf(c_93,plain,
( in(unordered_pair(unordered_pair(D,B),singleton(D)),A)
| ~ in(D,C)
| fiber(A,B) != C
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_57,c_49]) ).
cnf(c_135,plain,
relation(relation_restriction(sK1,A)),
inference(resolve,[status(thm)],[c_86,c_60]) ).
cnf(c_142,plain,
in(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),fiber(relation_restriction(sK1,sK2),sK3)),
inference(resolve,[status(thm)],[c_87,c_55]) ).
cnf(c_144,negated_conjecture,
~ in(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),fiber(sK1,sK3)),
inference(resolve,[status(thm)],[c_56,c_87]) ).
cnf(c_8417,plain,
( in(unordered_pair(unordered_pair(D,B),singleton(D)),relation_restriction(sK1,A))
| ~ in(D,C)
| fiber(relation_restriction(sK1,A),B) != C ),
inference(resolve,[status(thm)],[c_93,c_135]) ).
cnf(c_8418,plain,
( in(unordered_pair(unordered_pair(A,C),singleton(A)),relation_restriction(sK1,B))
| ~ in(A,fiber(relation_restriction(sK1,B),C)) ),
inference(xxres,[status(thm)],[c_8417]) ).
cnf(c_8419,plain,
in(unordered_pair(unordered_pair(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),sK3),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),relation_restriction(sK1,sK2)),
inference(resolve,[status(thm)],[c_8418,c_142]) ).
cnf(c_361,plain,
in(unordered_pair(unordered_pair(sK3,sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3))),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),relation_restriction(sK1,sK2)),
inference(paramod,[status(thm)],[c_46,c_8419]) ).
cnf(c_8420,plain,
( D != B
| ~ in(D,C)
| fiber(relation_restriction(sK1,A),B) != C ),
inference(resolve,[status(thm)],[c_48,c_135]) ).
cnf(c_8421,plain,
( A != C
| ~ in(A,fiber(relation_restriction(sK1,B),C)) ),
inference(xxres,[status(thm)],[c_8420]) ).
cnf(c_381,plain,
sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)) != sK3,
inference(resolve,[status(thm)],[c_8421,c_142]) ).
cnf(c_8422,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(C,A),singleton(C)),sK1)
| C = A
| in(C,B)
| fiber(sK1,A) != B ),
inference(resolve,[status(thm)],[c_92,c_86]) ).
cnf(c_8423,plain,
( ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),sK1)
| A = B
| in(A,fiber(sK1,B)) ),
inference(xxres,[status(thm)],[c_8422]) ).
cnf(c_8424,plain,
( ~ in(unordered_pair(unordered_pair(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),sK3),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),sK1)
| sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)) = sK3 ),
inference(resolve,[status(thm)],[c_8423,c_144]) ).
cnf(c_8425,plain,
~ in(unordered_pair(unordered_pair(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)),sK3),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),sK1),
inference(resolve,[status(thm)],[c_8424,c_381]) ).
cnf(c_1663,plain,
~ in(unordered_pair(unordered_pair(sK3,sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3))),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),sK1),
inference(paramod,[status(thm)],[c_46,c_8425]) ).
cnf(c_8426,plain,
( in(unordered_pair(unordered_pair(sK3,sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3))),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),sK1)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_361,c_73]) ).
cnf(c_8427,negated_conjecture,
in(unordered_pair(unordered_pair(sK3,sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3))),singleton(sK0(fiber(relation_restriction(sK1,sK2),sK3),fiber(sK1,sK3)))),sK1),
inference(resolve,[status(thm)],[c_86,c_8426]) ).
cnf(c_8416,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1663,c_8427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU251+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n002.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 09:01:20 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 1324017 was started by sandbox2 on n002,
% 0.10/0.35 % Sat Sep 26 09:01:20 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 100.21/13.78
% 100.21/13.78 % given #500 (W,wt=17): 3684 empty(fiber(c5,A)) | f2(fiber(c5,A),empty_set) != A. [resolve(3160,b,65,a(flip)),rewrite([65(5),65(8)])].
% 100.21/13.78
% 100.21/13.78 % SZS status Theorem for theBenchmark
% 100.21/13.78
% 100.21/13.78 % Proof 1 at 4.64 (+ 0.69) seconds.
% 100.21/13.78 % Length of proof is 27.
% 100.21/13.78 % Level of proof is 5.
% 100.21/13.78 % Maximum clause weight is 40.000.
% 100.21/13.78 % Given clauses 621.
% 100.21/13.78
% 100.21/13.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------