%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU293+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 : n004.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 08:45:42 AM UTC 2026
% Result : Theorem 2.25s 0.78s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 15 unt; 0 def)
% Number of atoms : 186 ( 42 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 207 ( 80 ~; 81 |; 27 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 96 ( 8 sgn 29 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d13_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_1) ).
fof(d1_funct_2,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('theBenchmark.p',d1_funct_2) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('theBenchmark.p',redefinition_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(t46_funct_2,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
file('theBenchmark.p',t46_funct_2) ).
fof(t46_funct_2_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( B != empty_set
=> ! [E] :
( in(E,relation_inverse_image(D,C))
<=> ( in(apply(D,E),C)
& in(E,A) ) ) ) ),
inference(assume_negation,[status(cth)],[t46_funct_2]) ).
cnf(c_55,plain,
( in(D,relation_dom(A))
| ~ in(D,C)
| relation_inverse_image(A,B) != C
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d13_funct_1]) ).
cnf(c_56,plain,
( in(apply(A,D),B)
| ~ in(D,C)
| relation_inverse_image(A,B) != C
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d13_funct_1]) ).
cnf(c_57,plain,
( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A))
| in(D,C)
| relation_inverse_image(A,B) != C
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d13_funct_1]) ).
fof(nnf_52,plain,
? [A,B,C,D] :
( ? [E] :
( ( ~ in(apply(D,E),C)
| ~ in(E,A)
| ~ in(E,relation_inverse_image(D,C)) )
& ( ( in(apply(D,E),C)
& in(E,A) )
| in(E,relation_inverse_image(D,C)) ) )
& empty_set != B
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(fof_nnf,[status(thm)],[t46_funct_2_neg]) ).
fof(sk_t46_funct_2_neg_sk,plain,
( ( ~ in(apply(sK0,sK3),sK4)
| ~ in(sK3,sK1)
| ~ in(sK3,relation_inverse_image(sK0,sK4)) )
& ( ( in(apply(sK0,sK3),sK4)
& in(sK3,sK1) )
| in(sK3,relation_inverse_image(sK0,sK4)) )
& empty_set != sK2
& relation_of2_as_subset(sK0,sK1,sK2)
& quasi_total(sK0,sK1,sK2)
& function(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK4),skolemize(D,sK0),skolemize(E,sK3)],[nnf_52]) ).
fof(sk_t46_funct_2_neg,plain,
( ( ~ in(apply(sK0,sK3),sK4)
| ~ in(sK3,sK1)
| ~ in(sK3,relation_inverse_image(sK0,sK4)) )
& ( in(apply(sK0,sK3),sK4)
| in(sK3,relation_inverse_image(sK0,sK4)) )
& ( in(sK3,sK1)
| in(sK3,relation_inverse_image(sK0,sK4)) )
& empty_set != sK2
& relation_of2_as_subset(sK0,sK1,sK2)
& quasi_total(sK0,sK1,sK2)
& function(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t46_funct_2_neg_sk]) ).
cnf(c_68,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_70,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_76,plain,
( relation_dom_as_subset(B,C,A) = B
| ~ quasi_total(A,B,C)
| empty_set = C
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[d1_funct_2]) ).
cnf(c_77,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_78,plain,
( ~ relation_of2(A,B,C)
| relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_79,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_81,negated_conjecture,
relation_of2(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_79,c_77]) ).
cnf(c_87,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2(A,B,C) ),
inference(resolve,[status(thm)],[c_78,c_70]) ).
cnf(c_89,plain,
( relation_dom_as_subset(B,C,A) = relation_dom(A)
| ~ relation_of2(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_k4_relset_1]) ).
cnf(c_133,negated_conjecture,
relation_dom_as_subset(sK1,sK2,sK0) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_89,c_81]) ).
cnf(c_135,negated_conjecture,
element(sK0,powerset(cartesian_product2(sK1,sK2))),
inference(resolve,[status(thm)],[c_87,c_81]) ).
cnf(c_142,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_179,negated_conjecture,
quasi_total(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_180,negated_conjecture,
empty_set != sK2,
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_181,negated_conjecture,
sK2 != empty_set,
inference(copy,[status(thm)],[c_180]) ).
cnf(c_182,negated_conjecture,
( in(sK3,sK1)
| in(sK3,relation_inverse_image(sK0,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_183,negated_conjecture,
( in(apply(sK0,sK3),sK4)
| in(sK3,relation_inverse_image(sK0,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_184,negated_conjecture,
( ~ in(apply(sK0,sK3),sK4)
| ~ in(sK3,sK1)
| ~ in(sK3,relation_inverse_image(sK0,sK4)) ),
inference(split_conjunct,[status(thm)],[sk_t46_funct_2_neg]) ).
cnf(c_278,negated_conjecture,
( ~ in(apply(sK0,C),A)
| ~ in(C,relation_dom(sK0))
| in(C,B)
| relation_inverse_image(sK0,A) != B
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_68,c_57]) ).
cnf(c_279,negated_conjecture,
( in(apply(sK0,C),A)
| ~ in(C,B)
| relation_inverse_image(sK0,A) != B
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_68,c_56]) ).
cnf(c_280,negated_conjecture,
( in(C,relation_dom(sK0))
| ~ in(C,B)
| relation_inverse_image(sK0,A) != B
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_68,c_55]) ).
cnf(c_298,negated_conjecture,
( relation_dom_as_subset(sK1,sK2,sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(resolve,[status(thm)],[c_79,c_76]) ).
cnf(c_2539,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| empty_set = sK2 ),
inference(paramod,[status(thm)],[c_133,c_298]) ).
cnf(c_2540,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2)
| sK2 = empty_set ),
inference(copy,[status(thm)],[c_2539]) ).
cnf(c_2541,negated_conjecture,
( relation_dom(sK0) = sK1
| ~ quasi_total(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_181,c_2540]) ).
cnf(c_299,negated_conjecture,
relation_dom(sK0) = sK1,
inference(resolve,[status(thm)],[c_179,c_2541]) ).
cnf(c_335,negated_conjecture,
( in(C,sK1)
| ~ in(C,B)
| relation_inverse_image(sK0,A) != B
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_299,c_280]) ).
cnf(c_336,negated_conjecture,
( ~ in(apply(sK0,C),A)
| ~ in(C,sK1)
| in(C,B)
| relation_inverse_image(sK0,A) != B
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_299,c_278]) ).
cnf(c_344,plain,
relation(sK0),
inference(resolve,[status(thm)],[c_142,c_135]) ).
cnf(c_349,negated_conjecture,
( ~ in(apply(sK0,C),A)
| ~ in(C,sK1)
| in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(resolve,[status(thm)],[c_344,c_336]) ).
cnf(c_350,negated_conjecture,
( in(C,sK1)
| ~ in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(resolve,[status(thm)],[c_344,c_335]) ).
cnf(c_353,negated_conjecture,
( in(apply(sK0,C),A)
| ~ in(C,B)
| relation_inverse_image(sK0,A) != B ),
inference(resolve,[status(thm)],[c_344,c_279]) ).
cnf(c_1299,plain,
( in(sK3,relation_inverse_image(sK0,sK4))
| ~ in(sK3,sK1)
| in(sK3,A)
| relation_inverse_image(sK0,sK4) != A ),
inference(resolve,[status(thm)],[c_349,c_183]) ).
cnf(c_2542,plain,
( ~ in(sK3,sK1)
| in(sK3,relation_inverse_image(sK0,sK4))
| relation_inverse_image(sK0,sK4) != relation_inverse_image(sK0,sK4) ),
inference(factor,[status(thm)],[c_1299]) ).
cnf(c_1306,plain,
( ~ in(sK3,sK1)
| in(sK3,relation_inverse_image(sK0,sK4)) ),
inference(copy,[status(thm)],[c_2542]) ).
cnf(c_2543,negated_conjecture,
( in(sK3,sK1)
| in(sK3,sK1)
| relation_inverse_image(sK0,A) != relation_inverse_image(sK0,sK4) ),
inference(resolve,[status(thm)],[c_350,c_182]) ).
cnf(c_2544,negated_conjecture,
( in(sK3,sK1)
| in(sK3,sK1)
| relation_inverse_image(sK0,sK4) != relation_inverse_image(sK0,A) ),
inference(copy,[status(thm)],[c_2543]) ).
cnf(c_2545,negated_conjecture,
( in(sK3,sK1)
| in(sK3,sK1) ),
inference(copy,[status(thm)],[c_2544]) ).
cnf(c_1342,negated_conjecture,
in(sK3,sK1),
inference(copy,[status(thm)],[c_2545]) ).
cnf(c_1348,plain,
in(sK3,relation_inverse_image(sK0,sK4)),
inference(resolve,[status(thm)],[c_1342,c_1306]) ).
cnf(c_2546,negated_conjecture,
( ~ in(apply(sK0,sK3),sK4)
| ~ in(sK3,sK1) ),
inference(resolve,[status(thm)],[c_1348,c_184]) ).
cnf(c_1349,negated_conjecture,
~ in(apply(sK0,sK3),sK4),
inference(resolve,[status(thm)],[c_1342,c_2546]) ).
cnf(c_1446,plain,
( in(apply(sK0,A),B)
| ~ in(A,relation_inverse_image(sK0,B)) ),
inference(xxres,[status(thm)],[c_353]) ).
cnf(c_2547,plain,
in(apply(sK0,sK3),sK4),
inference(resolve,[status(thm)],[c_1446,c_1348]) ).
cnf(c_2538,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1349,c_2547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU293+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 09:06:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 1333362 was started by sandbox2 on n004,
% 0.12/0.37 % Sat Sep 26 09:06:36 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 2.25/0.78
% 2.25/0.78 % SZS status Theorem for theBenchmark
% 2.25/0.78
% 2.25/0.78 % Proof 1 at 0.30 (+ 0.08) seconds.
% 2.25/0.78 % Length of proof is 46.
% 2.25/0.78 % Level of proof is 11.
% 2.25/0.78 % Maximum clause weight is 29.000.
% 2.25/0.78 % Given clauses 325.
% 2.25/0.78
% 2.25/0.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------