%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:44:57 AM UTC 2026
% Result : Theorem 35.32s 4.99s
% Output : CNFRefutation 35.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 137 ( 57 unt; 0 def)
% Number of atoms : 340 ( 132 equ)
% Maximal formula atoms : 23 ( 2 avg)
% Number of connectives : 325 ( 122 ~; 146 |; 39 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 192 ( 20 sgn 75 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t117_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('theBenchmark.p',t117_funct_1) ).
fof(t149_relat_1,axiom,
! [A] :
( relation(A)
=> relation_image(A,empty_set) = empty_set ),
file('theBenchmark.p',t149_relat_1) ).
fof(t17_zfmisc_1,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ),
file('theBenchmark.p',t17_zfmisc_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t122_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B,C] : relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
file('theBenchmark.p',t122_funct_1) ).
fof(t122_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B,C] : relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
inference(assume_negation,[status(cth)],[t122_funct_1]) ).
fof(nnf_8,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& apply(A,C) = apply(A,B)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(sk_d8_funct_1_sk,plain,
! [A] :
( ( ( ( sK1(A) != sK0(A)
& apply(A,sK1(A)) = apply(A,sK0(A))
& in(sK1(A),relation_dom(A))
& in(sK0(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0(A)),skolemize(C,sK1(A))],[nnf_8]) ).
fof(sk_d8_funct_1,plain,
( ! [VAR_0] :
( sK1(VAR_0) != sK0(VAR_0)
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( apply(VAR_0,sK1(VAR_0)) = apply(VAR_0,sK0(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK1(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK0(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| apply(VAR_0,VAR_2) != apply(VAR_0,VAR_1)
| ~ in(VAR_2,relation_dom(VAR_0))
| ~ in(VAR_1,relation_dom(VAR_0))
| ~ one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_funct_1_sk]) ).
cnf(c_49,plain,
( in(sK0(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_50,plain,
( in(sK1(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_51,plain,
( apply(A,sK1(A)) = apply(A,sK0(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_52,plain,
( sK1(A) != sK0(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_56,plain,
( relation_image(A,singleton(B)) = singleton(apply(A,B))
| ~ in(B,relation_dom(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t117_funct_1]) ).
fof(nnf_45,plain,
? [A] :
( ~ one_to_one(A)
& ! [B,C] : relation_image(A,set_intersection2(B,C)) = set_intersection2(relation_image(A,B),relation_image(A,C))
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t122_funct_1_neg]) ).
fof(sk_t122_funct_1_neg,plain,
( ~ one_to_one(sK2)
& ! [B,C] : relation_image(sK2,set_intersection2(B,C)) = set_intersection2(relation_image(sK2,B),relation_image(sK2,C))
& function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_45]) ).
cnf(c_57,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t122_funct_1_neg]) ).
cnf(c_58,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_60,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_61,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_58,c_60]) ).
cnf(c_62,negated_conjecture,
( in(sK0(sK2),relation_dom(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_49]) ).
cnf(c_63,negated_conjecture,
( in(sK1(sK2),relation_dom(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_50]) ).
cnf(c_64,negated_conjecture,
( apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2))
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_51]) ).
cnf(c_65,negated_conjecture,
( sK1(sK2) != sK0(sK2)
| one_to_one(sK2)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_52]) ).
cnf(c_66,negated_conjecture,
( relation_image(sK2,singleton(A)) = singleton(apply(sK2,A))
| ~ in(A,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_57,c_56]) ).
cnf(c_67,negated_conjecture,
( singleton(apply(sK2,A)) = relation_image(sK2,singleton(A))
| ~ in(A,relation_dom(sK2))
| ~ relation(sK2) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_90,negated_conjecture,
~ one_to_one(sK2),
inference(split_conjunct,[status(thm)],[sk_t122_funct_1_neg]) ).
cnf(c_91,negated_conjecture,
relation_image(sK2,set_intersection2(A,B)) = set_intersection2(relation_image(sK2,A),relation_image(sK2,B)),
inference(split_conjunct,[status(thm)],[sk_t122_funct_1_neg]) ).
cnf(c_92,negated_conjecture,
set_intersection2(relation_image(sK2,A),relation_image(sK2,B)) = relation_image(sK2,set_intersection2(A,B)),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_93,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t122_funct_1_neg]) ).
cnf(c_96,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_97,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_99,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_101,plain,
( element(A,B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t1_subset]) ).
cnf(c_102,plain,
( disjoint(singleton(B),singleton(A))
| A = B ),
inference(clausify,[status(thm)],[t17_zfmisc_1]) ).
cnf(c_103,plain,
( relation_image(A,empty_set) = empty_set
| ~ relation(A) ),
inference(clausify,[status(thm)],[t149_relat_1]) ).
fof(nnf_25,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(sk_rc2_subset_1,plain,
! [A] :
( empty(sK3(A))
& element(sK3(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(B,sK3(A))],[nnf_25]) ).
cnf(c_112,plain,
empty(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
cnf(c_125,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_130,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc4_relat_1]) ).
cnf(c_132,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
fof(nnf_9,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(sk_existence_m1_subset_1,plain,
! [A] : element(sK4(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(B,sK4(A))],[nnf_9]) ).
cnf(c_134,plain,
element(sK4(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_m1_subset_1]) ).
cnf(c_136,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
fof(nnf_6,plain,
! [A,B] :
( ( ? [C] :
( ( C != A
| ~ in(C,B) )
& ( C = A
| in(C,B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(sk_d1_tarski_sk,plain,
! [A,B] :
( ( ( ( sK5(A,B) != A
| ~ in(sK5(A,B),B) )
& ( sK5(A,B) = A
| in(sK5(A,B),B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(C,sK5(A,B))],[nnf_6]) ).
fof(sk_d1_tarski,plain,
( ! [VAR_0,VAR_1] :
( sK5(VAR_0,VAR_1) != VAR_0
| ~ in(sK5(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( sK5(VAR_0,VAR_1) = VAR_0
| in(sK5(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 != VAR_0
| in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_0
| ~ in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_tarski_sk]) ).
cnf(c_137,plain,
( sK5(A,B) != A
| ~ in(sK5(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_138,plain,
( sK5(A,B) = A
| in(sK5(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_139,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_141,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_12116,negated_conjecture,
( sK1(sK2) != sK0(sK2)
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_93,c_65]) ).
cnf(c_144,negated_conjecture,
sK1(sK2) != sK0(sK2),
inference(resolve,[status(thm)],[c_90,c_12116]) ).
cnf(c_12117,negated_conjecture,
( apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_93,c_64]) ).
cnf(c_145,negated_conjecture,
apply(sK2,sK1(sK2)) = apply(sK2,sK0(sK2)),
inference(resolve,[status(thm)],[c_90,c_12117]) ).
cnf(c_12118,negated_conjecture,
( in(sK1(sK2),relation_dom(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_93,c_63]) ).
cnf(c_146,negated_conjecture,
in(sK1(sK2),relation_dom(sK2)),
inference(resolve,[status(thm)],[c_90,c_12118]) ).
cnf(c_12119,negated_conjecture,
( in(sK0(sK2),relation_dom(sK2))
| one_to_one(sK2) ),
inference(resolve,[status(thm)],[c_93,c_62]) ).
cnf(c_147,negated_conjecture,
in(sK0(sK2),relation_dom(sK2)),
inference(resolve,[status(thm)],[c_90,c_12119]) ).
cnf(c_148,negated_conjecture,
( singleton(apply(sK2,A)) = relation_image(sK2,singleton(A))
| ~ in(A,relation_dom(sK2)) ),
inference(resolve,[status(thm)],[c_93,c_67]) ).
cnf(c_12120,plain,
( in(A,powerset(A))
| empty(powerset(A)) ),
inference(resolve,[status(thm)],[c_99,c_61]) ).
cnf(c_169,plain,
in(A,powerset(A)),
inference(resolve,[status(thm)],[c_132,c_12120]) ).
cnf(c_170,plain,
relation_image(sK2,empty_set) = empty_set,
inference(resolve,[status(thm)],[c_103,c_93]) ).
cnf(c_12121,plain,
empty_set = sK3(A),
inference(resolve,[status(thm)],[c_112,c_96]) ).
cnf(c_175,plain,
sK3(A) = empty_set,
inference(copy,[status(thm)],[c_12121]) ).
cnf(c_12122,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_97,c_61]) ).
cnf(c_12123,plain,
~ in(A,sK3(B)),
inference(resolve,[status(thm)],[c_12122,c_112]) ).
cnf(c_177,plain,
~ in(A,empty_set),
inference(paramod,[status(thm)],[c_175,c_12123]) ).
cnf(c_223,plain,
( in(sK4(A),A)
| empty(A) ),
inference(resolve,[status(thm)],[c_134,c_99]) ).
cnf(c_231,plain,
( B = A
| set_intersection2(singleton(A),singleton(B)) = empty_set ),
inference(resolve,[status(thm)],[c_136,c_102]) ).
cnf(c_232,plain,
( element(sK5(A,B),B)
| sK5(A,B) = A
| singleton(A) = B ),
inference(resolve,[status(thm)],[c_138,c_101]) ).
cnf(c_12124,plain,
( sK5(C,A) = C
| singleton(C) = A
| ~ empty(B)
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_97,c_138]) ).
cnf(c_12125,plain,
( sK5(B,A) = B
| singleton(B) = A
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_12124,c_61]) ).
cnf(c_239,plain,
( sK5(A,empty_set) = A
| singleton(A) = empty_set ),
inference(resolve,[status(thm)],[c_12125,c_130]) ).
cnf(c_12126,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_125]) ).
cnf(c_12127,plain,
( A != B
| in(A,set_intersection2(singleton(B),singleton(B))) ),
inference(resolve,[status(thm)],[c_139,c_12126]) ).
cnf(c_12128,plain,
in(set_intersection2(A,B),set_intersection2(singleton(set_intersection2(B,A)),singleton(set_intersection2(B,A)))),
inference(resolve,[status(thm)],[c_12127,c_141]) ).
cnf(c_248,plain,
in(set_intersection2(A,B),singleton(set_intersection2(B,A))),
inference(paramod,[status(thm)],[c_125,c_12128]) ).
cnf(c_264,plain,
singleton(apply(sK2,sK0(sK2))) = relation_image(sK2,singleton(sK0(sK2))),
inference(resolve,[status(thm)],[c_148,c_147]) ).
cnf(c_12129,negated_conjecture,
singleton(apply(sK2,sK1(sK2))) = relation_image(sK2,singleton(sK1(sK2))),
inference(resolve,[status(thm)],[c_148,c_146]) ).
cnf(c_12130,negated_conjecture,
singleton(apply(sK2,sK0(sK2))) = relation_image(sK2,singleton(sK1(sK2))),
inference(paramod,[status(thm)],[c_145,c_12129]) ).
cnf(c_12131,negated_conjecture,
relation_image(sK2,singleton(sK0(sK2))) = relation_image(sK2,singleton(sK1(sK2))),
inference(paramod,[status(thm)],[c_264,c_12130]) ).
cnf(c_265,negated_conjecture,
relation_image(sK2,singleton(sK1(sK2))) = relation_image(sK2,singleton(sK0(sK2))),
inference(copy,[status(thm)],[c_12131]) ).
cnf(c_12132,plain,
( B != A
| singleton(A) != empty_set ),
inference(resolve,[status(thm)],[c_139,c_177]) ).
cnf(c_300,plain,
singleton(A) != empty_set,
inference(resolve,[status(thm)],[c_12132,c_125]) ).
cnf(c_301,plain,
sK5(A,empty_set) = A,
inference(resolve,[status(thm)],[c_300,c_239]) ).
cnf(c_12133,plain,
A = sK5(A,empty_set),
inference(copy,[status(thm)],[c_301]) ).
cnf(c_12134,plain,
( A != B
| in(A,sK5(singleton(B),empty_set)) ),
inference(resolve,[status(thm)],[c_139,c_12133]) ).
cnf(c_12135,negated_conjecture,
in(apply(sK2,sK1(sK2)),sK5(singleton(apply(sK2,sK0(sK2))),empty_set)),
inference(resolve,[status(thm)],[c_12134,c_145]) ).
cnf(c_12136,negated_conjecture,
in(apply(sK2,sK0(sK2)),sK5(singleton(apply(sK2,sK0(sK2))),empty_set)),
inference(paramod,[status(thm)],[c_145,c_12135]) ).
cnf(c_12137,negated_conjecture,
in(apply(sK2,sK0(sK2)),sK5(relation_image(sK2,singleton(sK0(sK2))),empty_set)),
inference(paramod,[status(thm)],[c_264,c_12136]) ).
cnf(c_586,negated_conjecture,
in(apply(sK2,sK0(sK2)),relation_image(sK2,singleton(sK0(sK2)))),
inference(paramod,[status(thm)],[c_301,c_12137]) ).
cnf(c_12138,plain,
( empty(A)
| ~ empty(B)
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_97,c_223]) ).
cnf(c_12139,plain,
( sK5(B,powerset(A)) = B
| singleton(B) = powerset(A)
| empty(sK5(B,powerset(A)))
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_12138,c_232]) ).
cnf(c_12140,plain,
( sK5(A,powerset(empty_set)) = A
| singleton(A) = powerset(empty_set)
| empty(sK5(A,powerset(empty_set))) ),
inference(resolve,[status(thm)],[c_12139,c_130]) ).
cnf(c_817,plain,
( sK5(A,powerset(empty_set)) = A
| powerset(empty_set) = singleton(A)
| empty(sK5(A,powerset(empty_set))) ),
inference(copy,[status(thm)],[c_12140]) ).
cnf(c_875,plain,
element(set_intersection2(A,B),singleton(set_intersection2(B,A))),
inference(resolve,[status(thm)],[c_248,c_101]) ).
cnf(c_12141,plain,
element(relation_image(sK2,set_intersection2(A,B)),singleton(set_intersection2(relation_image(sK2,B),relation_image(sK2,A)))),
inference(paramod,[status(thm)],[c_92,c_875]) ).
cnf(c_895,plain,
element(relation_image(sK2,set_intersection2(A,B)),singleton(relation_image(sK2,set_intersection2(B,A)))),
inference(paramod,[status(thm)],[c_92,c_12141]) ).
cnf(c_12142,plain,
set_intersection2(relation_image(sK2,A),relation_image(sK2,singleton(sK0(sK2)))) = relation_image(sK2,set_intersection2(A,singleton(sK1(sK2)))),
inference(paramod,[status(thm)],[c_265,c_92]) ).
cnf(c_12143,plain,
relation_image(sK2,set_intersection2(A,singleton(sK0(sK2)))) = relation_image(sK2,set_intersection2(A,singleton(sK1(sK2)))),
inference(paramod,[status(thm)],[c_92,c_12142]) ).
cnf(c_2369,plain,
relation_image(sK2,set_intersection2(A,singleton(sK1(sK2)))) = relation_image(sK2,set_intersection2(A,singleton(sK0(sK2)))),
inference(copy,[status(thm)],[c_12143]) ).
cnf(c_12144,plain,
( empty_set = sK5(A,powerset(empty_set))
| sK5(A,powerset(empty_set)) = A
| powerset(empty_set) = singleton(A) ),
inference(resolve,[status(thm)],[c_817,c_96]) ).
cnf(c_4970,plain,
( sK5(A,powerset(empty_set)) = empty_set
| sK5(A,powerset(empty_set)) = A
| powerset(empty_set) = singleton(A) ),
inference(copy,[status(thm)],[c_12144]) ).
cnf(c_4985,plain,
( sK5(empty_set,powerset(empty_set)) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(factor,[status(thm)],[c_4970]) ).
cnf(c_12145,plain,
( sK5(empty_set,powerset(empty_set)) != empty_set
| ~ in(empty_set,powerset(empty_set))
| singleton(empty_set) = powerset(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(paramod,[status(thm)],[c_4985,c_137]) ).
cnf(c_12146,plain,
( sK5(empty_set,powerset(empty_set)) != empty_set
| ~ in(empty_set,powerset(empty_set))
| powerset(empty_set) = singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(copy,[status(thm)],[c_12145]) ).
cnf(c_12147,plain,
( sK5(empty_set,powerset(empty_set)) != empty_set
| ~ in(empty_set,powerset(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(copy,[status(thm)],[c_12146]) ).
cnf(c_5001,plain,
( sK5(empty_set,powerset(empty_set)) != empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(resolve,[status(thm)],[c_169,c_12147]) ).
cnf(c_12148,plain,
( powerset(empty_set) = singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(resolve,[status(thm)],[c_5001,c_4985]) ).
cnf(c_5002,plain,
powerset(empty_set) = singleton(empty_set),
inference(copy,[status(thm)],[c_12148]) ).
cnf(c_12149,plain,
( ~ empty(empty_set)
| ~ element(B,singleton(empty_set))
| ~ in(A,B) ),
inference(paramod,[status(thm)],[c_5002,c_97]) ).
cnf(c_5042,plain,
( ~ element(B,singleton(empty_set))
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_130,c_12149]) ).
cnf(c_12150,plain,
( element(relation_image(sK2,set_intersection2(singleton(A),singleton(B))),singleton(relation_image(sK2,empty_set)))
| A = B ),
inference(paramod,[status(thm)],[c_231,c_895]) ).
cnf(c_6246,plain,
( element(relation_image(sK2,set_intersection2(singleton(A),singleton(B))),singleton(empty_set))
| A = B ),
inference(paramod,[status(thm)],[c_170,c_12150]) ).
cnf(c_11612,plain,
( ~ in(C,relation_image(sK2,set_intersection2(singleton(A),singleton(B))))
| A = B ),
inference(resolve,[status(thm)],[c_6246,c_5042]) ).
cnf(c_12151,negated_conjecture,
~ in(A,relation_image(sK2,set_intersection2(singleton(sK1(sK2)),singleton(sK0(sK2))))),
inference(resolve,[status(thm)],[c_11612,c_144]) ).
cnf(c_12152,negated_conjecture,
~ in(A,relation_image(sK2,set_intersection2(singleton(sK0(sK2)),singleton(sK1(sK2))))),
inference(paramod,[status(thm)],[c_141,c_12151]) ).
cnf(c_12153,negated_conjecture,
~ in(A,relation_image(sK2,set_intersection2(singleton(sK0(sK2)),singleton(sK0(sK2))))),
inference(paramod,[status(thm)],[c_2369,c_12152]) ).
cnf(c_12114,negated_conjecture,
~ in(A,relation_image(sK2,singleton(sK0(sK2)))),
inference(paramod,[status(thm)],[c_125,c_12153]) ).
cnf(c_12115,plain,
$false,
inference(resolve,[status(thm)],[c_12114,c_586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 08:32:06 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2340555 was started by sandbox2 on n013,
% 0.17/0.43 % Sat Sep 26 08:32:06 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 35.32/4.99
% 35.32/4.99 % given #500 (W,wt=21): 744 -in(singleton(c6),singleton(powerset(A))). [ur(140,a,301,a(flip),c,514,a(flip)),rewrite([301(6)])].
% 35.32/4.99
% 35.32/4.99 % SZS status Theorem for theBenchmark
% 35.32/4.99
% 35.32/4.99 % Proof 1 at 3.27 (+ 1.22) seconds.
% 35.32/4.99 % Length of proof is 86.
% 35.32/4.99 % Level of proof is 11.
% 35.32/4.99 % Maximum clause weight is 40.000.
% 35.32/4.99 % Given clauses 949.
% 35.32/4.99
% 35.32/4.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------