%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU230+2 : 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 : n010.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 08:45:30 AM UTC 2026
% Result : Theorem 9.23s 1.78s
% Output : CNFRefutation 9.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 41 unt; 0 def)
% Number of atoms : 335 ( 146 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 399 ( 146 ~; 169 |; 68 &)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 2 con; 0-4 aty)
% Number of variables : 268 ( 23 sgn 159 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d12_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t60_relat_1,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('theBenchmark.p',t60_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('theBenchmark.p',d2_zfmisc_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t10_ordinal1,conjecture,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_ordinal1_neg,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(assume_negation,[status(cth)],[t10_ordinal1]) ).
cnf(c_255,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_207,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D != B
& D != A )
| ~ in(D,C) )
& ( D = B
| D = A
| in(D,C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(sk_d2_tarski_sk,plain,
! [A,B,C] :
( ( ( ( ( sK0(A,B,C) != B
& sK0(A,B,C) != A )
| ~ in(sK0(A,B,C),C) )
& ( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_207]) ).
fof(sk_d2_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_1
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_0
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) = VAR_1
| sK0(VAR_0,VAR_1,VAR_2) = VAR_0
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_1
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_0
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_1
| VAR_3 = VAR_0
| ~ in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_tarski_sk]) ).
cnf(c_267,plain,
( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C)
| unordered_pair(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
fof(nnf_208,plain,
! [A,B,C] :
( ( ? [D] :
( ( ! [E,F] :
( ordered_pair(E,F) != D
| ~ in(F,B)
| ~ in(E,A) )
| ~ in(D,C) )
& ( ? [X0,X6] :
( ordered_pair(X0,X6) = D
& in(X6,B)
& in(X0,A) )
| in(D,C) ) )
| cartesian_product2(A,B) = C )
& ( ! [X1] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X1
| ~ in(X5,B)
| ~ in(X4,A) )
| in(X1,C) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X1
& in(X3,B)
& in(X2,A) )
| ~ in(X1,C) ) )
| cartesian_product2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_zfmisc_1]) ).
fof(sk_d2_zfmisc_1_sk,plain,
! [A,B,C] :
( ( ( ( ! [E,F] :
( ordered_pair(E,F) != sK1(A,B,C)
| ~ in(F,B)
| ~ in(E,A) )
| ~ in(sK1(A,B,C),C) )
& ( ( ordered_pair(sK7(A,B,C),sK2(A,B,C)) = sK1(A,B,C)
& in(sK2(A,B,C),B)
& in(sK7(A,B,C),A) )
| in(sK1(A,B,C),C) ) )
| cartesian_product2(A,B) = C )
& ( ! [X1] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X1
| ~ in(X5,B)
| ~ in(X4,A) )
| in(X1,C) )
& ( ( ordered_pair(sK5(A,B,C,X1),sK6(A,B,C,X1)) = X1
& in(sK6(A,B,C,X1),B)
& in(sK5(A,B,C,X1),A) )
| ~ in(X1,C) ) )
| cartesian_product2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK1,sK7,sK2]),skolemize(X2,sK5(A,B,C,X1)),skolemize(X3,sK6(A,B,C,X1)),skolemize(D,sK1(A,B,C)),skolemize(X0,sK7(A,B,C)),skolemize(X6,sK2(A,B,C))],[nnf_208]) ).
fof(sk_d2_zfmisc_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ordered_pair(VAR_3,VAR_4) != sK1(VAR_0,VAR_1,VAR_2)
| ~ in(VAR_4,VAR_1)
| ~ in(VAR_3,VAR_0)
| ~ in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( ordered_pair(sK7(VAR_0,VAR_1,VAR_2),sK2(VAR_0,VAR_1,VAR_2)) = sK1(VAR_0,VAR_1,VAR_2)
| in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK2(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK7(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| cartesian_product2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ordered_pair(VAR_4,VAR_5) != VAR_3
| ~ in(VAR_5,VAR_1)
| ~ in(VAR_4,VAR_0)
| in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ordered_pair(sK5(VAR_0,VAR_1,VAR_2,VAR_3),sK6(VAR_0,VAR_1,VAR_2,VAR_3)) = VAR_3
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK6(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK5(VAR_0,VAR_1,VAR_2,VAR_3),VAR_0)
| ~ in(VAR_3,VAR_2)
| cartesian_product2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_zfmisc_1_sk]) ).
cnf(c_275,plain,
( in(sK2(A,B,C),B)
| in(sK1(A,B,C),C)
| cartesian_product2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_zfmisc_1]) ).
cnf(c_286,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc12_relat_1]) ).
cnf(c_287,plain,
relation(empty_set),
inference(clausify,[status(thm)],[fc12_relat_1]) ).
cnf(c_316,plain,
( in(A,C)
| ~ subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
cnf(c_330,plain,
( function(A)
| ~ empty(A) ),
inference(clausify,[status(thm)],[cc1_funct_1]) ).
cnf(c_333,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_341,plain,
( subset(B,A)
| A != B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
fof(nnf_10,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ! [E] :
( apply(A,E) != D
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
| ~ in(D,C) )
& ( ? [X0] :
( apply(A,X0) = D
& in(X0,B)
& in(X0,relation_dom(A)) )
| in(D,C) ) )
| relation_image(A,B) = C )
& ( ! [X6] :
( ( ! [X1] :
( apply(A,X1) != X6
| ~ in(X1,B)
| ~ in(X1,relation_dom(A)) )
| in(X6,C) )
& ( ? [X4] :
( apply(A,X4) = X6
& in(X4,B)
& in(X4,relation_dom(A)) )
| ~ in(X6,C) ) )
| relation_image(A,B) != C ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(sk_d12_funct_1_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ! [E] :
( apply(A,E) != sK8(A,B,C)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
| ~ in(sK8(A,B,C),C) )
& ( ( apply(A,sK9(A,B,C)) = sK8(A,B,C)
& in(sK9(A,B,C),B)
& in(sK9(A,B,C),relation_dom(A)) )
| in(sK8(A,B,C),C) ) )
| relation_image(A,B) = C )
& ( ! [X6] :
( ( ! [X1] :
( apply(A,X1) != X6
| ~ in(X1,B)
| ~ in(X1,relation_dom(A)) )
| in(X6,C) )
& ( ( apply(A,sK3(A,B,C,X6)) = X6
& in(sK3(A,B,C,X6),B)
& in(sK3(A,B,C,X6),relation_dom(A)) )
| ~ in(X6,C) ) )
| relation_image(A,B) != C ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK8,sK9]),skolemize(X4,sK3(A,B,C,X6)),skolemize(D,sK8(A,B,C)),skolemize(X0,sK9(A,B,C))],[nnf_10]) ).
fof(sk_d12_funct_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( apply(VAR_0,VAR_3) != sK8(VAR_0,VAR_1,VAR_2)
| ~ in(VAR_3,VAR_1)
| ~ in(VAR_3,relation_dom(VAR_0))
| ~ in(sK8(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( apply(VAR_0,sK9(VAR_0,VAR_1,VAR_2)) = sK8(VAR_0,VAR_1,VAR_2)
| in(sK8(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK9(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK8(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK9(VAR_0,VAR_1,VAR_2),relation_dom(VAR_0))
| in(sK8(VAR_0,VAR_1,VAR_2),VAR_2)
| relation_image(VAR_0,VAR_1) = VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( apply(VAR_0,VAR_4) != VAR_3
| ~ in(VAR_4,VAR_1)
| ~ in(VAR_4,relation_dom(VAR_0))
| in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( apply(VAR_0,sK3(VAR_0,VAR_1,VAR_2,VAR_3)) = VAR_3
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK3(VAR_0,VAR_1,VAR_2,VAR_3),VAR_1)
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(sK3(VAR_0,VAR_1,VAR_2,VAR_3),relation_dom(VAR_0))
| ~ in(VAR_3,VAR_2)
| relation_image(VAR_0,VAR_1) != VAR_2
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d12_funct_1_sk]) ).
cnf(c_350,plain,
( in(sK3(A,B,C,D),relation_dom(A))
| ~ in(D,C)
| relation_image(A,B) != C
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d12_funct_1]) ).
cnf(c_383,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_397,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_415,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_448,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_623,plain,
set_intersection2(A,empty_set) = empty_set,
inference(clausify,[status(thm)],[t2_boole]) ).
cnf(c_639,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_660,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_661,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_660]) ).
cnf(c_689,plain,
relation_dom(empty_set) = empty_set,
inference(clausify,[status(thm)],[t60_relat_1]) ).
fof(nnf_253,plain,
? [A] : ~ in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1_neg]) ).
fof(sk_t10_ordinal1_neg,plain,
~ in(sK4,succ(sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(A,sK4)],[nnf_253]) ).
cnf(c_734,negated_conjecture,
~ in(sK4,succ(sK4)),
inference(split_conjunct,[status(thm)],[sk_t10_ordinal1_neg]) ).
cnf(c_735,negated_conjecture,
~ in(sK4,set_union2(sK4,singleton(sK4))),
inference(paramod,[status(thm)],[c_383,c_734]) ).
cnf(c_772,plain,
( ~ in(C,B)
| set_difference(A,B) != B ),
inference(factor,[status(thm)],[c_448]) ).
cnf(c_3884,plain,
set_difference(A,set_difference(A,empty_set)) = empty_set,
inference(paramod,[status(thm)],[c_661,c_623]) ).
cnf(c_827,plain,
set_difference(A,A) = empty_set,
inference(paramod,[status(thm)],[c_639,c_3884]) ).
cnf(c_879,plain,
function(empty_set),
inference(resolve,[status(thm)],[c_330,c_286]) ).
cnf(c_1033,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_772,c_827]) ).
cnf(c_1050,plain,
( in(sK1(A,empty_set,B),B)
| cartesian_product2(A,empty_set) = B ),
inference(resolve,[status(thm)],[c_1033,c_275]) ).
cnf(c_1094,plain,
subset(unordered_pair(A,B),unordered_pair(B,A)),
inference(resolve,[status(thm)],[c_341,c_255]) ).
cnf(c_1120,plain,
in(A,unordered_pair(B,A)),
inference(resolve,[status(thm)],[c_1094,c_316]) ).
cnf(c_3885,plain,
( in(sK3(empty_set,A,B,C),relation_dom(empty_set))
| ~ in(C,B)
| relation_image(empty_set,A) != B
| ~ function(empty_set) ),
inference(resolve,[status(thm)],[c_350,c_287]) ).
cnf(c_3886,plain,
( in(sK3(empty_set,A,B,C),empty_set)
| ~ in(C,B)
| relation_image(empty_set,A) != B
| ~ function(empty_set) ),
inference(paramod,[status(thm)],[c_689,c_3885]) ).
cnf(c_3887,plain,
( in(sK3(empty_set,A,B,C),empty_set)
| ~ in(C,B)
| relation_image(empty_set,A) != B ),
inference(resolve,[status(thm)],[c_879,c_3886]) ).
cnf(c_1388,plain,
( ~ in(C,B)
| relation_image(empty_set,A) != B ),
inference(resolve,[status(thm)],[c_1033,c_3887]) ).
cnf(c_1404,plain,
~ in(A,relation_image(empty_set,B)),
inference(xxres,[status(thm)],[c_1388]) ).
cnf(c_1405,plain,
relation_image(empty_set,A) != unordered_pair(B,C),
inference(resolve,[status(thm)],[c_1388,c_1120]) ).
cnf(c_3888,plain,
( sK0(A,B,relation_image(empty_set,C)) = B
| sK0(A,B,relation_image(empty_set,C)) = A
| unordered_pair(A,B) = relation_image(empty_set,C) ),
inference(resolve,[status(thm)],[c_1404,c_267]) ).
cnf(c_3889,plain,
( sK0(A,B,relation_image(empty_set,C)) = B
| sK0(A,B,relation_image(empty_set,C)) = A
| relation_image(empty_set,C) = unordered_pair(A,B) ),
inference(copy,[status(thm)],[c_3888]) ).
cnf(c_1421,plain,
( sK0(A,B,relation_image(empty_set,C)) = B
| sK0(A,B,relation_image(empty_set,C)) = A ),
inference(resolve,[status(thm)],[c_1405,c_3889]) ).
cnf(c_1423,plain,
sK0(A,A,relation_image(empty_set,B)) = A,
inference(factor,[status(thm)],[c_1421]) ).
cnf(c_2175,plain,
cartesian_product2(A,empty_set) = relation_image(empty_set,B),
inference(resolve,[status(thm)],[c_1050,c_1404]) ).
cnf(c_2180,plain,
cartesian_product2(A,empty_set) = empty_set,
inference(resolve,[status(thm)],[c_1050,c_1033]) ).
cnf(c_3890,plain,
empty_set = relation_image(empty_set,B),
inference(paramod,[status(thm)],[c_2180,c_2175]) ).
cnf(c_2234,plain,
relation_image(empty_set,A) = empty_set,
inference(copy,[status(thm)],[c_3890]) ).
cnf(c_2246,plain,
sK0(A,A,empty_set) = A,
inference(paramod,[status(thm)],[c_2234,c_1423]) ).
cnf(c_3891,plain,
A = sK0(A,A,empty_set),
inference(copy,[status(thm)],[c_2246]) ).
cnf(c_3892,plain,
( A != B
| in(A,sK0(singleton(B),singleton(B),empty_set)) ),
inference(resolve,[status(thm)],[c_397,c_3891]) ).
cnf(c_3337,plain,
( A != B
| in(A,singleton(B)) ),
inference(paramod,[status(thm)],[c_2246,c_3892]) ).
cnf(c_3893,plain,
in(sK0(A,A,empty_set),singleton(A)),
inference(resolve,[status(thm)],[c_3337,c_2246]) ).
cnf(c_3372,plain,
in(A,singleton(A)),
inference(paramod,[status(thm)],[c_2246,c_3893]) ).
cnf(c_3850,plain,
( ~ in(A,C)
| in(A,set_union2(B,C)) ),
inference(resolve,[status(thm)],[c_415,c_333]) ).
cnf(c_3882,plain,
in(A,set_union2(B,singleton(A))),
inference(resolve,[status(thm)],[c_3850,c_3372]) ).
cnf(c_3883,plain,
$false,
inference(resolve,[status(thm)],[c_3882,c_735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 08:55:32 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2958615 was started by sandbox2 on n010,
% 0.19/0.46 % Sat Sep 26 08:55:32 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.56
% 0.23/0.56 % From the command line: assign(max_seconds, 300).
% 0.23/0.56
% 0.23/0.56 % SInE: 205 to sos, 49 to usable, of 254 axioms (tolerance 2.00, depth 0 fixpoint).
% 9.23/1.78
% 9.23/1.78 % SZS status Theorem for theBenchmark
% 9.23/1.78
% 9.23/1.78 % Proof 1 at 0.98 (+ 0.18) seconds.
% 9.23/1.78 % Length of proof is 60.
% 9.23/1.78 % Level of proof is 13.
% 9.23/1.78 % Maximum clause weight is 330.000.
% 9.23/1.78 % Given clauses 348.
% 9.23/1.78
% 9.23/1.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------