%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:46:19 AM UTC 2026
% Result : Theorem 0.17s 5.55s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 17 unt; 0 def)
% Number of atoms : 206 ( 87 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 213 ( 75 ~; 95 |; 32 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 10 sgn 56 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_xboole_0,axiom,
! [A] :
( A = k1_xboole_0
<=> ! [B] : ~ r2_hidden(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = k3_tarski(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k5_setfam_1(A,B) = k3_tarski(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t30_relset_2,conjecture,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( k5_setfam_1(A,B) = k1_xboole_0
<=> ! [C] :
( r2_hidden(C,B)
=> C = k1_xboole_0 ) ) ),
file('theBenchmark.p',t30_relset_2) ).
fof(t30_relset_2_neg,negated_conjecture,
~ ! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( k5_setfam_1(A,B) = k1_xboole_0
<=> ! [C] :
( r2_hidden(C,B)
=> C = k1_xboole_0 ) ) ),
inference(assume_negation,[status(cth)],[t30_relset_2]) ).
fof(nnf_29,plain,
? [A,B] :
( ( ? [C] :
( C != k1_xboole_0
& r2_hidden(C,B) )
| k5_setfam_1(A,B) != k1_xboole_0 )
& ( ! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,B) )
| k5_setfam_1(A,B) = k1_xboole_0 )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(fof_nnf,[status(thm)],[t30_relset_2_neg]) ).
fof(sk_t30_relset_2_neg_sk,plain,
( ( ( sK2 != k1_xboole_0
& r2_hidden(sK2,sK1) )
| k5_setfam_1(sK0,sK1) != k1_xboole_0 )
& ( ! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1) )
| k5_setfam_1(sK0,sK1) = k1_xboole_0 )
& m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_29]) ).
fof(sk_t30_relset_2_neg,plain,
( ( sK2 != k1_xboole_0
| k5_setfam_1(sK0,sK1) != k1_xboole_0 )
& ( r2_hidden(sK2,sK1)
| k5_setfam_1(sK0,sK1) != k1_xboole_0 )
& ! [VAR_0] :
( VAR_0 = k1_xboole_0
| ~ r2_hidden(VAR_0,sK1)
| k5_setfam_1(sK0,sK1) = k1_xboole_0 )
& m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
inference(cnf_transformation,[status(thm)],[sk_t30_relset_2_neg_sk]) ).
cnf(c_34,negated_conjecture,
( sK2 != k1_xboole_0
| k5_setfam_1(sK0,sK1) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[sk_t30_relset_2_neg]) ).
cnf(c_35,negated_conjecture,
( r2_hidden(sK2,sK1)
| k5_setfam_1(sK0,sK1) != k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[sk_t30_relset_2_neg]) ).
cnf(c_36,negated_conjecture,
( A = k1_xboole_0
| ~ r2_hidden(A,sK1)
| k5_setfam_1(sK0,sK1) = k1_xboole_0 ),
inference(split_conjunct,[status(thm)],[sk_t30_relset_2_neg]) ).
cnf(c_37,negated_conjecture,
( k1_xboole_0 = A
| ~ r2_hidden(A,sK1)
| k5_setfam_1(sK0,sK1) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,negated_conjecture,
m1_subset_1(sK1,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(split_conjunct,[status(thm)],[sk_t30_relset_2_neg]) ).
cnf(c_40,plain,
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_41,plain,
( k1_xboole_0 = A
| ~ v1_xboole_0(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
cnf(c_46,plain,
( k3_tarski(A) = k5_setfam_1(B,A)
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(clausify,[status(thm)],[redefinition_k5_setfam_1]) ).
cnf(c_47,plain,
( k5_setfam_1(B,A) = k3_tarski(A)
| ~ m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(B))) ),
inference(copy,[status(thm)],[c_46]) ).
fof(nnf_17,plain,
! [A] :
? [B] :
( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(sk_rc2_subset_1,plain,
! [A] :
( v1_xboole_0(sK3(A))
& m1_subset_1(sK3(A),k1_zfmisc_1(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(B,sK3(A))],[nnf_17]) ).
cnf(c_48,plain,
v1_xboole_0(sK3(A)),
inference(split_conjunct,[status(thm)],[sk_rc2_subset_1]) ).
fof(nnf_4,plain,
! [A,B] :
( ( ? [C] :
( ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| ~ r2_hidden(C,B) )
& ( ? [X0] :
( r2_hidden(X0,A)
& r2_hidden(C,X0) )
| r2_hidden(C,B) ) )
| k3_tarski(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ r2_hidden(X3,A)
| ~ r2_hidden(X1,X3) )
| r2_hidden(X1,B) )
& ( ? [X2] :
( r2_hidden(X2,A)
& r2_hidden(X1,X2) )
| ~ r2_hidden(X1,B) ) )
| k3_tarski(A) != B ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(sk_d4_tarski_sk,plain,
! [A,B] :
( ( ( ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(sK4(A,B),D) )
| ~ r2_hidden(sK4(A,B),B) )
& ( ( r2_hidden(sK5(A,B),A)
& r2_hidden(sK4(A,B),sK5(A,B)) )
| r2_hidden(sK4(A,B),B) ) )
| k3_tarski(A) = B )
& ( ! [X1] :
( ( ! [X3] :
( ~ r2_hidden(X3,A)
| ~ r2_hidden(X1,X3) )
| r2_hidden(X1,B) )
& ( ( r2_hidden(sK6(A,B,X1),A)
& r2_hidden(X1,sK6(A,B,X1)) )
| ~ r2_hidden(X1,B) ) )
| k3_tarski(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK4,sK5]),skolemize(X2,sK6(A,B,X1)),skolemize(C,sK4(A,B)),skolemize(X0,sK5(A,B))],[nnf_4]) ).
fof(sk_d4_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ r2_hidden(VAR_2,VAR_0)
| ~ r2_hidden(sK4(VAR_0,VAR_1),VAR_2)
| ~ r2_hidden(sK4(VAR_0,VAR_1),VAR_1)
| k3_tarski(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( r2_hidden(sK5(VAR_0,VAR_1),VAR_0)
| r2_hidden(sK4(VAR_0,VAR_1),VAR_1)
| k3_tarski(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( r2_hidden(sK4(VAR_0,VAR_1),sK5(VAR_0,VAR_1))
| r2_hidden(sK4(VAR_0,VAR_1),VAR_1)
| k3_tarski(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ r2_hidden(VAR_3,VAR_0)
| ~ r2_hidden(VAR_2,VAR_3)
| r2_hidden(VAR_2,VAR_1)
| k3_tarski(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( r2_hidden(sK6(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ r2_hidden(VAR_2,VAR_1)
| k3_tarski(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( r2_hidden(VAR_2,sK6(VAR_0,VAR_1,VAR_2))
| ~ r2_hidden(VAR_2,VAR_1)
| k3_tarski(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_tarski_sk]) ).
cnf(c_59,plain,
( r2_hidden(sK5(A,B),A)
| r2_hidden(sK4(A,B),B)
| k3_tarski(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_60,plain,
( r2_hidden(sK4(A,B),sK5(A,B))
| r2_hidden(sK4(A,B),B)
| k3_tarski(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_61,plain,
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D)
| r2_hidden(C,B)
| k3_tarski(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
cnf(c_62,plain,
( r2_hidden(sK6(A,B,C),A)
| ~ r2_hidden(C,B)
| k3_tarski(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d4_tarski]) ).
fof(nnf_3,plain,
! [A] :
( ( ? [B] : r2_hidden(B,A)
| k1_xboole_0 = A )
& ( ! [X0] : ~ r2_hidden(X0,A)
| k1_xboole_0 != A ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(sk_d1_xboole_0_sk,plain,
! [A] :
( ( r2_hidden(sK7(A),A)
| k1_xboole_0 = A )
& ( ! [X0] : ~ r2_hidden(X0,A)
| k1_xboole_0 != A ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(B,sK7(A))],[nnf_3]) ).
fof(sk_d1_xboole_0,plain,
( ! [VAR_0] :
( r2_hidden(sK7(VAR_0),VAR_0)
| k1_xboole_0 = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ r2_hidden(VAR_1,VAR_0)
| k1_xboole_0 != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_xboole_0_sk]) ).
cnf(c_64,plain,
( r2_hidden(sK7(A),A)
| k1_xboole_0 = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_73,plain,
k5_setfam_1(sK0,sK1) = k3_tarski(sK1),
inference(resolve,[status(thm)],[c_47,c_38]) ).
cnf(c_75,negated_conjecture,
( k1_xboole_0 = A
| ~ r2_hidden(A,sK1)
| k3_tarski(sK1) = k1_xboole_0 ),
inference(paramod,[status(thm)],[c_73,c_37]) ).
cnf(c_76,negated_conjecture,
( r2_hidden(sK2,sK1)
| k3_tarski(sK1) != k1_xboole_0 ),
inference(paramod,[status(thm)],[c_73,c_35]) ).
cnf(c_77,negated_conjecture,
( sK2 != k1_xboole_0
| k3_tarski(sK1) != k1_xboole_0 ),
inference(paramod,[status(thm)],[c_73,c_34]) ).
cnf(c_634,plain,
k1_xboole_0 = sK3(A),
inference(resolve,[status(thm)],[c_48,c_41]) ).
cnf(c_79,plain,
sK3(A) = k1_xboole_0,
inference(copy,[status(thm)],[c_634]) ).
cnf(c_635,plain,
~ r2_hidden(A,sK3(B)),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_80,plain,
~ r2_hidden(A,k1_xboole_0),
inference(paramod,[status(thm)],[c_79,c_635]) ).
cnf(c_636,plain,
( r2_hidden(sK6(B,k3_tarski(B),A),B)
| ~ r2_hidden(A,k3_tarski(B)) ),
inference(xxres,[status(thm)],[c_62]) ).
cnf(c_172,plain,
~ r2_hidden(A,k3_tarski(k1_xboole_0)),
inference(resolve,[status(thm)],[c_636,c_80]) ).
cnf(c_637,plain,
k1_xboole_0 = k3_tarski(k1_xboole_0),
inference(resolve,[status(thm)],[c_172,c_64]) ).
cnf(c_192,plain,
k3_tarski(k1_xboole_0) = k1_xboole_0,
inference(copy,[status(thm)],[c_637]) ).
cnf(c_638,plain,
( r2_hidden(sK4(k3_tarski(k1_xboole_0),A),A)
| k3_tarski(k3_tarski(k1_xboole_0)) = A ),
inference(resolve,[status(thm)],[c_172,c_59]) ).
cnf(c_639,plain,
( r2_hidden(sK4(k3_tarski(k1_xboole_0),A),A)
| k3_tarski(k1_xboole_0) = A ),
inference(paramod,[status(thm)],[c_192,c_638]) ).
cnf(c_640,plain,
( r2_hidden(sK4(k3_tarski(k1_xboole_0),A),A)
| k1_xboole_0 = A ),
inference(paramod,[status(thm)],[c_192,c_639]) ).
cnf(c_193,plain,
( r2_hidden(sK4(k1_xboole_0,A),A)
| k1_xboole_0 = A ),
inference(paramod,[status(thm)],[c_192,c_640]) ).
cnf(c_641,negated_conjecture,
( r2_hidden(sK4(sK1,A),A)
| k3_tarski(sK1) = A
| k1_xboole_0 = sK5(sK1,A)
| k3_tarski(sK1) = k1_xboole_0 ),
inference(resolve,[status(thm)],[c_75,c_59]) ).
cnf(c_196,negated_conjecture,
( r2_hidden(sK4(sK1,A),A)
| k3_tarski(sK1) = A
| sK5(sK1,A) = k1_xboole_0
| k3_tarski(sK1) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_641]) ).
cnf(c_642,plain,
( r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| sK5(sK1,k1_xboole_0) = k1_xboole_0
| k3_tarski(sK1) = k1_xboole_0 ),
inference(factor,[status(thm)],[c_196]) ).
cnf(c_197,plain,
( sK5(sK1,k1_xboole_0) = k1_xboole_0
| k3_tarski(sK1) = k1_xboole_0 ),
inference(resolve,[status(thm)],[c_80,c_642]) ).
cnf(c_643,plain,
( r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| k3_tarski(sK1) = k1_xboole_0
| k3_tarski(sK1) = k1_xboole_0 ),
inference(paramod,[status(thm)],[c_197,c_60]) ).
cnf(c_644,plain,
( r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| k3_tarski(sK1) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_643]) ).
cnf(c_645,plain,
( r2_hidden(sK4(sK1,k1_xboole_0),k1_xboole_0)
| k3_tarski(sK1) = k1_xboole_0 ),
inference(copy,[status(thm)],[c_644]) ).
cnf(c_511,plain,
k3_tarski(sK1) = k1_xboole_0,
inference(resolve,[status(thm)],[c_80,c_645]) ).
cnf(c_646,negated_conjecture,
( sK2 != k1_xboole_0
| k1_xboole_0 != k1_xboole_0 ),
inference(paramod,[status(thm)],[c_511,c_77]) ).
cnf(c_513,negated_conjecture,
sK2 != k1_xboole_0,
inference(copy,[status(thm)],[c_646]) ).
cnf(c_647,negated_conjecture,
( r2_hidden(sK2,sK1)
| k1_xboole_0 != k1_xboole_0 ),
inference(paramod,[status(thm)],[c_511,c_76]) ).
cnf(c_514,negated_conjecture,
r2_hidden(sK2,sK1),
inference(copy,[status(thm)],[c_647]) ).
cnf(c_648,plain,
( ~ r2_hidden(B,sK1)
| ~ r2_hidden(A,B)
| r2_hidden(A,k1_xboole_0) ),
inference(resolve,[status(thm)],[c_61,c_511]) ).
cnf(c_649,plain,
( ~ r2_hidden(B,sK1)
| ~ r2_hidden(A,B) ),
inference(resolve,[status(thm)],[c_648,c_80]) ).
cnf(c_607,negated_conjecture,
~ r2_hidden(A,sK2),
inference(resolve,[status(thm)],[c_649,c_514]) ).
cnf(c_650,plain,
k1_xboole_0 = sK2,
inference(resolve,[status(thm)],[c_607,c_193]) ).
cnf(c_651,plain,
sK2 = k1_xboole_0,
inference(copy,[status(thm)],[c_650]) ).
cnf(c_633,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_513,c_651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU430+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.40 % Computer : n018.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Sat Sep 26 09:47:13 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.41 % Process 187441 was started by sandbox on n018,
% 0.13/5.41 % Sat Sep 26 09:47:13 2026
% 0.13/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/5.42
% 0.13/5.42 % From the command line: assign(max_seconds, 300).
% 0.17/5.55
% 0.17/5.55 % SZS status Theorem for theBenchmark
% 0.17/5.55
% 0.17/5.55 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.17/5.55 % Length of proof is 38.
% 0.17/5.55 % Level of proof is 10.
% 0.17/5.55 % Maximum clause weight is 31.000.
% 0.17/5.55 % Given clauses 155.
% 0.17/5.55
% 0.17/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
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