%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU430+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 : Thu Sep 24 02:20:35 PM UTC 2026
% Result : Theorem 17.93s 7.22s
% Output : CNFRefutation 19.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 9 unt; 0 def)
% Number of atoms : 156 ( 64 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 173 ( 63 ~; 73 |; 26 &)
% ( 5 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 86 ( 72 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( B = k3_tarski(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
( A = k1_xboole_0
<=> ! [B] : ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f669,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> k5_setfam_1(A,B) = k3_tarski(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19101,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19102,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(negated_conjecture,[status(cth)],[f19101]) ).
fof(f19133,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B = k3_tarski(A) )
& ( ! [C] :
( ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f19134,plain,
( ! [A,B] :
( ? [C] :
( ( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| r2_hidden(C,B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B = k3_tarski(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ! [C] :
( ? [D] :
( r2_hidden(D,A)
& r2_hidden(C,D) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(miniscoping,[status(thm)],[f19133]) ).
fof(f19135,plain,
( ! [A,B] :
( ( ( ( r2_hidden(sK6_skl(B,A),A)
& r2_hidden(sK5_skl(B,A),sK6_skl(B,A)) )
| r2_hidden(sK5_skl(B,A),B) )
& ( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(sK5_skl(B,A),D) )
| ~ r2_hidden(sK5_skl(B,A),B) ) )
| B = k3_tarski(A) )
& ! [A,B] :
( ( ! [C] :
( ! [D] :
( ~ r2_hidden(D,A)
| ~ r2_hidden(C,D) )
| r2_hidden(C,B) )
& ! [C] :
( ( r2_hidden(sK4_skl(C,B,A),A)
& r2_hidden(C,sK4_skl(C,B,A)) )
| ~ r2_hidden(C,B) ) )
| B != k3_tarski(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f19134]) ).
fof(f19138,plain,
! [X0,X1,X2,X3] :
( ~ r2_hidden(X3,X1)
| ~ r2_hidden(X2,X3)
| r2_hidden(X2,X0)
| X0 != k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f19135]) ).
fof(f19140,plain,
! [X0,X1] :
( r2_hidden(sK5_skl(X0,X1),sK6_skl(X0,X1))
| r2_hidden(sK5_skl(X0,X1),X0)
| X0 = k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f19135]) ).
fof(f19141,plain,
! [X0,X1] :
( r2_hidden(sK6_skl(X0,X1),X1)
| r2_hidden(sK5_skl(X0,X1),X0)
| X0 = k3_tarski(X1) ),
inference(cnf_transformation,[status(thm)],[f19135]) ).
fof(f19192,plain,
! [A] :
( ( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f19193,plain,
( ! [A] :
( ? [B] : r2_hidden(B,A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(miniscoping,[status(thm)],[f19192]) ).
fof(f19194,plain,
( ! [A] :
( r2_hidden(sK22_skl(A),A)
| A = k1_xboole_0 )
& ! [A] :
( ! [B] : ~ r2_hidden(B,A)
| A != k1_xboole_0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl]),skolemize(B,sK22_skl(A))],[f19193]) ).
fof(f19195,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| X0 != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f19194]) ).
fof(f19196,plain,
! [X0] :
( r2_hidden(sK22_skl(X0),X0)
| X0 = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f19194]) ).
fof(f20553,plain,
! [A,B] :
( k5_setfam_1(A,B) = k3_tarski(B)
| ~ m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f669]) ).
fof(f20554,plain,
! [X0,X1] :
( k5_setfam_1(X1,X0) = k3_tarski(X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k1_zfmisc_1(X1))) ),
inference(cnf_transformation,[status(thm)],[f20553]) ).
fof(f89326,plain,
? [A,B] :
( ( k5_setfam_1(A,B) = k1_xboole_0
<~> ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,B) ) )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f19102]) ).
fof(f89327,plain,
? [A,B] :
( ( ? [C] :
( C != k1_xboole_0
& r2_hidden(C,B) )
| k5_setfam_1(A,B) != k1_xboole_0 )
& ( ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,B) )
| k5_setfam_1(A,B) = k1_xboole_0 )
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ),
inference(NNF_transformation,[status(thm)],[f89326]) ).
fof(f89328,plain,
( ( ( sK6525_skl != k1_xboole_0
& r2_hidden(sK6525_skl,sK6524_skl) )
| k5_setfam_1(sK6523_skl,sK6524_skl) != k1_xboole_0 )
& ( ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,sK6524_skl) )
| k5_setfam_1(sK6523_skl,sK6524_skl) = k1_xboole_0 )
& m1_subset_1(sK6524_skl,k1_zfmisc_1(k1_zfmisc_1(sK6523_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6523_skl,sK6524_skl,sK6525_skl]),skolemize(A,sK6523_skl),skolemize(B,sK6524_skl),skolemize(C,sK6525_skl)],[f89327]) ).
fof(f89329,plain,
m1_subset_1(sK6524_skl,k1_zfmisc_1(k1_zfmisc_1(sK6523_skl))),
inference(cnf_transformation,[status(thm)],[f89328]) ).
fof(f89330,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK6524_skl)
| k5_setfam_1(sK6523_skl,sK6524_skl) = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f89328]) ).
fof(f89331,plain,
( r2_hidden(sK6525_skl,sK6524_skl)
| k5_setfam_1(sK6523_skl,sK6524_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f89328]) ).
fof(f89332,plain,
( sK6525_skl != k1_xboole_0
| k5_setfam_1(sK6523_skl,sK6524_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f89328]) ).
fof(f95912,plain,
! [X0,X1,X2] :
( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X0,X2)
| r2_hidden(X0,k3_tarski(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f19138]) ).
fof(f95915,plain,
! [X0] : ~ r2_hidden(X0,k1_xboole_0),
inference(destructive_equality_resolution,[status(thm)],[f19195]) ).
fof(f100874,plain,
k5_setfam_1(sK6523_skl,sK6524_skl) = k3_tarski(sK6524_skl),
inference(resolution,[status(thm)],[f20554,f89329]) ).
fof(f100892,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK6524_skl)
| k3_tarski(sK6524_skl) = k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f100874,f89330]) ).
fof(f100893,plain,
( r2_hidden(sK6525_skl,sK6524_skl)
| k3_tarski(sK6524_skl) != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f100874,f89331]) ).
fof(f100894,plain,
( sK6525_skl != k1_xboole_0
| k3_tarski(sK6524_skl) != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f100874,f89332]) ).
fof(f100976,plain,
! [X0] :
( sK6_skl(X0,sK6524_skl) = k1_xboole_0
| k3_tarski(sK6524_skl) = k1_xboole_0
| r2_hidden(sK5_skl(X0,sK6524_skl),X0)
| X0 = k3_tarski(sK6524_skl) ),
inference(resolution,[status(thm)],[f19141,f100892]) ).
fof(f101843,plain,
( sK6_skl(k1_xboole_0,sK6524_skl) = k1_xboole_0
| k3_tarski(sK6524_skl) = k1_xboole_0
| k1_xboole_0 = k3_tarski(sK6524_skl) ),
inference(resolution,[status(thm)],[f100976,f95915]) ).
fof(f101878,plain,
( sK6_skl(k1_xboole_0,sK6524_skl) = k1_xboole_0
| k1_xboole_0 = k3_tarski(sK6524_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f101843]) ).
fof(f101979,plain,
( k1_xboole_0 = k3_tarski(sK6524_skl)
| r2_hidden(sK5_skl(k1_xboole_0,sK6524_skl),k1_xboole_0)
| r2_hidden(sK5_skl(k1_xboole_0,sK6524_skl),k1_xboole_0)
| k1_xboole_0 = k3_tarski(sK6524_skl) ),
inference(paramodulation,[status(thm)],[f101878,f19140]) ).
fof(f101982,plain,
( r2_hidden(sK5_skl(k1_xboole_0,sK6524_skl),k1_xboole_0)
| k1_xboole_0 = k3_tarski(sK6524_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f101979]) ).
fof(f101983,plain,
k1_xboole_0 = k3_tarski(sK6524_skl),
inference(forward_subsumption_resolution,[status(thm)],[f101982,f95915]) ).
fof(f102000,plain,
( r2_hidden(sK6525_skl,sK6524_skl)
| k1_xboole_0 != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f101983,f100893]) ).
fof(f102003,plain,
( sK6525_skl != k1_xboole_0
| k1_xboole_0 != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f101983,f100894]) ).
fof(f102011,plain,
! [X0,X1] :
( ~ r2_hidden(X1,sK6524_skl)
| ~ r2_hidden(X0,X1)
| r2_hidden(X0,k1_xboole_0) ),
inference(paramodulation,[status(thm)],[f101983,f95912]) ).
fof(f102021,plain,
r2_hidden(sK6525_skl,sK6524_skl),
inference(trivial_equality_resolution,[status(thm)],[f102000]) ).
fof(f102022,plain,
sK6525_skl != k1_xboole_0,
inference(trivial_equality_resolution,[status(thm)],[f102003]) ).
fof(f102025,plain,
! [X0,X1] :
( ~ r2_hidden(X1,sK6524_skl)
| ~ r2_hidden(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f102011,f95915]) ).
fof(f102571,plain,
! [X0] : ~ r2_hidden(X0,sK6525_skl),
inference(resolution,[status(thm)],[f102025,f102021]) ).
fof(f102718,plain,
sK6525_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f102571,f19196]) ).
fof(f102730,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f102718,f102022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU430+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n013.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 06:28:16 UTC 2026
% 0.17/0.45 % CPUTime :
% 5.02/5.30 % Drodi V4.1.1
% 17.93/7.22 % Refutation found
% 17.93/7.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.93/7.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.41/8.03 % Elapsed time: 7.489539 seconds
% 5.41/8.03 % CPU time: 20.303330 seconds
% 5.41/8.03 % Total memory used: 5.316 GB
% 5.41/8.03 % Net memory used: 5.280 GB
%------------------------------------------------------------------------------