%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU430+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 02:20:34 PM UTC 2026
% Result : Theorem 1.09s 1.88s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 9 unt; 0 def)
% Number of atoms : 175 ( 69 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 191 ( 67 ~; 82 |; 28 &)
% ( 6 <=>; 6 =>; 0 <=; 2 <~>)
% 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 : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 99 ( 83 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f532,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(f4502,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(f4503,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)],[f4502]) ).
fof(f4506,plain,
! [A,B] :
( A = B
| ? [C] :
( r2_hidden(C,A)
<~> r2_hidden(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f4507,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ r2_hidden(C,B)
| ~ r2_hidden(C,A) )
& ( r2_hidden(C,B)
| r2_hidden(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f4506]) ).
fof(f4508,plain,
! [A,B] :
( A = B
| ( ( ~ r2_hidden(sK0_skl(B,A),B)
| ~ r2_hidden(sK0_skl(B,A),A) )
& ( r2_hidden(sK0_skl(B,A),B)
| r2_hidden(sK0_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f4507]) ).
fof(f4509,plain,
! [X0,X1] :
( X1 = X0
| r2_hidden(sK0_skl(X0,X1),X0)
| r2_hidden(sK0_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f4508]) ).
fof(f4534,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(f4535,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)],[f4534]) ).
fof(f4536,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))],[f4535]) ).
fof(f4539,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)],[f4536]) ).
fof(f4541,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)],[f4536]) ).
fof(f4542,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)],[f4536]) ).
fof(f4593,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(f4594,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)],[f4593]) ).
fof(f4595,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))],[f4594]) ).
fof(f4596,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| X0 != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f4595]) ).
fof(f5818,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)],[f532]) ).
fof(f5819,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)],[f5818]) ).
fof(f17605,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)],[f4503]) ).
fof(f17606,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)],[f17605]) ).
fof(f17607,plain,
( ( ( sK1208_skl != k1_xboole_0
& r2_hidden(sK1208_skl,sK1207_skl) )
| k5_setfam_1(sK1206_skl,sK1207_skl) != k1_xboole_0 )
& ( ! [C] :
( C = k1_xboole_0
| ~ r2_hidden(C,sK1207_skl) )
| k5_setfam_1(sK1206_skl,sK1207_skl) = k1_xboole_0 )
& m1_subset_1(sK1207_skl,k1_zfmisc_1(k1_zfmisc_1(sK1206_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1206_skl,sK1207_skl,sK1208_skl]),skolemize(A,sK1206_skl),skolemize(B,sK1207_skl),skolemize(C,sK1208_skl)],[f17606]) ).
fof(f17608,plain,
m1_subset_1(sK1207_skl,k1_zfmisc_1(k1_zfmisc_1(sK1206_skl))),
inference(cnf_transformation,[status(thm)],[f17607]) ).
fof(f17609,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1207_skl)
| k5_setfam_1(sK1206_skl,sK1207_skl) = k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f17607]) ).
fof(f17610,plain,
( r2_hidden(sK1208_skl,sK1207_skl)
| k5_setfam_1(sK1206_skl,sK1207_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f17607]) ).
fof(f17611,plain,
( sK1208_skl != k1_xboole_0
| k5_setfam_1(sK1206_skl,sK1207_skl) != k1_xboole_0 ),
inference(cnf_transformation,[status(thm)],[f17607]) ).
fof(f18870,plain,
! [X0,X1,X2] :
( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X0,X2)
| r2_hidden(X0,k3_tarski(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f4539]) ).
fof(f18873,plain,
! [X0] : ~ r2_hidden(X0,k1_xboole_0),
inference(destructive_equality_resolution,[status(thm)],[f4596]) ).
fof(f19892,plain,
! [X0] :
( k1_xboole_0 = X0
| r2_hidden(sK0_skl(X0,k1_xboole_0),X0) ),
inference(resolution,[status(thm)],[f4509,f18873]) ).
fof(f19948,plain,
k5_setfam_1(sK1206_skl,sK1207_skl) = k3_tarski(sK1207_skl),
inference(resolution,[status(thm)],[f5819,f17608]) ).
fof(f19961,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r2_hidden(X0,sK1207_skl)
| k3_tarski(sK1207_skl) = k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f19948,f17609]) ).
fof(f19962,plain,
( r2_hidden(sK1208_skl,sK1207_skl)
| k3_tarski(sK1207_skl) != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f19948,f17610]) ).
fof(f19963,plain,
( sK1208_skl != k1_xboole_0
| k3_tarski(sK1207_skl) != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f19948,f17611]) ).
fof(f20835,plain,
! [X0] :
( sK6_skl(X0,sK1207_skl) = k1_xboole_0
| k3_tarski(sK1207_skl) = k1_xboole_0
| r2_hidden(sK5_skl(X0,sK1207_skl),X0)
| X0 = k3_tarski(sK1207_skl) ),
inference(resolution,[status(thm)],[f4542,f19961]) ).
fof(f21071,plain,
( sK6_skl(k1_xboole_0,sK1207_skl) = k1_xboole_0
| k3_tarski(sK1207_skl) = k1_xboole_0
| k1_xboole_0 = k3_tarski(sK1207_skl) ),
inference(resolution,[status(thm)],[f20835,f18873]) ).
fof(f21107,plain,
( sK6_skl(k1_xboole_0,sK1207_skl) = k1_xboole_0
| k1_xboole_0 = k3_tarski(sK1207_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f21071]) ).
fof(f21501,plain,
( k1_xboole_0 = k3_tarski(sK1207_skl)
| r2_hidden(sK5_skl(k1_xboole_0,sK1207_skl),k1_xboole_0)
| r2_hidden(sK5_skl(k1_xboole_0,sK1207_skl),k1_xboole_0)
| k1_xboole_0 = k3_tarski(sK1207_skl) ),
inference(paramodulation,[status(thm)],[f21107,f4541]) ).
fof(f21504,plain,
( r2_hidden(sK5_skl(k1_xboole_0,sK1207_skl),k1_xboole_0)
| k1_xboole_0 = k3_tarski(sK1207_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f21501]) ).
fof(f21505,plain,
k1_xboole_0 = k3_tarski(sK1207_skl),
inference(forward_subsumption_resolution,[status(thm)],[f21504,f18873]) ).
fof(f21520,plain,
( r2_hidden(sK1208_skl,sK1207_skl)
| k1_xboole_0 != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f21505,f19962]) ).
fof(f21523,plain,
( sK1208_skl != k1_xboole_0
| k1_xboole_0 != k1_xboole_0 ),
inference(backward_demodulation,[status(thm)],[f21505,f19963]) ).
fof(f21534,plain,
! [X0,X1] :
( ~ r2_hidden(X1,sK1207_skl)
| ~ r2_hidden(X0,X1)
| r2_hidden(X0,k1_xboole_0) ),
inference(paramodulation,[status(thm)],[f21505,f18870]) ).
fof(f21539,plain,
r2_hidden(sK1208_skl,sK1207_skl),
inference(trivial_equality_resolution,[status(thm)],[f21520]) ).
fof(f21540,plain,
sK1208_skl != k1_xboole_0,
inference(trivial_equality_resolution,[status(thm)],[f21523]) ).
fof(f21542,plain,
! [X0,X1] :
( ~ r2_hidden(X1,sK1207_skl)
| ~ r2_hidden(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f21534,f18873]) ).
fof(f21625,plain,
! [X0] : ~ r2_hidden(X0,sK1208_skl),
inference(resolution,[status(thm)],[f21542,f21539]) ).
fof(f21639,plain,
k1_xboole_0 = sK1208_skl,
inference(resolution,[status(thm)],[f21625,f19892]) ).
fof(f21641,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21639,f21540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU430+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n026.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 06:30:52 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.79/1.06 % Drodi V4.1.1
% 1.09/1.88 % Refutation found
% 1.09/1.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.09/1.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.14/2.04 % Elapsed time: 1.600812 seconds
% 1.14/2.04 % CPU time: 7.263453 seconds
% 1.14/2.04 % Total memory used: 763.192 MB
% 1.14/2.04 % Net memory used: 752.152 MB
%------------------------------------------------------------------------------