%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:52:03 PM UTC 2026
% Result : Theorem 12.40s 2.17s
% Output : Proof 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 20 unt; 0 def)
% Number of atoms : 169 ( 36 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 171 ( 66 ~; 63 |; 27 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 10 sgn 74 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [A,B,C] :
( v1_relat_1(C)
=> ( ( r1_tarski(k2_relat_1(C),B)
& r1_tarski(k1_relat_1(C),A) )
=> m2_relset_1(C,A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_relset_1) ).
fof(f39_nnf,plain,
! [A,B,C] :
( m2_relset_1(C,A,B)
| ~ r1_tarski(k2_relat_1(C),B)
| ~ r1_tarski(k1_relat_1(C),A)
| ~ v1_relat_1(C) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [C,A,B] :
( m2_relset_1(C,A,B)
| ~ r1_tarski(k2_relat_1(C),B)
| ~ r1_tarski(k1_relat_1(C),A)
| ~ v1_relat_1(C) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c62,plain,
( m2_relset_1(X2,X0,X1)
| ~ r1_tarski(k2_relat_1(X2),X1)
| ~ r1_tarski(k1_relat_1(X2),X0)
| ~ v1_relat_1(X2) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f13,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(f13_nnf,plain,
! [A,B] :
( ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) )
| ~ v1_relat_1(B) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [B,A] :
( ( v1_funct_1(k5_relset_2(A,B))
& v1_relat_1(k5_relset_2(A,B)) )
| ~ v1_relat_1(B) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c22,plain,
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f3,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B] :
( v1_relat_1(C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f0,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relset_2) ).
fof(f0_neg,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
& v1_funct_1(k5_relset_2(A,C)) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A,B,C] :
( ( ~ m2_relset_1(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_2(k5_relset_2(A,C),k1_zfmisc_1(A),k1_zfmisc_1(k2_relat_1(C)))
| ~ v1_funct_1(k5_relset_2(A,C)) )
& m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ( ~ m2_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| ~ v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| ~ v1_funct_1(k5_relset_2(sk0,sk2)) )
& m1_subset_1(sk2,k1_zfmisc_1(k2_zfmisc_1(sk0,sk1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c0,plain,
m1_subset_1(sk2,k1_zfmisc_1(k2_zfmisc_1(sk0,sk1))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p74,plain,
v1_relat_1(sk2),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(p169,plain,
v1_relat_1(k5_relset_2(X0,sk2)),
inference(resolution,[status(thm)],[c22,p74]) ).
cnf(p384,plain,
( m2_relset_1(k5_relset_2(X0,sk2),X1,X2)
| ~ r1_tarski(k2_relat_1(k5_relset_2(X0,sk2)),X2)
| ~ r1_tarski(k1_zfmisc_1(X0),X1) ),
inference(resolution,[status(thm)],[c62,p169]) ).
fof(f38,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f38_nnf,plain,
! [A,B] : r1_tarski(A,A),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A] : r1_tarski(A,A),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c61,plain,
r1_tarski(X0,X0),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p468,plain,
( m2_relset_1(k5_relset_2(X0,sk2),k1_zfmisc_1(X0),X1)
| ~ r1_tarski(k2_relat_1(k5_relset_2(X0,sk2)),X1) ),
inference(resolution,[status(thm)],[p384,c61]) ).
fof(f41,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relset_2) ).
fof(f41_nnf,plain,
! [A,B,C] :
( r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C)))
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [C,A,B] :
( r1_tarski(k2_relat_1(k5_relset_2(A,C)),k1_zfmisc_1(k2_relat_1(C)))
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c64,plain,
( r1_tarski(k2_relat_1(k5_relset_2(X0,X2)),k1_zfmisc_1(k2_relat_1(X2)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p410,plain,
r1_tarski(k2_relat_1(k5_relset_2(sk0,sk2)),k1_zfmisc_1(k2_relat_1(sk2))),
inference(resolution,[status(thm)],[c64,c0]) ).
cnf(p470,plain,
m2_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2))),
inference(resolution,[status(thm)],[p468,p410]) ).
fof(f37,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f37_nnf,plain,
! [A,B,C] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [C,A,B] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c59,plain,
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p479,plain,
m1_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2))),
inference(resolution,[status(thm)],[p470,c59]) ).
fof(f36,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> k4_relset_1(A,B,C) = k1_relat_1(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f36_nnf,plain,
! [A,B,C] :
( k4_relset_1(A,B,C) = k1_relat_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [C,A,B] :
( k4_relset_1(A,B,C) = k1_relat_1(C)
| ~ m1_relset_1(C,A,B) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c58,plain,
( k4_relset_1(X0,X1,X2) = k1_relat_1(X2)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p481,plain,
k4_relset_1(k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)),k5_relset_2(sk0,sk2)) = k1_zfmisc_1(sk0),
inference(resolution,[status(thm)],[p479,c58]) ).
fof(f4,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( ( B = k1_xboole_0
=> ( ( v1_funct_2(C,A,B)
<=> C = k1_xboole_0 )
| A = k1_xboole_0 ) )
& ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> ( v1_funct_2(C,A,B)
<=> A = k4_relset_1(A,B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_funct_2) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ( ( ( C != k1_xboole_0
| v1_funct_2(C,A,B) )
& ( C = k1_xboole_0
| ~ v1_funct_2(C,A,B) ) )
| A = k1_xboole_0
| B != k1_xboole_0 )
& ( ( ( A != k4_relset_1(A,B,C)
| v1_funct_2(C,A,B) )
& ( A = k4_relset_1(A,B,C)
| ~ v1_funct_2(C,A,B) ) )
| ( A != k1_xboole_0
& B = k1_xboole_0 ) ) )
| ~ m2_relset_1(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B] :
( ( ( ( ( C != k1_xboole_0
| v1_funct_2(C,A,B) )
& ( C = k1_xboole_0
| ~ v1_funct_2(C,A,B) ) )
| A = k1_xboole_0
| B != k1_xboole_0 )
& ( ( ( A != k4_relset_1(A,B,C)
| v1_funct_2(C,A,B) )
& ( A = k4_relset_1(A,B,C)
| ~ v1_funct_2(C,A,B) ) )
| ( A != k1_xboole_0
& B = k1_xboole_0 ) ) )
| ~ m2_relset_1(C,A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( X0 != k4_relset_1(X0,X1,X2)
| v1_funct_2(X2,X0,X1)
| X1 = k1_xboole_0
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p473,plain,
( k1_zfmisc_1(sk0) != k4_relset_1(k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)),k5_relset_2(sk0,sk2))
| v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| k1_zfmisc_1(k2_relat_1(sk2)) = k1_xboole_0 ),
inference(resolution,[status(thm)],[p470,c6]) ).
cnf(p482,plain,
( k1_zfmisc_1(sk0) != k1_zfmisc_1(sk0)
| v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| k1_zfmisc_1(k2_relat_1(sk2)) = k1_xboole_0 ),
inference(demodulation,[status(thm)],[p481,p473]) ).
cnf(p545,plain,
( v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| k1_zfmisc_1(k2_relat_1(sk2)) = k1_xboole_0 ),
inference(equality_resolution,[status(thm)],[p482]) ).
cnf(c23,plain,
( v1_funct_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p209,plain,
v1_funct_1(k5_relset_2(X0,sk2)),
inference(resolution,[status(thm)],[c23,p74]) ).
cnf(c1,plain,
( ~ m2_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| ~ v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| ~ v1_funct_1(k5_relset_2(sk0,sk2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p223,plain,
( ~ m2_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| ~ v1_funct_2(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2))) ),
inference(resolution,[status(thm)],[p209,c1]) ).
cnf(p546,plain,
( ~ m2_relset_1(k5_relset_2(sk0,sk2),k1_zfmisc_1(sk0),k1_zfmisc_1(k2_relat_1(sk2)))
| k1_zfmisc_1(k2_relat_1(sk2)) = k1_xboole_0 ),
inference(resolution,[status(thm)],[p545,p223]) ).
cnf(p547,plain,
k1_zfmisc_1(k2_relat_1(sk2)) = k1_xboole_0,
inference(resolution,[status(thm)],[p546,p470]) ).
fof(f22,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f22_nnf,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c34,plain,
~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p585,plain,
~ v1_xboole_0(k1_xboole_0),
inference(superposition,[status(thm)],[p547,c34]) ).
fof(f21,axiom,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f21_nnf,plain,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( v3_relat_1(k1_xboole_0)
& v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c31,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p603,plain,
$false,
inference(resolution,[status(thm)],[p585,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU425+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 14:12:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.40/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.40/2.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------