%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU427+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 : n020.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 02:20:33 PM UTC 2026
% Result : Theorem 12.96s 4.15s
% Output : CNFRefutation 14.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 24 unt; 0 def)
% Number of atoms : 120 ( 66 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 45 ~; 37 |; 17 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 83 ( 72 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( v1_xboole_0(A)
<=> A = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A] : k2_xboole_0(A,k1_xboole_0) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f570,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(A))
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k4_subset_1(A,B,C) = k2_xboole_0(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19062,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A)))
=> k6_relset_2(A,B,C) = k5_relset_2(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19094,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) = k1_xboole_0
<=> C = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19097,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,E),k3_pua2mss1(C)) = k1_xboole_0
=> k8_relset_2(A,B,k4_subset_1(A,C,D),E) = k8_relset_2(A,B,D,E) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19098,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> ( k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,E),k3_pua2mss1(C)) = k1_xboole_0
=> k8_relset_2(A,B,k4_subset_1(A,C,D),E) = k8_relset_2(A,B,D,E) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19097]) ).
fof(f19178,plain,
v1_xboole_0(sK20_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(A,sK20_skl)],[f25]) ).
fof(f19179,plain,
v1_xboole_0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f19178]) ).
fof(f19220,plain,
! [A] :
( ( A != k1_xboole_0
| v1_xboole_0(A) )
& ( A = k1_xboole_0
| ~ v1_xboole_0(A) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f19221,plain,
( ! [A] :
( A != k1_xboole_0
| v1_xboole_0(A) )
& ! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ) ),
inference(miniscoping,[status(thm)],[f19220]) ).
fof(f19222,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f19221]) ).
fof(f19304,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f19311,plain,
! [X0] : k2_xboole_0(X0,k1_xboole_0) = X0,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f20317,plain,
! [A,B,C] :
( k4_subset_1(A,B,C) = k2_xboole_0(B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ m1_subset_1(B,k1_zfmisc_1(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f570]) ).
fof(f20318,plain,
! [X0,X1,X2] :
( k4_subset_1(X1,X0,X2) = k2_xboole_0(X0,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(X1))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f20317]) ).
fof(f89208,plain,
! [A,B,C] :
( k6_relset_2(A,B,C) = k5_relset_2(B,C)
| ~ m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ),
inference(pre_NNF_transformation,[status(thm)],[f19062]) ).
fof(f89209,plain,
! [X0,X1,X2] :
( k6_relset_2(X2,X1,X0) = k5_relset_2(X1,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f89208]) ).
fof(f89296,plain,
! [A,B,C] :
( ! [D] :
( ( k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) = k1_xboole_0
<=> C = k1_xboole_0 )
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f19094]) ).
fof(f89297,plain,
! [A,B,C] :
( ! [D] :
( ( ( C != k1_xboole_0
| k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) = k1_xboole_0 )
& ( C = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) != k1_xboole_0 ) )
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(NNF_transformation,[status(thm)],[f89296]) ).
fof(f89298,plain,
! [A,C] :
( ! [B,D] :
( ( ( C != k1_xboole_0
| k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) = k1_xboole_0 )
& ( C = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,D),k3_pua2mss1(C)) != k1_xboole_0 ) )
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(miniscoping,[status(thm)],[f89297]) ).
fof(f89299,plain,
! [X0,X1,X2,X3] :
( X0 = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(X1),X3,k6_relset_2(X3,X1,X2),k3_pua2mss1(X0)) != k1_xboole_0
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(cnf_transformation,[status(thm)],[f89298]) ).
fof(f89310,plain,
? [A,B,C] :
( ? [D] :
( ? [E] :
( k8_relset_2(A,B,k4_subset_1(A,C,D),E) != k8_relset_2(A,B,D,E)
& k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,E),k3_pua2mss1(C)) = k1_xboole_0
& m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
& m1_subset_1(D,k1_zfmisc_1(A)) )
& m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f19098]) ).
fof(f89311,plain,
? [A,C] :
( ? [D] :
( ? [B,E] :
( k8_relset_2(A,B,k4_subset_1(A,C,D),E) != k8_relset_2(A,B,D,E)
& k4_relset_2(k1_zfmisc_1(A),B,k6_relset_2(B,A,E),k3_pua2mss1(C)) = k1_xboole_0
& m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
& m1_subset_1(D,k1_zfmisc_1(A)) )
& m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(miniscoping,[status(thm)],[f89310]) ).
fof(f89312,plain,
( k8_relset_2(sK6523_skl,sK6526_skl,k4_subset_1(sK6523_skl,sK6524_skl,sK6525_skl),sK6527_skl) != k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl)
& k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k6_relset_2(sK6526_skl,sK6523_skl,sK6527_skl),k3_pua2mss1(sK6524_skl)) = k1_xboole_0
& m1_subset_1(sK6527_skl,k1_zfmisc_1(k2_zfmisc_1(sK6523_skl,sK6526_skl)))
& m1_subset_1(sK6525_skl,k1_zfmisc_1(sK6523_skl))
& m1_subset_1(sK6524_skl,k1_zfmisc_1(sK6523_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6523_skl,sK6524_skl,sK6525_skl,sK6526_skl,sK6527_skl]),skolemize(A,sK6523_skl),skolemize(C,sK6524_skl),skolemize(D,sK6525_skl),skolemize(B,sK6526_skl),skolemize(E,sK6527_skl)],[f89311]) ).
fof(f89313,plain,
m1_subset_1(sK6524_skl,k1_zfmisc_1(sK6523_skl)),
inference(cnf_transformation,[status(thm)],[f89312]) ).
fof(f89314,plain,
m1_subset_1(sK6525_skl,k1_zfmisc_1(sK6523_skl)),
inference(cnf_transformation,[status(thm)],[f89312]) ).
fof(f89315,plain,
m1_subset_1(sK6527_skl,k1_zfmisc_1(k2_zfmisc_1(sK6523_skl,sK6526_skl))),
inference(cnf_transformation,[status(thm)],[f89312]) ).
fof(f89316,plain,
k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k6_relset_2(sK6526_skl,sK6523_skl,sK6527_skl),k3_pua2mss1(sK6524_skl)) = k1_xboole_0,
inference(cnf_transformation,[status(thm)],[f89312]) ).
fof(f89317,plain,
k8_relset_2(sK6523_skl,sK6526_skl,k4_subset_1(sK6523_skl,sK6524_skl,sK6525_skl),sK6527_skl) != k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl),
inference(cnf_transformation,[status(thm)],[f89312]) ).
fof(f100756,plain,
sK20_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f19179,f19222]) ).
fof(f100812,plain,
k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k6_relset_2(sK6526_skl,sK6523_skl,sK6527_skl),k3_pua2mss1(sK6524_skl)) = sK20_skl,
inference(backward_demodulation,[status(thm)],[f100756,f89316]) ).
fof(f100847,plain,
! [X0] :
( k4_subset_1(sK6523_skl,X0,sK6525_skl) = k2_xboole_0(X0,sK6525_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6523_skl)) ),
inference(resolution,[status(thm)],[f20318,f89314]) ).
fof(f100964,plain,
k4_subset_1(sK6523_skl,sK6524_skl,sK6525_skl) = k2_xboole_0(sK6524_skl,sK6525_skl),
inference(resolution,[status(thm)],[f100847,f89313]) ).
fof(f101025,plain,
k8_relset_2(sK6523_skl,sK6526_skl,k2_xboole_0(sK6524_skl,sK6525_skl),sK6527_skl) != k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl),
inference(backward_demodulation,[status(thm)],[f100964,f89317]) ).
fof(f101179,plain,
k6_relset_2(sK6526_skl,sK6523_skl,sK6527_skl) = k5_relset_2(sK6523_skl,sK6527_skl),
inference(resolution,[status(thm)],[f89209,f89315]) ).
fof(f101223,plain,
k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k5_relset_2(sK6523_skl,sK6527_skl),k3_pua2mss1(sK6524_skl)) = sK20_skl,
inference(backward_demodulation,[status(thm)],[f101179,f100812]) ).
fof(f101484,plain,
! [X0,X1,X2,X3] :
( X0 = k1_xboole_0
| k4_relset_2(k1_zfmisc_1(X1),X3,k6_relset_2(X3,X1,X2),k3_pua2mss1(X0)) != sK20_skl
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(forward_demodulation,[status(thm)],[f100756,f89299]) ).
fof(f101485,plain,
! [X0,X1,X2,X3] :
( X0 = sK20_skl
| k4_relset_2(k1_zfmisc_1(X1),X3,k6_relset_2(X3,X1,X2),k3_pua2mss1(X0)) != sK20_skl
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(forward_demodulation,[status(thm)],[f100756,f101484]) ).
fof(f101488,plain,
! [X0] :
( X0 = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k6_relset_2(sK6526_skl,sK6523_skl,sK6527_skl),k3_pua2mss1(X0)) != sK20_skl
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6523_skl)) ),
inference(resolution,[status(thm)],[f101485,f89315]) ).
fof(f101492,plain,
! [X0] :
( X0 = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k5_relset_2(sK6523_skl,sK6527_skl),k3_pua2mss1(X0)) != sK20_skl
| ~ m1_subset_1(X0,k1_zfmisc_1(sK6523_skl)) ),
inference(forward_demodulation,[status(thm)],[f101179,f101488]) ).
fof(f101831,plain,
( sK6524_skl = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK6523_skl),sK6526_skl,k5_relset_2(sK6523_skl,sK6527_skl),k3_pua2mss1(sK6524_skl)) != sK20_skl ),
inference(resolution,[status(thm)],[f101492,f89313]) ).
fof(f101832,plain,
( sK6524_skl = sK20_skl
| sK20_skl != sK20_skl ),
inference(forward_demodulation,[status(thm)],[f101223,f101831]) ).
fof(f101833,plain,
sK6524_skl = sK20_skl,
inference(trivial_equality_resolution,[status(thm)],[f101832]) ).
fof(f101844,plain,
k8_relset_2(sK6523_skl,sK6526_skl,k2_xboole_0(sK20_skl,sK6525_skl),sK6527_skl) != k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl),
inference(backward_demodulation,[status(thm)],[f101833,f101025]) ).
fof(f102969,plain,
! [X0] : k2_xboole_0(X0,sK20_skl) = X0,
inference(forward_demodulation,[status(thm)],[f100756,f19311]) ).
fof(f102971,plain,
! [X0] : k2_xboole_0(sK20_skl,X0) = X0,
inference(paramodulation,[status(thm)],[f19304,f102969]) ).
fof(f103014,plain,
k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl) != k8_relset_2(sK6523_skl,sK6526_skl,sK6525_skl,sK6527_skl),
inference(backward_demodulation,[status(thm)],[f102971,f101844]) ).
fof(f103052,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f103014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU427+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 06:28:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 2.33/2.61 % Drodi V4.1.1
% 12.96/4.15 % Refutation found
% 12.96/4.15 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.96/4.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.32/4.59 % Elapsed time: 4.105136 seconds
% 6.32/4.59 % CPU time: 14.633345 seconds
% 6.32/4.59 % Total memory used: 5.337 GB
% 6.32/4.59 % Net memory used: 5.297 GB
%------------------------------------------------------------------------------