%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU427+4 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 95.00s 25.56s
% Output : CNFRefutation 49.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 25 unt; 0 def)
% Number of atoms : 126 ( 68 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 46 ~; 39 |; 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 : 92 ( 81 !; 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(f486,axiom,
! [A] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(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(f71073,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(f71105,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(f71108,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(f71109,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)],[f71108]) ).
fof(f71189,plain,
v1_xboole_0(sK20_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(A,sK20_skl)],[f25]) ).
fof(f71190,plain,
v1_xboole_0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f71189]) ).
fof(f71231,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(f71232,plain,
( ! [A] :
( A != k1_xboole_0
| v1_xboole_0(A) )
& ! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ) ),
inference(miniscoping,[status(thm)],[f71231]) ).
fof(f71233,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f71232]) ).
fof(f71315,plain,
! [X0,X1] : k2_xboole_0(X0,X1) = k2_xboole_0(X1,X0),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f71322,plain,
! [X0] : k2_xboole_0(X0,k1_xboole_0) = X0,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f72102,plain,
! [X0] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f486]) ).
fof(f72328,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(f72329,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)],[f72328]) ).
fof(f335911,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)],[f71073]) ).
fof(f335912,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)],[f335911]) ).
fof(f335999,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)],[f71105]) ).
fof(f336000,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)],[f335999]) ).
fof(f336001,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)],[f336000]) ).
fof(f336002,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)],[f336001]) ).
fof(f336013,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)],[f71109]) ).
fof(f336014,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)],[f336013]) ).
fof(f336015,plain,
( k8_relset_2(sK23836_skl,sK23839_skl,k4_subset_1(sK23836_skl,sK23837_skl,sK23838_skl),sK23840_skl) != k8_relset_2(sK23836_skl,sK23839_skl,sK23838_skl,sK23840_skl)
& k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k6_relset_2(sK23839_skl,sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) = k1_xboole_0
& m1_subset_1(sK23840_skl,k1_zfmisc_1(k2_zfmisc_1(sK23836_skl,sK23839_skl)))
& m1_subset_1(sK23838_skl,k1_zfmisc_1(sK23836_skl))
& m1_subset_1(sK23837_skl,k1_zfmisc_1(sK23836_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23836_skl,sK23837_skl,sK23838_skl,sK23839_skl,sK23840_skl]),skolemize(A,sK23836_skl),skolemize(C,sK23837_skl),skolemize(D,sK23838_skl),skolemize(B,sK23839_skl),skolemize(E,sK23840_skl)],[f336014]) ).
fof(f336016,plain,
m1_subset_1(sK23837_skl,k1_zfmisc_1(sK23836_skl)),
inference(cnf_transformation,[status(thm)],[f336015]) ).
fof(f336017,plain,
m1_subset_1(sK23838_skl,k1_zfmisc_1(sK23836_skl)),
inference(cnf_transformation,[status(thm)],[f336015]) ).
fof(f336018,plain,
m1_subset_1(sK23840_skl,k1_zfmisc_1(k2_zfmisc_1(sK23836_skl,sK23839_skl))),
inference(cnf_transformation,[status(thm)],[f336015]) ).
fof(f336019,plain,
k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k6_relset_2(sK23839_skl,sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) = k1_xboole_0,
inference(cnf_transformation,[status(thm)],[f336015]) ).
fof(f336020,plain,
k8_relset_2(sK23836_skl,sK23839_skl,k4_subset_1(sK23836_skl,sK23837_skl,sK23838_skl),sK23840_skl) != k8_relset_2(sK23836_skl,sK23839_skl,sK23838_skl,sK23840_skl),
inference(cnf_transformation,[status(thm)],[f336015]) ).
fof(f370933,plain,
sK20_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f71190,f71233]) ).
fof(f371208,plain,
! [X0,X1] :
( k4_subset_1(X1,k1_xboole_0,X0) = k2_xboole_0(k1_xboole_0,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(resolution,[status(thm)],[f72329,f72102]) ).
fof(f371355,plain,
k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k6_relset_2(sK23839_skl,sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) = sK20_skl,
inference(backward_demodulation,[status(thm)],[f370933,f336019]) ).
fof(f373336,plain,
k6_relset_2(sK23839_skl,sK23836_skl,sK23840_skl) = k5_relset_2(sK23836_skl,sK23840_skl),
inference(resolution,[status(thm)],[f335912,f336018]) ).
fof(f373375,plain,
! [X0] : k2_xboole_0(X0,sK20_skl) = X0,
inference(forward_demodulation,[status(thm)],[f370933,f71322]) ).
fof(f373385,plain,
! [X0] : k2_xboole_0(sK20_skl,X0) = X0,
inference(paramodulation,[status(thm)],[f71315,f373375]) ).
fof(f373586,plain,
k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k5_relset_2(sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) = sK20_skl,
inference(backward_demodulation,[status(thm)],[f373336,f371355]) ).
fof(f373967,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)],[f370933,f336002]) ).
fof(f373968,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)],[f370933,f373967]) ).
fof(f373982,plain,
! [X0,X1] :
( sK23837_skl = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK23836_skl),X1,k6_relset_2(X1,sK23836_skl,X0),k3_pua2mss1(sK23837_skl)) != sK20_skl
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(sK23836_skl,X1))) ),
inference(resolution,[status(thm)],[f373968,f336016]) ).
fof(f376060,plain,
( sK23837_skl = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k6_relset_2(sK23839_skl,sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) != sK20_skl ),
inference(resolution,[status(thm)],[f373982,f336018]) ).
fof(f376062,plain,
( sK23837_skl = sK20_skl
| k4_relset_2(k1_zfmisc_1(sK23836_skl),sK23839_skl,k5_relset_2(sK23836_skl,sK23840_skl),k3_pua2mss1(sK23837_skl)) != sK20_skl ),
inference(forward_demodulation,[status(thm)],[f373336,f376060]) ).
fof(f376063,plain,
( sK23837_skl = sK20_skl
| sK20_skl != sK20_skl ),
inference(forward_demodulation,[status(thm)],[f373586,f376062]) ).
fof(f376064,plain,
sK23837_skl = sK20_skl,
inference(trivial_equality_resolution,[status(thm)],[f376063]) ).
fof(f376109,plain,
k8_relset_2(sK23836_skl,sK23839_skl,k4_subset_1(sK23836_skl,sK20_skl,sK23838_skl),sK23840_skl) != k8_relset_2(sK23836_skl,sK23839_skl,sK23838_skl,sK23840_skl),
inference(backward_demodulation,[status(thm)],[f376064,f336020]) ).
fof(f378294,plain,
! [X0,X1] :
( k4_subset_1(X1,sK20_skl,X0) = k2_xboole_0(k1_xboole_0,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(forward_demodulation,[status(thm)],[f370933,f371208]) ).
fof(f378295,plain,
! [X0,X1] :
( k4_subset_1(X1,sK20_skl,X0) = k2_xboole_0(sK20_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(forward_demodulation,[status(thm)],[f370933,f378294]) ).
fof(f378296,plain,
! [X0,X1] :
( k4_subset_1(X1,sK20_skl,X0) = X0
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(forward_demodulation,[status(thm)],[f373385,f378295]) ).
fof(f378307,plain,
k4_subset_1(sK23836_skl,sK20_skl,sK23838_skl) = sK23838_skl,
inference(resolution,[status(thm)],[f378296,f336017]) ).
fof(f395848,plain,
k8_relset_2(sK23836_skl,sK23839_skl,sK23838_skl,sK23840_skl) != k8_relset_2(sK23836_skl,sK23839_skl,sK23838_skl,sK23840_skl),
inference(backward_demodulation,[status(thm)],[f378307,f376109]) ).
fof(f395849,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f395848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU427+4 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 : Mon Sep 21 06:29:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 15.06/15.36 % Drodi V4.1.1
% 95.00/25.56 % Refutation found
% 95.00/25.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 95.00/25.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 91.64/27.67 % Elapsed time: 26.338047 seconds
% 91.64/27.67 % CPU time: 88.032429 seconds
% 91.64/27.67 % Total memory used: 19.141 GB
% 91.64/27.67 % Net memory used: 18.983 GB
%------------------------------------------------------------------------------