%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:20:40 PM UTC 2026
% Result : Theorem 0.13s 0.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 85 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 29 ~; 22 |; 10 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 98 ( 95 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> k9_relset_2(A,A,B,k6_partfun1(A),C) = k9_relset_2(A,B,B,C,k6_partfun1(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A,B,C] :
( m2_relset_1(C,A,B)
=> k9_relset_2(A,A,B,k6_partfun1(A),C) = k9_relset_2(A,B,B,C,k6_partfun1(B)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f11,axiom,
! [A] :
( m2_relset_1(k6_partfun1(A),A,A)
& v1_partfun1(k6_partfun1(A),A,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(F,C,D)
& m1_relset_1(E,A,B) )
=> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C)))
& m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) )
=> k9_relset_2(A,B,C,D,E) = k5_relat_1(D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> ( k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C
& k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,plain,
? [A,B,C] :
( k9_relset_2(A,A,B,k6_partfun1(A),C) != k9_relset_2(A,B,B,C,k6_partfun1(B))
& m2_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f51,plain,
( k9_relset_2(sK0_skl,sK0_skl,sK1_skl,k6_partfun1(sK0_skl),sK2_skl) != k9_relset_2(sK0_skl,sK1_skl,sK1_skl,sK2_skl,k6_partfun1(sK1_skl))
& m2_relset_1(sK2_skl,sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f50]) ).
fof(f52,plain,
m2_relset_1(sK2_skl,sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
k9_relset_2(sK0_skl,sK0_skl,sK1_skl,k6_partfun1(sK0_skl),sK2_skl) != k9_relset_2(sK0_skl,sK1_skl,sK1_skl,sK2_skl,k6_partfun1(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f66,plain,
( ! [A] : m2_relset_1(k6_partfun1(A),A,A)
& ! [A] : v1_partfun1(k6_partfun1(A),A,A) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f68,plain,
! [X0] : m2_relset_1(k6_partfun1(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f74,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f75,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f133,plain,
! [A,B,C,D,E,F] :
( k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F)
| ~ m1_relset_1(F,C,D)
| ~ m1_relset_1(E,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f134,plain,
! [X0,X1,X2,X3,X4,X5] :
( k7_relset_1(X1,X2,X4,X5,X0,X3) = k5_relat_1(X0,X3)
| ~ m1_relset_1(X3,X4,X5)
| ~ m1_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [A,B,C,D,E] :
( k9_relset_2(A,B,C,D,E) = k5_relat_1(D,E)
| ~ m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C)))
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( k9_relset_2(X1,X2,X4,X0,X3) = k5_relat_1(X0,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X4)))
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,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)],[f39]) ).
fof(f138,plain,
( ! [A,B,C] :
( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ! [A,B,C] :
( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f137]) ).
fof(f139,plain,
! [X0,X1,X2] :
( m1_relset_1(X0,X1,X2)
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f145,plain,
! [A,B,C] :
( ( k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C
& k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C )
| ~ m2_relset_1(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f146,plain,
! [X0,X1,X2] :
( k7_relset_1(X1,X1,X1,X2,k6_partfun1(X1),X0) = X0
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( k7_relset_1(X1,X2,X2,X2,X0,k6_partfun1(X2)) = X0
| ~ m2_relset_1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f220,plain,
! [X0] : m1_subset_1(k6_partfun1(X0),k1_zfmisc_1(k2_zfmisc_1(X0,X0))),
inference(resolution,[status(thm)],[f75,f68]) ).
fof(f221,plain,
m1_subset_1(sK2_skl,k1_zfmisc_1(k2_zfmisc_1(sK0_skl,sK1_skl))),
inference(resolution,[status(thm)],[f75,f52]) ).
fof(f230,plain,
! [X0,X1] :
( k9_relset_2(sK0_skl,sK1_skl,X1,sK2_skl,X0) = k5_relat_1(sK2_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(sK1_skl,X1))) ),
inference(resolution,[status(thm)],[f221,f136]) ).
fof(f247,plain,
k9_relset_2(sK0_skl,sK1_skl,sK1_skl,sK2_skl,k6_partfun1(sK1_skl)) = k5_relat_1(sK2_skl,k6_partfun1(sK1_skl)),
inference(resolution,[status(thm)],[f220,f230]) ).
fof(f249,plain,
! [X0,X1,X2] :
( k9_relset_2(X1,X1,X2,k6_partfun1(X1),X0) = k5_relat_1(k6_partfun1(X1),X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ),
inference(resolution,[status(thm)],[f220,f136]) ).
fof(f251,plain,
k9_relset_2(sK0_skl,sK0_skl,sK1_skl,k6_partfun1(sK0_skl),sK2_skl) != k5_relat_1(sK2_skl,k6_partfun1(sK1_skl)),
inference(backward_demodulation,[status(thm)],[f247,f53]) ).
fof(f312,plain,
k9_relset_2(sK0_skl,sK0_skl,sK1_skl,k6_partfun1(sK0_skl),sK2_skl) = k5_relat_1(k6_partfun1(sK0_skl),sK2_skl),
inference(resolution,[status(thm)],[f249,f221]) ).
fof(f314,plain,
k5_relat_1(k6_partfun1(sK0_skl),sK2_skl) != k5_relat_1(sK2_skl,k6_partfun1(sK1_skl)),
inference(backward_demodulation,[status(thm)],[f312,f251]) ).
fof(f490,plain,
! [X0] : m1_relset_1(k6_partfun1(X0),X0,X0),
inference(resolution,[status(thm)],[f139,f68]) ).
fof(f491,plain,
m1_relset_1(sK2_skl,sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f139,f52]) ).
fof(f496,plain,
! [X0,X1,X2] :
( k7_relset_1(sK0_skl,sK1_skl,X1,X2,sK2_skl,X0) = k5_relat_1(sK2_skl,X0)
| ~ m1_relset_1(X0,X1,X2) ),
inference(resolution,[status(thm)],[f491,f134]) ).
fof(f499,plain,
! [X0,X1,X2,X3] :
( k7_relset_1(X3,X3,X1,X2,k6_partfun1(X3),X0) = k5_relat_1(k6_partfun1(X3),X0)
| ~ m1_relset_1(X0,X1,X2) ),
inference(resolution,[status(thm)],[f490,f134]) ).
fof(f525,plain,
k7_relset_1(sK0_skl,sK0_skl,sK0_skl,sK1_skl,k6_partfun1(sK0_skl),sK2_skl) = sK2_skl,
inference(resolution,[status(thm)],[f146,f52]) ).
fof(f533,plain,
k7_relset_1(sK0_skl,sK1_skl,sK1_skl,sK1_skl,sK2_skl,k6_partfun1(sK1_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f147,f52]) ).
fof(f788,plain,
! [X0] : k7_relset_1(sK0_skl,sK1_skl,X0,X0,sK2_skl,k6_partfun1(X0)) = k5_relat_1(sK2_skl,k6_partfun1(X0)),
inference(resolution,[status(thm)],[f496,f490]) ).
fof(f793,plain,
k5_relat_1(sK2_skl,k6_partfun1(sK1_skl)) = sK2_skl,
inference(backward_demodulation,[status(thm)],[f788,f533]) ).
fof(f794,plain,
k5_relat_1(k6_partfun1(sK0_skl),sK2_skl) != sK2_skl,
inference(backward_demodulation,[status(thm)],[f793,f314]) ).
fof(f1105,plain,
! [X0] : k7_relset_1(X0,X0,sK0_skl,sK1_skl,k6_partfun1(X0),sK2_skl) = k5_relat_1(k6_partfun1(X0),sK2_skl),
inference(resolution,[status(thm)],[f499,f491]) ).
fof(f1110,plain,
k5_relat_1(k6_partfun1(sK0_skl),sK2_skl) = sK2_skl,
inference(backward_demodulation,[status(thm)],[f1105,f525]) ).
fof(f1114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1110,f794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:35:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.53 % Refutation found
% 0.13/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.55 % Elapsed time: 0.185544 seconds
% 0.13/0.55 % CPU time: 1.202613 seconds
% 0.13/0.55 % Total memory used: 135.031 MB
% 0.13/0.55 % Net memory used: 132.801 MB
%------------------------------------------------------------------------------