%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 01:40:25 PM UTC 2026
% Result : Theorem 0.06s 0.36s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 132 ( 51 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 149 ( 55 ~; 61 |; 26 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 84 ( 78 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( succ(A) = succ(B)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( succ(A) = succ(B)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f37,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f47,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f49,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f50,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f56,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f57,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f56]) ).
fof(f58,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f116,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f117,plain,
? [A,B] :
( A != B
& succ(A) = succ(B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f118,plain,
( sK13_skl != sK14_skl
& succ(sK13_skl) = succ(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f117]) ).
fof(f119,plain,
succ(sK13_skl) = succ(sK14_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
sK13_skl != sK14_skl,
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f134,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f136,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f140,plain,
in(sK14_skl,succ(sK13_skl)),
inference(paramodulation,[status(thm)],[f119,f116]) ).
fof(f145,plain,
! [X0] : succ(X0) = set_union2(singleton(X0),X0),
inference(paramodulation,[status(thm)],[f48,f47]) ).
fof(f163,plain,
! [X0,X1] :
( in(X0,X1)
| in(X0,singleton(X1))
| ~ in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f145,f136]) ).
fof(f169,plain,
! [X0,X1] :
( X0 = X1
| in(X0,X1)
| ~ in(X0,succ(X1)) ),
inference(resolution,[status(thm)],[f163,f134]) ).
fof(f172,plain,
( sK14_skl = sK13_skl
| in(sK14_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f169,f140]) ).
fof(f174,plain,
! [X0] :
( X0 = sK14_skl
| in(X0,sK14_skl)
| ~ in(X0,succ(sK13_skl)) ),
inference(paramodulation,[status(thm)],[f119,f169]) ).
fof(f175,plain,
in(sK14_skl,sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f172,f120]) ).
fof(f176,plain,
~ in(sK13_skl,sK14_skl),
inference(resolution,[status(thm)],[f175,f38]) ).
fof(f179,plain,
( sK13_skl = sK14_skl
| in(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f174,f116]) ).
fof(f180,plain,
sK13_skl = sK14_skl,
inference(forward_subsumption_resolution,[status(thm)],[f179,f176]) ).
fof(f181,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f180,f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM385+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.32 % Computer : n011.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Mon Sep 21 02:26:40 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.33 % Drodi V4.1.1
% 0.06/0.36 % Refutation found
% 0.06/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.40 % Elapsed time: 0.060281 seconds
% 0.10/0.40 % CPU time: 0.160365 seconds
% 0.10/0.40 % Total memory used: 102.650 MB
% 0.10/0.40 % Net memory used: 102.623 MB
%------------------------------------------------------------------------------