%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 02:19:17 PM UTC 2026
% Result : Theorem 0.11s 0.62s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 91 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 106 ( 40 ~; 40 |; 21 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A,B] : subset(A,set_union2(A,B)),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f35,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f47,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)],[f6]) ).
fof(f48,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)],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f56,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f57,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( in(sK2_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(sK2_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f118,plain,
? [A,B] : ~ subset(A,set_union2(A,B)),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f119,plain,
~ subset(sK8_skl,set_union2(sK8_skl,sK9_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f118]) ).
fof(f120,plain,
~ subset(sK8_skl,set_union2(sK8_skl,sK9_skl)),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f133,plain,
~ subset(sK8_skl,set_union2(sK9_skl,sK8_skl)),
inference(backward_demodulation,[status(thm)],[f35,f120]) ).
fof(f291,plain,
in(sK2_skl(set_union2(sK9_skl,sK8_skl),sK8_skl),sK8_skl),
inference(resolution,[status(thm)],[f61,f133]) ).
fof(f310,plain,
! [X0] : in(sK2_skl(set_union2(sK9_skl,sK8_skl),sK8_skl),set_union2(X0,sK8_skl)),
inference(resolution,[status(thm)],[f291,f129]) ).
fof(f382,plain,
subset(sK8_skl,set_union2(sK9_skl,sK8_skl)),
inference(resolution,[status(thm)],[f310,f62]) ).
fof(f394,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f382,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.59 % Computer : n014.cluster.edu
% 0.11/0.59 % Model : x86_64 x86_64
% 0.11/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.59 % Memory : 8046.5625MB
% 0.11/0.59 % OS : Linux 6.8.0-71-generic
% 0.11/0.59 % CPULimit : 300
% 0.11/0.59 % WCLimit : 300
% 0.11/0.59 % DateTime : Mon Sep 21 05:51:20 UTC 2026
% 0.11/0.59 % CPUTime :
% 0.11/0.60 % Drodi V4.1.1
% 0.11/0.62 % Refutation found
% 0.11/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.64 % Elapsed time: 0.046362 seconds
% 0.16/0.64 % CPU time: 0.191332 seconds
% 0.16/0.64 % Total memory used: 34.091 MB
% 0.16/0.64 % Net memory used: 33.699 MB
%------------------------------------------------------------------------------