%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET874+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 : 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 02:10:52 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 63 ( 43 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 77 ( 30 ~; 29 |; 15 &)
% ( 2 <=>; 1 =>; 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f17,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ! [A,B,C] :
( ( ( sK0_skl(C,B,A) = B
| sK0_skl(C,B,A) = A
| in(sK0_skl(C,B,A),C) )
& ( ( sK0_skl(C,B,A) != B
& sK0_skl(C,B,A) != A )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f18]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f34,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f40,plain,
? [A,B] : set_union2(singleton(A),unordered_pair(A,B)) != unordered_pair(A,B),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f41,plain,
set_union2(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)) != unordered_pair(sK3_skl,sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f40]) ).
fof(f42,plain,
set_union2(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)) != unordered_pair(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f56,plain,
~ in(sK3_skl,unordered_pair(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f35,f42]) ).
fof(f66,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET874+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n014.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 05:42:34 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.49 % Elapsed time: 0.066963 seconds
% 0.20/0.49 % CPU time: 0.179650 seconds
% 0.20/0.49 % Total memory used: 101.415 MB
% 0.20/0.49 % Net memory used: 101.000 MB
%------------------------------------------------------------------------------