%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:10:53 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 69 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 85 ( 33 ~; 32 |; 17 &)
% ( 3 <=>; 0 =>; 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; 3 con; 0-3 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,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)],[f3]) ).
fof(f14,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)],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f23,plain,
! [A,B] :
( ( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
( ! [A,B] :
( ~ in(A,B)
| set_difference(singleton(A),B) = empty_set )
& ! [A,B] :
( in(A,B)
| set_difference(singleton(A),B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_difference(singleton(X0),X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f31,plain,
? [A,B] : set_difference(singleton(A),unordered_pair(A,B)) != empty_set,
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
set_difference(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)) != empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f31]) ).
fof(f33,plain,
set_difference(singleton(sK3_skl),unordered_pair(sK3_skl,sK4_skl)) != empty_set,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f17]) ).
fof(f49,plain,
~ in(sK3_skl,unordered_pair(sK3_skl,sK4_skl)),
inference(resolution,[status(thm)],[f26,f33]) ).
fof(f51,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f49,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n011.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 05:42:25 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.46 % Refutation found
% 0.17/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.48 % Elapsed time: 0.053198 seconds
% 0.17/0.48 % CPU time: 0.122632 seconds
% 0.17/0.48 % Total memory used: 28.535 MB
% 0.17/0.48 % Net memory used: 28.481 MB
%------------------------------------------------------------------------------