%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET930+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 02:11:00 PM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 9 unt; 2 def)
% Number of atoms : 104 ( 47 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 128 ( 59 ~; 35 |; 29 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 55 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(B,C)
& ~ in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = empty_set
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
~ ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [A,B,C] :
( ( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [A,B,C] :
( ( A != B
& ~ in(B,C) )
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) )
& ! [A,B,C] :
( ( ( A = B
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f25,plain,
! [A,B,C] :
( ( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
& ( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [A,B,C] :
( in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ~ in(B,C)
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f30,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| set_difference(unordered_pair(A,B),C) = empty_set )
& ( ( in(B,C)
& in(A,C) )
| set_difference(unordered_pair(A,B),C) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
( ! [A,B,C] :
( ~ in(B,C)
| ~ in(A,C)
| set_difference(unordered_pair(A,B),C) = empty_set )
& ! [A,B,C] :
( ( in(B,C)
& in(A,C) )
| set_difference(unordered_pair(A,B),C) != empty_set ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = empty_set ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
& set_difference(unordered_pair(A,B),C) != singleton(B)
& set_difference(unordered_pair(A,B),C) != singleton(A)
& set_difference(unordered_pair(A,B),C) != empty_set ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != unordered_pair(sK2_skl,sK3_skl)
& set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK3_skl)
& set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl)
& set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f35]) ).
fof(f37,plain,
set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != empty_set,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f39,plain,
set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK3_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != unordered_pair(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f47,plain,
set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl) != singleton(sK3_skl),
inference(paramodulation,[status(thm)],[f13,f39]) ).
fof(f49,plain,
set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl) != empty_set,
inference(paramodulation,[status(thm)],[f13,f37]) ).
fof(f70,plain,
( ~ in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f19,f38]) ).
fof(f76,definition,
( sQ0_spl
<=> in(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f79,definition,
( sQ1_spl
<=> in(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f76,f79]) ).
fof(f84,plain,
( ~ in(sK2_skl,sK4_skl)
| in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f47,f19]) ).
fof(f85,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f84,f79,f76]) ).
fof(f98,plain,
( in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f29,f40]) ).
fof(f121,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f76,f79]) ).
fof(f159,plain,
( ~ in(sK2_skl,sK4_skl)
| ~ in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f34,f49]) ).
fof(f167,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f159,f79,f76]) ).
fof(f169,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f85,f121,f167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 05:44:10 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.42 % Elapsed time: 0.049380 seconds
% 0.13/5.42 % CPU time: 0.159588 seconds
% 0.13/5.42 % Total memory used: 101.919 MB
% 0.13/5.42 % Net memory used: 101.525 MB
%------------------------------------------------------------------------------