%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET927+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 : n002.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 02:10:59 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 3 unt; 4 def)
% Number of atoms : 130 ( 48 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 142 ( 54 ~; 64 |; 16 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,conjecture,
! [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(f6,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,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(f8,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<~> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
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
| in(B,C) )
& ~ in(A,C) )
| set_difference(unordered_pair(A,B),C) = singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
( ( ( sK2_skl != sK3_skl
& ~ in(sK3_skl,sK4_skl) )
| in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl) )
& ( ( ( sK2_skl = sK3_skl
| in(sK3_skl,sK4_skl) )
& ~ in(sK2_skl,sK4_skl) )
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = singleton(sK2_skl) ) ),
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)],[f16]) ).
fof(f18,plain,
( ~ in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
( sK2_skl = sK3_skl
| in(sK3_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
( ~ in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
( sK2_skl != sK3_skl
| in(sK2_skl,sK4_skl)
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f22,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)],[f7]) ).
fof(f23,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)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( X0 = X1
| in(X1,X2)
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
! [X0,X1,X2] :
( X0 != X1
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f28,definition,
( sQ0_spl
<=> set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( ~ sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f30,plain,
( sQ0_spl
| set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl) != singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
( sQ1_spl
<=> in(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f28,f31]) ).
fof(f35,definition,
( sQ2_spl
<=> in(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f38,definition,
( sQ3_spl
<=> sK2_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ3_spl
| sK2_skl = sK3_skl ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ3_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f28,f35,f38]) ).
fof(f42,plain,
( ~ sQ2_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f28,f31,f35]) ).
fof(f43,plain,
( ~ sQ3_spl
| sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f28,f31,f38]) ).
fof(f44,plain,
! [X0,X1] :
( in(X0,X1)
| set_difference(unordered_pair(X0,X0),X1) = singleton(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f49,plain,
( sQ0_spl
| set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl) != singleton(sK2_skl) ),
inference(paramodulation,[status(thm)],[f8,f30]) ).
fof(f68,plain,
( sQ0_spl
| ~ in(sK3_skl,sK4_skl)
| in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f26,f30]) ).
fof(f76,plain,
( sQ0_spl
| ~ sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f68,f31,f35,f28]) ).
fof(f77,plain,
( sQ0_spl
| ~ sQ3_spl
| set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl) != singleton(sK3_skl) ),
inference(backward_demodulation,[status(thm)],[f39,f49]) ).
fof(f80,plain,
( sQ0_spl
| ~ sQ3_spl
| set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl) != singleton(sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f39,f77]) ).
fof(f83,plain,
( sQ0_spl
| ~ sQ3_spl
| in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f80,f44]) ).
fof(f86,plain,
( sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f83,f35,f38,f28]) ).
fof(f92,plain,
( ~ sQ0_spl
| sK2_skl = sK3_skl
| in(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f29,f25]) ).
fof(f93,plain,
( ~ sQ0_spl
| ~ in(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f29,f24]) ).
fof(f101,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f92,f35,f38,f28]) ).
fof(f102,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f93,f31,f28]) ).
fof(f114,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f41,f42,f43,f76,f86,f101,f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:46:47 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.052504 seconds
% 0.13/0.42 % CPU time: 0.156569 seconds
% 0.13/0.42 % Total memory used: 101.684 MB
% 0.13/0.42 % Net memory used: 101.208 MB
%------------------------------------------------------------------------------