%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET901+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 : n004.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 02:10:55 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 7 unt; 5 def)
% Number of atoms : 170 ( 79 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 192 ( 77 ~; 80 |; 25 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f17,plain,
? [A,B,C] :
( subset(A,unordered_pair(B,C))
<~> ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
? [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| ~ subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| subset(A,unordered_pair(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
( ( ( sK2_skl != unordered_pair(sK3_skl,sK4_skl)
& sK2_skl != singleton(sK4_skl)
& sK2_skl != singleton(sK3_skl)
& sK2_skl != empty_set )
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) )
& ( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,unordered_pair(sK3_skl,sK4_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)],[f18]) ).
fof(f20,plain,
( sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set
| subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( sK2_skl != empty_set
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
( sK2_skl != singleton(sK3_skl)
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
( sK2_skl != singleton(sK4_skl)
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
( sK2_skl != unordered_pair(sK3_skl,sK4_skl)
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f25,plain,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
( ! [A,B,C] :
( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ! [A,B,C] :
( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| X0 = singleton(X2)
| X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 != empty_set
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( X0 != singleton(X2)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f33,definition,
( sQ0_spl
<=> subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( ~ sQ0_spl
| subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f35,plain,
( sQ0_spl
| ~ subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> sK2_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ1_spl
| sK2_skl = empty_set ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ2_spl
<=> sK2_skl = singleton(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( ~ sQ2_spl
| sK2_skl = singleton(sK3_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
( sQ3_spl
<=> sK2_skl = singleton(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ3_spl
| sK2_skl = singleton(sK4_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ4_spl
<=> sK2_skl = unordered_pair(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ4_spl
| sK2_skl = unordered_pair(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f33,f36,f39,f42,f45]) ).
fof(f49,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f33,f36]) ).
fof(f50,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f33,f39]) ).
fof(f51,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f33,f42]) ).
fof(f52,plain,
( ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f33,f45]) ).
fof(f53,plain,
! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f54,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f55,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f57,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ subset(sK2_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f46,f35]) ).
fof(f58,plain,
( sQ0_spl
| ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f57,f11]) ).
fof(f59,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f77,plain,
( ~ sQ0_spl
| sK2_skl = unordered_pair(sK3_skl,sK4_skl)
| sK2_skl = singleton(sK4_skl)
| sK2_skl = singleton(sK3_skl)
| sK2_skl = empty_set ),
inference(resolution,[status(thm)],[f28,f34]) ).
fof(f88,plain,
( ~ sQ0_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f77,f36,f39,f42,f45,f33]) ).
fof(f89,plain,
! [X0] :
( ~ sQ3_spl
| subset(sK2_skl,unordered_pair(X0,sK4_skl)) ),
inference(paramodulation,[status(thm)],[f43,f55]) ).
fof(f105,plain,
( sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f89]) ).
fof(f106,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sQ1_spl
| subset(sK2_skl,unordered_pair(X0,X1)) ),
inference(backward_demodulation,[status(thm)],[f37,f53]) ).
fof(f112,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f109]) ).
fof(f113,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0] :
( ~ sQ2_spl
| subset(sK2_skl,unordered_pair(sK3_skl,X0)) ),
inference(paramodulation,[status(thm)],[f40,f54]) ).
fof(f130,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f115]) ).
fof(f134,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f130]) ).
fof(f135,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f49,f50,f51,f52,f59,f88,f106,f113,f134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:43:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.044463 seconds
% 0.14/0.41 % CPU time: 0.074623 seconds
% 0.14/0.41 % Total memory used: 12.769 MB
% 0.14/0.41 % Net memory used: 12.760 MB
%------------------------------------------------------------------------------