%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET902+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 02:10:56 PM UTC 2026
% Result : Theorem 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 14 unt; 5 def)
% Number of atoms : 139 ( 81 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 154 ( 70 ~; 56 |; 22 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% 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 : 38 ( 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f36,plain,
? [A,B,C] :
( ( C != empty_set
| B != singleton(A) )
& ( C != singleton(A)
| B != empty_set )
& ( C != singleton(A)
| B != singleton(A) )
& singleton(A) = set_union2(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
( ( sK4_skl != empty_set
| sK3_skl != singleton(sK2_skl) )
& ( sK4_skl != singleton(sK2_skl)
| sK3_skl != empty_set )
& ( sK4_skl != singleton(sK2_skl)
| sK3_skl != singleton(sK2_skl) )
& singleton(sK2_skl) = set_union2(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)],[f36]) ).
fof(f38,plain,
singleton(sK2_skl) = set_union2(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
( sK4_skl != singleton(sK2_skl)
| sK3_skl != singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
( sK4_skl != singleton(sK2_skl)
| sK3_skl != empty_set ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f41,plain,
( sK4_skl != empty_set
| sK3_skl != singleton(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f42,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f43,definition,
( sQ0_spl
<=> sK3_skl = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( sQ0_spl
| sK3_skl != singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,definition,
( sQ1_spl
<=> sK4_skl = singleton(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f47,plain,
( ~ sQ1_spl
| sK4_skl = singleton(sK2_skl) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f43,f46]) ).
fof(f50,definition,
( sQ2_spl
<=> sK3_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f40,f50,f46]) ).
fof(f54,definition,
( sQ3_spl
<=> sK4_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ3_spl
| sK4_skl = empty_set ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f43,f54]) ).
fof(f60,plain,
singleton(sK2_skl) = set_union2(sK4_skl,sK3_skl),
inference(paramodulation,[status(thm)],[f38,f14]) ).
fof(f100,plain,
subset(sK4_skl,singleton(sK2_skl)),
inference(paramodulation,[status(thm)],[f60,f42]) ).
fof(f101,plain,
subset(sK3_skl,singleton(sK2_skl)),
inference(paramodulation,[status(thm)],[f38,f42]) ).
fof(f110,plain,
( sK4_skl = singleton(sK2_skl)
| sK4_skl = empty_set ),
inference(resolution,[status(thm)],[f100,f27]) ).
fof(f111,plain,
( sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f110,f54,f46]) ).
fof(f115,plain,
( ~ sQ1_spl
| sK4_skl = set_union2(sK3_skl,sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f47,f38]) ).
fof(f118,plain,
! [X0] :
( ~ sQ1_spl
| X0 = singleton(sK2_skl)
| X0 = empty_set
| ~ subset(X0,sK4_skl) ),
inference(paramodulation,[status(thm)],[f47,f27]) ).
fof(f120,plain,
! [X0] :
( ~ sQ1_spl
| X0 = sK4_skl
| X0 = empty_set
| ~ subset(X0,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f47,f118]) ).
fof(f124,plain,
( ~ sQ1_spl
| subset(sK3_skl,sK4_skl) ),
inference(paramodulation,[status(thm)],[f115,f42]) ).
fof(f142,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = singleton(X1)
| X0 = sK4_skl
| ~ subset(X0,singleton(X1)) ),
inference(backward_demodulation,[status(thm)],[f55,f27]) ).
fof(f143,plain,
! [X0] :
( ~ sQ3_spl
| singleton(X0) != sK4_skl ),
inference(backward_demodulation,[status(thm)],[f55,f24]) ).
fof(f151,plain,
( ~ sQ3_spl
| sK3_skl = singleton(sK2_skl)
| sK3_skl = sK4_skl ),
inference(resolution,[status(thm)],[f142,f101]) ).
fof(f154,definition,
( sQ9_spl
<=> sK3_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ9_spl
| sK3_skl = sK4_skl ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ sQ3_spl
| sQ0_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f151,f154,f43,f54]) ).
fof(f165,plain,
( ~ sQ9_spl
| singleton(sK2_skl) = set_union2(sK4_skl,sK4_skl) ),
inference(backward_demodulation,[status(thm)],[f155,f60]) ).
fof(f168,plain,
( sQ0_spl
| ~ sQ9_spl
| sK4_skl != singleton(sK2_skl) ),
inference(backward_demodulation,[status(thm)],[f155,f45]) ).
fof(f170,plain,
( ~ sQ9_spl
| singleton(sK2_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f23,f165]) ).
fof(f171,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f143]) ).
fof(f172,plain,
( ~ sQ9_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f206,plain,
( ~ sQ1_spl
| sK3_skl = sK4_skl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f120,f124]) ).
fof(f209,plain,
( ~ sQ1_spl
| sQ9_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f206,f50,f154,f46]) ).
fof(f215,plain,
( sQ0_spl
| ~ sQ9_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f168,f46,f154,f43]) ).
fof(f219,plain,
$false,
inference(sat_refutation,[status(thm)],[f49,f53,f57,f111,f157,f172,f209,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n014.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:43:20 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.054658 seconds
% 0.12/0.41 % CPU time: 0.089476 seconds
% 0.12/0.41 % Total memory used: 16.038 MB
% 0.12/0.41 % Net memory used: 16.020 MB
%------------------------------------------------------------------------------