%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU104+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 : n007.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 02:19:13 PM UTC 2026
% Result : Theorem 0.14s 5.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 11 unt; 7 def)
% Number of atoms : 169 ( 2 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 178 ( 69 ~; 67 |; 23 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 61 ( 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B] : set_union2(A,B) = symmetric_difference(A,set_difference(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f119,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f121,plain,
! [A] :
( ( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
| preboolean(A) )
& ( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(NNF_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
( ! [A] :
( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
| preboolean(A) )
& ! [A] :
( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
( ! [A] :
( ( ( ~ in(set_difference(sK10_skl(A),sK11_skl(A)),A)
| ~ in(set_union2(sK10_skl(A),sK11_skl(A)),A) )
& in(sK11_skl(A),A)
& in(sK10_skl(A),A) )
| preboolean(A) )
& ! [A] :
( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(B,sK10_skl(A)),skolemize(C,sK11_skl(A))],[f122]) ).
fof(f126,plain,
! [X0] :
( in(sK10_skl(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f127,plain,
! [X0] :
( in(sK11_skl(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,plain,
! [X0] :
( ~ in(set_difference(sK10_skl(X0),sK11_skl(X0)),X0)
| ~ in(set_union2(sK10_skl(X0),sK11_skl(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f129,plain,
? [A] :
( ~ preboolean(A)
& ! [B] :
( ! [C] :
( ( in(set_difference(B,C),A)
& in(symmetric_difference(B,C),A) )
| ~ element(C,A) )
| ~ element(B,A) )
& ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f130,plain,
( ~ preboolean(sK12_skl)
& ! [B] :
( ! [C] :
( ( in(set_difference(B,C),sK12_skl)
& in(symmetric_difference(B,C),sK12_skl) )
| ~ element(C,sK12_skl) )
| ~ element(B,sK12_skl) )
& ~ empty(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f129]) ).
fof(f132,plain,
! [X0,X1] :
( in(symmetric_difference(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f133,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f134,plain,
~ preboolean(sK12_skl),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f136,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f137,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f161,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f278,plain,
! [X0,X1] :
( in(set_union2(X0,X1),sK12_skl)
| ~ element(set_difference(X1,X0),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(paramodulation,[status(thm)],[f161,f132]) ).
fof(f301,plain,
! [X0,X1] :
( ~ in(set_difference(X1,X0),sK12_skl)
| in(set_union2(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f278,f137]) ).
fof(f325,plain,
! [X0,X1] :
( ~ element(X0,sK12_skl)
| ~ element(X1,sK12_skl)
| in(set_union2(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f301,f133]) ).
fof(f327,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| in(set_union2(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f325]) ).
fof(f331,definition,
( sQ11_spl
<=> preboolean(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ11_spl
| preboolean(sK12_skl) ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f593,plain,
( ~ in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl)
| preboolean(sK12_skl)
| ~ element(sK11_skl(sK12_skl),sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f133,f128]) ).
fof(f599,definition,
( sQ27_spl
<=> element(sK10_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( sQ27_spl
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,definition,
( sQ28_spl
<=> element(sK11_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( sQ28_spl
| ~ element(sK11_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,definition,
( sQ29_spl
<=> in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ29_spl
| ~ in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl) ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f608,plain,
( ~ sQ29_spl
| sQ11_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f593,f599,f602,f331,f605]) ).
fof(f804,definition,
( sQ36_spl
<=> in(sK10_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f806,plain,
( sQ36_spl
| ~ in(sK10_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f807,definition,
( sQ37_spl
<=> in(sK11_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f809,plain,
( sQ37_spl
| ~ in(sK11_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f825,plain,
( sQ37_spl
| preboolean(sK12_skl) ),
inference(resolution,[status(thm)],[f809,f127]) ).
fof(f826,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f134]) ).
fof(f827,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f835,plain,
( sQ36_spl
| preboolean(sK12_skl) ),
inference(resolution,[status(thm)],[f806,f126]) ).
fof(f836,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f835,f134]) ).
fof(f837,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f836]) ).
fof(f840,plain,
( sQ28_spl
| ~ in(sK11_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f604,f137]) ).
fof(f841,plain,
( sQ28_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f840,f807,f602]) ).
fof(f854,plain,
( sQ27_spl
| ~ in(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f601,f137]) ).
fof(f855,plain,
( sQ27_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f854,f804,f599]) ).
fof(f859,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f134]) ).
fof(f860,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f859]) ).
fof(f1069,definition,
( sQ41_spl
<=> subset(sK12_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1071,plain,
( sQ41_spl
| ~ subset(sK12_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f1069]) ).
fof(f1087,plain,
( sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1071,f119]) ).
fof(f1088,plain,
sQ41_spl,
inference(contradiction_clause,[status(thm)],[f1087]) ).
fof(f1197,plain,
( sQ29_spl
| ~ element(sK11_skl(sK12_skl),sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f327,f607]) ).
fof(f1207,plain,
( sQ29_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1197,f599,f602,f605]) ).
fof(f1212,plain,
$false,
inference(sat_refutation,[status(thm)],[f608,f827,f837,f841,f855,f860,f1088,f1207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU104+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n007.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Mon Sep 21 05:48:25 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Drodi V4.1.1
% 0.14/5.45 % Refutation found
% 0.14/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.47 % Elapsed time: 0.101500 seconds
% 0.14/5.47 % CPU time: 0.524341 seconds
% 0.14/5.47 % Total memory used: 111.580 MB
% 0.14/5.47 % Net memory used: 110.564 MB
%------------------------------------------------------------------------------