%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU105+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 02:19:13 PM UTC 2026
% Result : Theorem 0.14s 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 14 unt; 7 def)
% Number of atoms : 200 ( 7 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 214 ( 87 ~; 85 |; 23 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] : set_difference(A,B) = symmetric_difference(A,set_intersection2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,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(f34,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f37,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B] : set_union2(A,B) = symmetric_difference(symmetric_difference(A,B),set_intersection2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f21]) ).
fof(f91,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f105,plain,
empty(sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f25]) ).
fof(f106,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f135,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f136,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)],[f33]) ).
fof(f137,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)],[f136]) ).
fof(f138,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)],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f142,plain,
! [X0] :
( in(sK10_skl(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
! [X0] :
( in(sK11_skl(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f144,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)],[f139]) ).
fof(f145,plain,
? [A] :
( ~ preboolean(A)
& ! [B] :
( ! [C] :
( ( in(set_intersection2(B,C),A)
& in(symmetric_difference(B,C),A) )
| ~ element(C,A) )
| ~ element(B,A) )
& ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f146,plain,
( ~ preboolean(sK12_skl)
& ! [B] :
( ! [C] :
( ( in(set_intersection2(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)],[f145]) ).
fof(f148,plain,
! [X0,X1] :
( in(symmetric_difference(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
! [X0,X1] :
( in(set_intersection2(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f150,plain,
~ preboolean(sK12_skl),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f152,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f153,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f178,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f179,plain,
! [X0] :
( in(X0,sK12_skl)
| ~ element(X0,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(paramodulation,[status(thm)],[f91,f149]) ).
fof(f180,plain,
! [X0] :
( in(X0,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f179]) ).
fof(f417,definition,
( sQ11_spl
<=> preboolean(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( ~ sQ11_spl
| preboolean(sK12_skl) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f522,plain,
! [X0,X1] :
( element(set_intersection2(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f149,f153]) ).
fof(f631,plain,
! [X0,X1] :
( element(symmetric_difference(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f148,f153]) ).
fof(f637,plain,
! [X0,X1] :
( in(set_union2(X0,X1),sK12_skl)
| ~ element(set_intersection2(X0,X1),sK12_skl)
| ~ element(symmetric_difference(X0,X1),sK12_skl) ),
inference(paramodulation,[status(thm)],[f178,f148]) ).
fof(f674,plain,
! [X0] :
( element(sK10_skl(X0),X0)
| preboolean(X0) ),
inference(resolution,[status(thm)],[f142,f153]) ).
fof(f691,plain,
! [X0] :
( element(sK11_skl(X0),X0)
| preboolean(X0) ),
inference(resolution,[status(thm)],[f143,f153]) ).
fof(f705,definition,
! [X0] :
( sQ20_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f706,plain,
! [X0] :
( ~ sQ20_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f716,plain,
( in(sK10_skl(sK12_skl),sK12_skl)
| preboolean(sK12_skl) ),
inference(resolution,[status(thm)],[f674,f180]) ).
fof(f718,definition,
( sQ21_spl
<=> in(sK10_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( ~ sQ21_spl
| in(sK10_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f721,plain,
( sQ21_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f716,f417,f718]) ).
fof(f722,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f150]) ).
fof(f723,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( ~ sQ21_spl
| element(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f719,f153]) ).
fof(f734,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK12_skl)
| ~ element(set_intersection2(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(paramodulation,[status(thm)],[f135,f148]) ).
fof(f807,plain,
( in(sK11_skl(sK12_skl),sK12_skl)
| preboolean(sK12_skl) ),
inference(resolution,[status(thm)],[f691,f180]) ).
fof(f809,definition,
( sQ24_spl
<=> in(sK11_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ24_spl
| in(sK11_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f809]) ).
fof(f812,plain,
( sQ24_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f807,f417,f809]) ).
fof(f814,plain,
( ~ sQ24_spl
| element(sK11_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f810,f153]) ).
fof(f942,plain,
( ~ sQ20_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f106,f706]) ).
fof(f949,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f942]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| in(set_difference(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f734,f522]) ).
fof(f1045,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| in(set_difference(X0,X1),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1039]) ).
fof(f1068,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| in(set_union2(X0,X1),sK12_skl)
| ~ element(symmetric_difference(X0,X1),sK12_skl) ),
inference(resolution,[status(thm)],[f637,f522]) ).
fof(f1074,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| in(set_union2(X0,X1),sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1068,f631]) ).
fof(f1387,plain,
( ~ in(set_difference(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)],[f1074,f144]) ).
fof(f1400,definition,
( sQ44_spl
<=> element(sK10_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1402,plain,
( sQ44_spl
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f1400]) ).
fof(f1403,definition,
( sQ45_spl
<=> element(sK11_skl(sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( sQ45_spl
| ~ element(sK11_skl(sK12_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f1403]) ).
fof(f1406,definition,
( sQ46_spl
<=> in(set_difference(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1408,plain,
( sQ46_spl
| ~ in(set_difference(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl) ),
inference(component_clause,[status(thm)],[f1406]) ).
fof(f1409,plain,
( ~ sQ46_spl
| sQ11_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f1387,f1400,f1403,f417,f1406]) ).
fof(f1419,plain,
( sQ46_spl
| ~ element(sK11_skl(sK12_skl),sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f1408,f1045]) ).
fof(f1421,plain,
( sQ46_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f1419,f1400,f1403,f1406]) ).
fof(f1423,plain,
( sQ45_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1405,f814]) ).
fof(f1424,plain,
( sQ45_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f1423]) ).
fof(f1425,plain,
( sQ44_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1402,f725]) ).
fof(f1426,plain,
( sQ44_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1425]) ).
fof(f1427,plain,
$false,
inference(sat_refutation,[status(thm)],[f721,f723,f812,f949,f1409,f1421,f1424,f1426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:53:31 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.181940 seconds
% 0.14/0.53 % CPU time: 1.236652 seconds
% 0.14/0.53 % Total memory used: 127.181 MB
% 0.14/0.53 % Net memory used: 124.837 MB
%------------------------------------------------------------------------------