%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU106+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 : n010.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 02:19:14 PM UTC 2026
% Result : Theorem 5.66s 1.12s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 144 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 170 ( 70 ~; 65 |; 23 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 74 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] : set_difference(A,B) = symmetric_difference(A,set_intersection2(A,B)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f34,conjecture,
! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_union2(B,C),A)
& in(symmetric_difference(B,C),A) ) ) )
=> preboolean(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ( ! [B] :
( element(B,A)
=> ! [C] :
( element(C,A)
=> ( in(set_union2(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/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B] : set_intersection2(A,B) = symmetric_difference(symmetric_difference(A,B),set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
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_union2(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_union2(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_union2(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_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f209,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| element(set_union2(X0,X1),sK12_skl) ),
inference(resolution,[status(thm)],[f153,f149]) ).
fof(f210,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| element(symmetric_difference(X0,X1),sK12_skl) ),
inference(resolution,[status(thm)],[f153,f148]) ).
fof(f689,plain,
! [X0] :
( element(sK10_skl(X0),X0)
| preboolean(X0) ),
inference(resolution,[status(thm)],[f142,f153]) ).
fof(f701,plain,
! [X0] :
( element(sK11_skl(X0),X0)
| preboolean(X0) ),
inference(resolution,[status(thm)],[f143,f153]) ).
fof(f743,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(f804,plain,
! [X0,X1] :
( in(set_difference(X0,X1),sK12_skl)
| ~ element(set_intersection2(X1,X0),sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(paramodulation,[status(thm)],[f62,f743]) ).
fof(f957,plain,
! [X0,X1] :
( in(set_intersection2(X0,X1),sK12_skl)
| ~ element(set_union2(X0,X1),sK12_skl)
| ~ element(symmetric_difference(X0,X1),sK12_skl) ),
inference(paramodulation,[status(thm)],[f178,f148]) ).
fof(f995,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| in(set_intersection2(X0,X1),sK12_skl)
| ~ element(set_union2(X0,X1),sK12_skl) ),
inference(resolution,[status(thm)],[f957,f210]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl)
| in(set_intersection2(X0,X1),sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f995,f209]) ).
fof(f1167,plain,
! [X0,X1] :
( element(set_intersection2(X0,X1),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f1008,f153]) ).
fof(f1176,plain,
! [X0,X1] :
( in(set_difference(X1,X0),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f1167,f804]) ).
fof(f1190,plain,
! [X0,X1] :
( in(set_difference(X1,X0),sK12_skl)
| ~ element(X1,sK12_skl)
| ~ element(X0,sK12_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1176]) ).
fof(f1202,plain,
( ~ in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl)
| preboolean(sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl)
| ~ element(sK11_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f1190,f144]) ).
fof(f1210,plain,
( ~ in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl)
| preboolean(sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1202,f701]) ).
fof(f4135,plain,
( ~ in(set_union2(sK10_skl(sK12_skl),sK11_skl(sK12_skl)),sK12_skl)
| preboolean(sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1210,f689]) ).
fof(f4136,plain,
( ~ element(sK11_skl(sK12_skl),sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl)
| preboolean(sK12_skl) ),
inference(resolution,[status(thm)],[f4135,f149]) ).
fof(f4138,plain,
( ~ element(sK11_skl(sK12_skl),sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f4136,f150]) ).
fof(f4344,plain,
( preboolean(sK12_skl)
| ~ element(sK10_skl(sK12_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f4138,f701]) ).
fof(f4345,plain,
preboolean(sK12_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4344,f689]) ).
fof(f4346,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4345,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.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 05:51:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 5.66/1.12 % Refutation found
% 5.66/1.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.66/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.66/1.14 % Elapsed time: 0.778607 seconds
% 5.66/1.14 % CPU time: 5.892109 seconds
% 5.66/1.14 % Total memory used: 186.497 MB
% 5.66/1.14 % Net memory used: 180.527 MB
%------------------------------------------------------------------------------