%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:19:18 PM UTC 2026
% Result : Theorem 0.08s 0.49s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 7 unt; 4 def)
% Number of atoms : 160 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 180 ( 73 ~; 71 |; 25 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 94 ( 84 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f21,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f28,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f30,plain,
( ! [A,B,C] :
( ( ( ( in(sK1_skl(C,B,A),B)
& in(sK1_skl(C,B,A),A) )
| in(sK1_skl(C,B,A),C) )
& ( ~ in(sK1_skl(C,B,A),B)
| ~ in(sK1_skl(C,B,A),A)
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f29]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f46,plain,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f47,plain,
? [A,B] :
( ? [C] : ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
( ~ subset(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK6_skl))
& subset(sK4_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f47]) ).
fof(f49,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
~ subset(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK6_skl)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f60,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f61,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f33]) ).
fof(f74,plain,
~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),set_intersection2(sK5_skl,sK6_skl)),
inference(resolution,[status(thm)],[f27,f50]) ).
fof(f127,plain,
( ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK6_skl)
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK5_skl) ),
inference(resolution,[status(thm)],[f74,f62]) ).
fof(f131,definition,
( sQ0_spl
<=> in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,definition,
( sQ1_spl
<=> in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK6_skl) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f127,f131,f134]) ).
fof(f145,definition,
! [X0] :
( sQ2_spl
<=> ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ2_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),X0) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f152,plain,
( ~ sQ2_spl
| subset(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f146,f26]) ).
fof(f157,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f50]) ).
fof(f158,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f169,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),X0)
| ~ subset(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f133,f25]) ).
fof(f198,plain,
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f169,f49]) ).
fof(f201,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),set_intersection2(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f198,f61]) ).
fof(f204,plain,
! [X0] :
( sQ0_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK4_skl)
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),X0) ),
inference(resolution,[status(thm)],[f201,f62]) ).
fof(f211,definition,
( sQ4_spl
<=> in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ4_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),sK4_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ0_spl
| ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f204,f145,f211,f131]) ).
fof(f216,plain,
! [X0] :
( sQ4_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),set_intersection2(sK4_skl,X0)) ),
inference(resolution,[status(thm)],[f213,f60]) ).
fof(f218,plain,
! [X0] :
( sQ1_spl
| ~ in(sK0_skl(set_intersection2(sK5_skl,sK6_skl),set_intersection2(sK4_skl,sK6_skl)),set_intersection2(X0,sK6_skl)) ),
inference(resolution,[status(thm)],[f136,f61]) ).
fof(f324,plain,
( sQ1_spl
| subset(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f218,f26]) ).
fof(f332,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f324,f50]) ).
fof(f333,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f361,plain,
( sQ4_spl
| subset(set_intersection2(sK4_skl,sK6_skl),set_intersection2(sK5_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f216,f26]) ).
fof(f370,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f50]) ).
fof(f371,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f370]) ).
fof(f372,plain,
$false,
inference(sat_refutation,[status(thm)],[f137,f158,f214,f333,f371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU129+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 05:51:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.49 % Refutation found
% 0.08/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.55/0.54 % Elapsed time: 0.165370 seconds
% 0.55/0.54 % CPU time: 0.791565 seconds
% 0.55/0.54 % Total memory used: 90.985 MB
% 0.55/0.54 % Net memory used: 89.802 MB
%------------------------------------------------------------------------------