%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET956+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 : n003.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 02:11:03 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 2 def)
% Number of atoms : 101 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 39 ~; 32 |; 24 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 80 ( 66 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C,D] :
~ ( ! [E,F] :
~ ( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
& in(D,A)
& subset(A,cartesian_product2(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C,D] :
( ( ! [E,F] :
( in(ordered_pair(E,F),A)
=> in(ordered_pair(E,F),D) )
& subset(A,cartesian_product2(B,C)) )
=> subset(A,D) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f15,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f16,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)],[f15]) ).
fof(f17,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)],[f16]) ).
fof(f18,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))],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f30,plain,
! [A,B,C,D] :
( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
| ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [B,C,D] :
( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,C)
& in(E,B) )
| ! [A] :
( ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [B,C,D] :
( ( D = ordered_pair(sK3_skl(D,C,B),sK4_skl(D,C,B))
& in(sK4_skl(D,C,B),C)
& in(sK3_skl(D,C,B),B) )
| ! [A] :
( ~ in(D,A)
| ~ subset(A,cartesian_product2(B,C)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(E,sK3_skl(D,C,B)),skolemize(F,sK4_skl(D,C,B))],[f31]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( X3 = ordered_pair(sK3_skl(X3,X2,X1),sK4_skl(X3,X2,X1))
| ~ in(X3,X0)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
? [A,B,C,D] :
( ~ subset(A,D)
& ! [E,F] :
( in(ordered_pair(E,F),D)
| ~ in(ordered_pair(E,F),A) )
& subset(A,cartesian_product2(B,C)) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
? [A,D] :
( ~ subset(A,D)
& ! [E,F] :
( in(ordered_pair(E,F),D)
| ~ in(ordered_pair(E,F),A) )
& ? [B,C] : subset(A,cartesian_product2(B,C)) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ~ subset(sK5_skl,sK6_skl)
& ! [E,F] :
( in(ordered_pair(E,F),sK6_skl)
| ~ in(ordered_pair(E,F),sK5_skl) )
& subset(sK5_skl,cartesian_product2(sK7_skl,sK8_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK5_skl),skolemize(D,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f37]) ).
fof(f39,plain,
subset(sK5_skl,cartesian_product2(sK7_skl,sK8_skl)),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),sK6_skl)
| ~ in(ordered_pair(X0,X1),sK5_skl) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
~ subset(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f46,plain,
in(sK0_skl(sK6_skl,sK5_skl),sK5_skl),
inference(resolution,[status(thm)],[f20,f41]) ).
fof(f53,plain,
~ in(sK0_skl(sK6_skl,sK5_skl),sK6_skl),
inference(resolution,[status(thm)],[f21,f41]) ).
fof(f103,plain,
! [X0] :
( X0 = ordered_pair(sK3_skl(X0,sK8_skl,sK7_skl),sK4_skl(X0,sK8_skl,sK7_skl))
| ~ in(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f35,f39]) ).
fof(f135,plain,
sK0_skl(sK6_skl,sK5_skl) = ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),
inference(resolution,[status(thm)],[f103,f46]) ).
fof(f275,plain,
( in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl)
| ~ in(sK0_skl(sK6_skl,sK5_skl),sK5_skl) ),
inference(paramodulation,[status(thm)],[f135,f40]) ).
fof(f276,definition,
( sQ12_spl
<=> in(sK0_skl(sK6_skl,sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ12_spl
| ~ in(sK0_skl(sK6_skl,sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ13_spl
<=> in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ13_spl
| in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f275,f276,f279]) ).
fof(f283,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f46]) ).
fof(f284,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
( ~ sQ13_spl
| in(sK0_skl(sK6_skl,sK5_skl),sK6_skl) ),
inference(forward_demodulation,[status(thm)],[f135,f280]) ).
fof(f286,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f53]) ).
fof(f287,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f288,plain,
$false,
inference(sat_refutation,[status(thm)],[f282,f284,f287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.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 05:46:15 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.045112 seconds
% 0.13/0.40 % CPU time: 0.125569 seconds
% 0.13/0.40 % Total memory used: 48.615 MB
% 0.13/0.40 % Net memory used: 48.417 MB
%------------------------------------------------------------------------------