%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET958+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 : n004.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 6 unt; 2 def)
% Number of atoms : 78 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 33 ~; 26 |; 14 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% 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,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f29,plain,
? [A,B] :
( ~ subset(A,B)
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
( ~ subset(sK3_skl,sK4_skl)
& ! [C,D] :
( in(ordered_pair(C,D),sK4_skl)
| ~ in(ordered_pair(C,D),sK3_skl) )
& ! [C] :
( C = ordered_pair(sK5_skl(C),sK6_skl(C))
| ~ in(C,sK3_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(D,sK5_skl(C)),skolemize(E,sK6_skl(C))],[f29]) ).
fof(f31,plain,
! [X0] :
( X0 = ordered_pair(sK5_skl(X0),sK6_skl(X0))
| ~ in(X0,sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),sK4_skl)
| ~ in(ordered_pair(X0,X1),sK3_skl) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
~ subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f38,plain,
in(sK0_skl(sK4_skl,sK3_skl),sK3_skl),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f39,plain,
sK0_skl(sK4_skl,sK3_skl) = ordered_pair(sK5_skl(sK0_skl(sK4_skl,sK3_skl)),sK6_skl(sK0_skl(sK4_skl,sK3_skl))),
inference(resolution,[status(thm)],[f38,f31]) ).
fof(f43,plain,
( in(ordered_pair(sK5_skl(sK0_skl(sK4_skl,sK3_skl)),sK6_skl(sK0_skl(sK4_skl,sK3_skl))),sK4_skl)
| ~ in(sK0_skl(sK4_skl,sK3_skl),sK3_skl) ),
inference(paramodulation,[status(thm)],[f39,f32]) ).
fof(f44,definition,
( sQ0_spl
<=> in(sK0_skl(sK4_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ0_spl
| ~ in(sK0_skl(sK4_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> in(ordered_pair(sK5_skl(sK0_skl(sK4_skl,sK3_skl)),sK6_skl(sK0_skl(sK4_skl,sK3_skl))),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ1_spl
| in(ordered_pair(sK5_skl(sK0_skl(sK4_skl,sK3_skl)),sK6_skl(sK0_skl(sK4_skl,sK3_skl))),sK4_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f51,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f38]) ).
fof(f52,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f51]) ).
fof(f53,plain,
( ~ sQ1_spl
| in(sK0_skl(sK4_skl,sK3_skl),sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f39,f48]) ).
fof(f58,plain,
( ~ sQ1_spl
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f20,f53]) ).
fof(f59,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f33]) ).
fof(f60,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f52,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET958+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 : n004.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 05:45:34 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.056534 seconds
% 0.12/0.42 % CPU time: 0.154774 seconds
% 0.12/0.42 % Total memory used: 101.526 MB
% 0.12/0.42 % Net memory used: 101.078 MB
%------------------------------------------------------------------------------