%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET912+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 : n011.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 02:10:57 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 41 ( 15 ~; 11 |; 11 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f24,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [A,B,C] :
( ( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
( ! [A,B,C] :
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) )
& ! [A,B,C] :
( ( in(B,C)
& in(A,C) )
| ~ subset(unordered_pair(A,B),C) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,C),B) != unordered_pair(A,C)
& in(C,B)
& in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
( set_intersection2(unordered_pair(sK2_skl,sK4_skl),sK3_skl) != unordered_pair(sK2_skl,sK4_skl)
& in(sK4_skl,sK3_skl)
& in(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f31]) ).
fof(f33,plain,
in(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
in(sK4_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
set_intersection2(unordered_pair(sK2_skl,sK4_skl),sK3_skl) != unordered_pair(sK2_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f65,plain,
! [X0] :
( ~ in(X0,sK3_skl)
| subset(unordered_pair(X0,sK4_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f30,f34]) ).
fof(f70,plain,
subset(unordered_pair(sK2_skl,sK4_skl),sK3_skl),
inference(resolution,[status(thm)],[f65,f33]) ).
fof(f76,plain,
set_intersection2(unordered_pair(sK2_skl,sK4_skl),sK3_skl) = unordered_pair(sK2_skl,sK4_skl),
inference(resolution,[status(thm)],[f70,f25]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f76,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET912+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:43:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.051411 seconds
% 0.11/0.43 % CPU time: 0.123193 seconds
% 0.11/0.43 % Total memory used: 47.835 MB
% 0.11/0.43 % Net memory used: 47.534 MB
%------------------------------------------------------------------------------