%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET920+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:10:58 PM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 117 ( 49 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 148 ( 53 ~; 55 |; 34 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 68 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f9,conjecture,
! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
=> in(A,C) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f15,plain,
! [A,B,C] :
( ( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ( ! [D] :
( ( ( D != B
& D != A )
| in(D,C) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [A,B,C] :
( ? [D] :
( ( D = B
| D = A
| in(D,C) )
& ( ( D != B
& D != A )
| ~ in(D,C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B,C] :
( ( ( sK0_skl(C,B,A) = B
| sK0_skl(C,B,A) = A
| in(sK0_skl(C,B,A),C) )
& ( ( sK0_skl(C,B,A) != B
& sK0_skl(C,B,A) != A )
| ~ in(sK0_skl(C,B,A),C) ) )
| C = unordered_pair(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( D != B
& D != A )
| in(D,C) )
& ! [D] :
( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f24,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)],[f5]) ).
fof(f25,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)],[f24]) ).
fof(f26,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))],[f25]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f39,plain,
? [A,B,C] :
( ~ in(A,C)
& set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
? [A,C] :
( ~ in(A,C)
& ? [B] : set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
( ~ in(sK4_skl,sK5_skl)
& set_intersection2(unordered_pair(sK4_skl,sK6_skl),sK5_skl) = unordered_pair(sK4_skl,sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(C,sK5_skl),skolemize(B,sK6_skl)],[f40]) ).
fof(f42,plain,
set_intersection2(unordered_pair(sK4_skl,sK6_skl),sK5_skl) = unordered_pair(sK4_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
~ in(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f48,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f82,plain,
! [X0] :
( in(X0,sK5_skl)
| ~ in(X0,unordered_pair(sK4_skl,sK6_skl)) ),
inference(paramodulation,[status(thm)],[f42,f48]) ).
fof(f87,plain,
in(sK4_skl,sK5_skl),
inference(resolution,[status(thm)],[f82,f45]) ).
fof(f90,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f87,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET920+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n002.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:46:32 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.045185 seconds
% 0.11/0.39 % CPU time: 0.136589 seconds
% 0.11/0.39 % Total memory used: 92.110 MB
% 0.11/0.39 % Net memory used: 91.823 MB
%------------------------------------------------------------------------------