%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU127+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 : n012.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 02:19:17 PM UTC 2026
% Result : Theorem 0.07s 0.33s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 91 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 108 ( 42 ~; 39 |; 22 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B] : subset(set_intersection2(A,B),A),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f20,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(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(f32,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f46,plain,
? [A,B] : ~ subset(set_intersection2(A,B),A),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f47,plain,
~ subset(set_intersection2(sK4_skl,sK5_skl),sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f46]) ).
fof(f48,plain,
~ subset(set_intersection2(sK4_skl,sK5_skl),sK4_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f59,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f61,plain,
~ subset(set_intersection2(sK5_skl,sK4_skl),sK4_skl),
inference(backward_demodulation,[status(thm)],[f20,f48]) ).
fof(f79,plain,
~ in(sK0_skl(sK4_skl,set_intersection2(sK5_skl,sK4_skl)),sK4_skl),
inference(resolution,[status(thm)],[f27,f61]) ).
fof(f81,plain,
! [X0] : ~ in(sK0_skl(sK4_skl,set_intersection2(sK5_skl,sK4_skl)),set_intersection2(X0,sK4_skl)),
inference(resolution,[status(thm)],[f79,f59]) ).
fof(f83,plain,
subset(set_intersection2(sK5_skl,sK4_skl),sK4_skl),
inference(resolution,[status(thm)],[f81,f26]) ).
fof(f91,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f83,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU127+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Mon Sep 21 05:51:37 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Drodi V4.1.1
% 0.07/0.33 % Refutation found
% 0.07/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.044282 seconds
% 0.07/0.34 % CPU time: 0.087935 seconds
% 0.07/0.34 % Total memory used: 101.710 MB
% 0.07/0.34 % Net memory used: 101.392 MB
%------------------------------------------------------------------------------