%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET906+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 : 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 02:10:56 PM UTC 2026
% Result : Theorem 0.08s 0.33s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 152 ( 47 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 181 ( 65 ~; 68 |; 39 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 116 ( 104 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,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(f20,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)],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
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_union2(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_union2(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_union2(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_union2(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,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f37,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f38,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)],[f37]) ).
fof(f39,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)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ( ~ in(sK2_skl(B,A),B)
& in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f58,plain,
? [A,B,C] :
( ~ in(A,C)
& subset(set_union2(unordered_pair(A,B),C),C) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f59,plain,
? [A,C] :
( ~ in(A,C)
& ? [B] : subset(set_union2(unordered_pair(A,B),C),C) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( ~ in(sK5_skl,sK6_skl)
& subset(set_union2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(C,sK6_skl),skolemize(B,sK7_skl)],[f59]) ).
fof(f61,plain,
subset(set_union2(unordered_pair(sK5_skl,sK7_skl),sK6_skl),sK6_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
~ in(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f65,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f71,plain,
subset(set_union2(unordered_pair(sK7_skl,sK5_skl),sK6_skl),sK6_skl),
inference(backward_demodulation,[status(thm)],[f17,f61]) ).
fof(f92,plain,
subset(set_union2(sK6_skl,unordered_pair(sK7_skl,sK5_skl)),sK6_skl),
inference(forward_demodulation,[status(thm)],[f18,f71]) ).
fof(f93,plain,
! [X0,X1,X2] : in(X0,set_union2(unordered_pair(X1,X0),X2)),
inference(resolution,[status(thm)],[f67,f65]) ).
fof(f101,plain,
! [X0,X1,X2] : in(X0,set_union2(X1,unordered_pair(X2,X0))),
inference(paramodulation,[status(thm)],[f18,f93]) ).
fof(f132,plain,
! [X0] :
( in(X0,sK6_skl)
| ~ in(X0,set_union2(sK6_skl,unordered_pair(sK7_skl,sK5_skl))) ),
inference(resolution,[status(thm)],[f41,f92]) ).
fof(f154,plain,
in(sK5_skl,sK6_skl),
inference(resolution,[status(thm)],[f132,f101]) ).
fof(f155,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f154,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 05:43:07 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.08/0.33 % Refutation found
% 0.08/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.36 % Elapsed time: 0.038610 seconds
% 0.08/0.36 % CPU time: 0.106008 seconds
% 0.08/0.36 % Total memory used: 99.083 MB
% 0.08/0.36 % Net memory used: 98.795 MB
%------------------------------------------------------------------------------