%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:19:24 PM UTC 2026
% Result : Theorem 0.09s 0.56s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 103 ( 71 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 127 ( 46 ~; 48 |; 27 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 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 : 69 ( 59 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = 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(f7,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
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] :
( ( ( sK1_skl(C,B,A) = B
| sK1_skl(C,B,A) = A
| in(sK1_skl(C,B,A),C) )
& ( ( sK1_skl(C,B,A) != B
& sK1_skl(C,B,A) != A )
| ~ in(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f20]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f32,plain,
? [A,B,C] :
( A != B
& singleton(A) = unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
? [A,B] :
( A != B
& ? [C] : singleton(A) = unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( sK4_skl != sK5_skl
& singleton(sK4_skl) = unordered_pair(sK5_skl,sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f33]) ).
fof(f35,plain,
singleton(sK4_skl) = unordered_pair(sK5_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
sK4_skl != sK5_skl,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f46,plain,
in(sK5_skl,singleton(sK4_skl)),
inference(paramodulation,[status(thm)],[f35,f40]) ).
fof(f53,plain,
sK5_skl = sK4_skl,
inference(resolution,[status(thm)],[f46,f37]) ).
fof(f54,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f53,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU149+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n013.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Mon Sep 21 05:52:36 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Drodi V4.1.1
% 0.09/0.56 % Refutation found
% 0.09/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.59 % Elapsed time: 0.056030 seconds
% 0.13/0.59 % CPU time: 0.154410 seconds
% 0.13/0.59 % Total memory used: 101.449 MB
% 0.13/0.59 % Net memory used: 101.000 MB
%------------------------------------------------------------------------------