%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU142+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 : n015.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 02:19:21 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 133 ( 96 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 154 ( 54 ~; 72 |; 24 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 86 ( 81 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,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(f14,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)],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( sK0_skl(X0,X1) != X1
| ~ in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
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) )
& ( ! [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(f21,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)],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| X3 = X1
| ~ in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( X3 != X2
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f34,plain,
? [A] : unordered_pair(A,A) != singleton(A),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
unordered_pair(sK3_skl,sK3_skl) != singleton(sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f34]) ).
fof(f36,plain,
unordered_pair(sK3_skl,sK3_skl) != singleton(sK3_skl),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ in(X0,unordered_pair(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f23]) ).
fof(f41,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sK0_skl(unordered_pair(X0,X1),X2) = X1
| sK0_skl(unordered_pair(X0,X1),X2) = X0
| sK0_skl(unordered_pair(X0,X1),X2) = X2
| unordered_pair(X0,X1) = singleton(X2) ),
inference(resolution,[status(thm)],[f19,f39]) ).
fof(f74,plain,
! [X0,X1,X2] :
( sK0_skl(unordered_pair(X0,X1),X2) = X1
| sK0_skl(unordered_pair(X0,X1),X2) = X0
| sK0_skl(unordered_pair(X1,X0),X2) = X2
| unordered_pair(X0,X1) = singleton(X2) ),
inference(paramodulation,[status(thm)],[f12,f62]) ).
fof(f93,plain,
! [X0,X1] :
( sK0_skl(unordered_pair(X0,X0),X1) = X0
| X1 != X0
| sK0_skl(unordered_pair(X0,X0),X1) = X0
| unordered_pair(X0,X0) = singleton(X1) ),
inference(equality_factoring,[status(thm)],[f74]) ).
fof(f96,plain,
! [X0,X1] :
( X1 != X0
| sK0_skl(unordered_pair(X0,X0),X1) = X0
| unordered_pair(X0,X0) = singleton(X1) ),
inference(duplicate_literals_removal,[status(thm)],[f93]) ).
fof(f97,plain,
! [X0] :
( sK0_skl(unordered_pair(X0,X0),X0) = X0
| unordered_pair(X0,X0) = singleton(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f96]) ).
fof(f100,plain,
! [X0] :
( ~ in(sK0_skl(unordered_pair(X0,X0),X0),unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0)
| unordered_pair(X0,X0) = singleton(X0) ),
inference(resolution,[status(thm)],[f97,f18]) ).
fof(f107,plain,
! [X0] :
( ~ in(sK0_skl(unordered_pair(X0,X0),X0),unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f100]) ).
fof(f123,plain,
! [X0] :
( unordered_pair(X0,X0) = singleton(X0)
| ~ in(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0) ),
inference(paramodulation,[status(thm)],[f97,f107]) ).
fof(f127,plain,
! [X0] :
( ~ in(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = singleton(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f123]) ).
fof(f128,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(forward_subsumption_resolution,[status(thm)],[f127,f41]) ).
fof(f131,plain,
singleton(sK3_skl) != singleton(sK3_skl),
inference(backward_demodulation,[status(thm)],[f128,f36]) ).
fof(f141,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:55:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.43 % Elapsed time: 0.040899 seconds
% 0.16/0.43 % CPU time: 0.080055 seconds
% 0.16/0.43 % Total memory used: 9.760 MB
% 0.16/0.43 % Net memory used: 9.737 MB
%------------------------------------------------------------------------------