%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET887+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 : n010.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 02:10:54 PM UTC 2026
% Result : Theorem 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 14 unt; 6 def)
% Number of atoms : 203 ( 125 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 231 ( 94 ~; 84 |; 41 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 115 ( 103 !; 12 ?)
% 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] :
( A = empty_set
<=> ! [B] : ~ in(B,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(f6,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ! [A] :
( in(sK0_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,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(f23,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)],[f22]) ).
fof(f24,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))],[f23]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( X3 != X1
| in(X3,X0)
| X0 != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f32,plain,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f33,plain,
! [A,B,C] :
( ( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B,C] :
( ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set )
| subset(A,unordered_pair(B,C)) )
& ! [A,B,C] :
( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( X0 = unordered_pair(X1,X2)
| X0 = singleton(X2)
| X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f46,plain,
! [A,B,C,D] :
( A = D
| A = C
| unordered_pair(A,B) != unordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f47,plain,
! [A,D] :
( A = D
| ! [C] :
( A = C
| ! [B] : unordered_pair(A,B) != unordered_pair(C,D) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
? [A,B,C,D] :
( A != D
& A != C
& subset(unordered_pair(A,B),unordered_pair(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f50,plain,
? [A,D] :
( A != D
& ? [C] :
( A != C
& ? [B] : subset(unordered_pair(A,B),unordered_pair(C,D)) ) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
( sK4_skl != sK5_skl
& sK4_skl != sK6_skl
& subset(unordered_pair(sK4_skl,sK7_skl),unordered_pair(sK6_skl,sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK4_skl),skolemize(D,sK5_skl),skolemize(C,sK6_skl),skolemize(B,sK7_skl)],[f50]) ).
fof(f52,plain,
subset(unordered_pair(sK4_skl,sK7_skl),unordered_pair(sK6_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
sK4_skl != sK6_skl,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f54,plain,
sK4_skl != sK5_skl,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f55,plain,
! [A,B,C] :
( A = B
| singleton(A) != unordered_pair(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f56,plain,
! [A,B] :
( A = B
| ! [C] : singleton(A) != unordered_pair(B,C) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f60,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f26]) ).
fof(f86,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f60]) ).
fof(f172,plain,
( unordered_pair(sK4_skl,sK7_skl) = unordered_pair(sK6_skl,sK5_skl)
| unordered_pair(sK4_skl,sK7_skl) = singleton(sK5_skl)
| unordered_pair(sK4_skl,sK7_skl) = singleton(sK6_skl)
| unordered_pair(sK4_skl,sK7_skl) = empty_set ),
inference(resolution,[status(thm)],[f35,f52]) ).
fof(f196,definition,
( sQ6_spl
<=> unordered_pair(sK4_skl,sK7_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ6_spl
| unordered_pair(sK4_skl,sK7_skl) = empty_set ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ7_spl
<=> unordered_pair(sK4_skl,sK7_skl) = singleton(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ7_spl
| unordered_pair(sK4_skl,sK7_skl) = singleton(sK6_skl) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ8_spl
<=> unordered_pair(sK4_skl,sK7_skl) = singleton(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ8_spl
| unordered_pair(sK4_skl,sK7_skl) = singleton(sK5_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ9_spl
<=> unordered_pair(sK4_skl,sK7_skl) = unordered_pair(sK6_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ9_spl
| unordered_pair(sK4_skl,sK7_skl) = unordered_pair(sK6_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ9_spl
| sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f172,f196,f199,f202,f205]) ).
fof(f223,plain,
( ~ sQ6_spl
| in(sK7_skl,empty_set) ),
inference(paramodulation,[status(thm)],[f197,f86]) ).
fof(f247,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f58]) ).
fof(f248,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f366,plain,
( ~ sQ8_spl
| sK5_skl = sK4_skl ),
inference(resolution,[status(thm)],[f203,f57]) ).
fof(f389,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f54]) ).
fof(f390,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f395,plain,
( ~ sQ7_spl
| sK6_skl = sK4_skl ),
inference(resolution,[status(thm)],[f200,f57]) ).
fof(f418,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f53]) ).
fof(f419,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f463,plain,
( ~ sQ9_spl
| sK4_skl = sK5_skl
| sK4_skl = sK6_skl ),
inference(resolution,[status(thm)],[f206,f48]) ).
fof(f496,definition,
( sQ28_spl
<=> sK4_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( ~ sQ28_spl
| sK4_skl = sK6_skl ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,definition,
( sQ29_spl
<=> sK4_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ29_spl
| sK4_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ9_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f463,f496,f499,f205]) ).
fof(f518,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f53]) ).
fof(f519,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f54]) ).
fof(f521,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f522,plain,
$false,
inference(sat_refutation,[status(thm)],[f208,f248,f390,f419,f502,f519,f521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET887+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n010.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:43:25 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.38 % Refutation found
% 0.07/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.059799 seconds
% 0.14/0.40 % CPU time: 0.167570 seconds
% 0.14/0.40 % Total memory used: 102.662 MB
% 0.14/0.40 % Net memory used: 102.299 MB
%------------------------------------------------------------------------------