%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 08:35:29 AM UTC 2026
% Result : Theorem 0.25s 10.50s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of formulae : 57 ( 8 unt; 0 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 170 ( 46 ~; 109 |; 11 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel43_1,axiom,
! [X,Y] :
( set_equal(X,Y)
<=> ! [Z] :
( element(Z,X)
<=> element(Z,Y) ) ),
file('theBenchmark.p',pel43_1) ).
fof(pel43,conjecture,
! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
file('theBenchmark.p',pel43) ).
fof(pel43_neg,negated_conjecture,
~ ! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
inference(assume_negation,[status(cth)],[pel43]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [Z] :
( ( ~ element(Z,Y)
| ~ element(Z,X) )
& ( element(Z,Y)
| element(Z,X) ) )
| set_equal(X,Y) )
& ( ! [X0] :
( ( ~ element(X0,Y)
| element(X0,X) )
& ( element(X0,Y)
| ~ element(X0,X) ) )
| ~ set_equal(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel43_1]) ).
fof(sk_pel43_1_sk,plain,
! [X,Y] :
( ( ( ( ~ element(sK0(X,Y),Y)
| ~ element(sK0(X,Y),X) )
& ( element(sK0(X,Y),Y)
| element(sK0(X,Y),X) ) )
| set_equal(X,Y) )
& ( ! [X0] :
( ( ~ element(X0,Y)
| element(X0,X) )
& ( element(X0,Y)
| ~ element(X0,X) ) )
| ~ set_equal(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X,Y))],[nnf_1]) ).
fof(sk_pel43_1,plain,
( ! [VAR_0,VAR_1] :
( ~ element(sK0(VAR_0,VAR_1),VAR_1)
| ~ element(sK0(VAR_0,VAR_1),VAR_0)
| set_equal(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( element(sK0(VAR_0,VAR_1),VAR_1)
| element(sK0(VAR_0,VAR_1),VAR_0)
| set_equal(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ element(VAR_2,VAR_1)
| element(VAR_2,VAR_0)
| ~ set_equal(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(VAR_2,VAR_1)
| ~ element(VAR_2,VAR_0)
| ~ set_equal(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel43_1_sk]) ).
cnf(c_3,plain,
( element(C,B)
| ~ element(C,A)
| ~ set_equal(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel43_1]) ).
cnf(c_4,plain,
( ~ element(C,B)
| element(C,A)
| ~ set_equal(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel43_1]) ).
cnf(c_5,plain,
( element(sK0(A,B),B)
| element(sK0(A,B),A)
| set_equal(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel43_1]) ).
cnf(c_6,plain,
( ~ element(sK0(A,B),B)
| ~ element(sK0(A,B),A)
| set_equal(A,B) ),
inference(split_conjunct,[status(thm)],[sk_pel43_1]) ).
fof(nnf_2,plain,
? [X,Y] :
( ( ~ set_equal(Y,X)
| ~ set_equal(X,Y) )
& ( set_equal(Y,X)
| set_equal(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel43_neg]) ).
fof(sk_pel43_neg,plain,
( ( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) )
& ( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X,sK1),skolemize(Y,sK2)],[nnf_2]) ).
cnf(c_7,negated_conjecture,
( set_equal(sK2,sK1)
| set_equal(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel43_neg]) ).
cnf(c_8,negated_conjecture,
( ~ set_equal(sK2,sK1)
| ~ set_equal(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel43_neg]) ).
cnf(c_11,plain,
( ~ element(C,B)
| element(C,A)
| element(sK0(A,B),B)
| element(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_12,plain,
( element(C,B)
| ~ element(C,A)
| element(sK0(A,B),B)
| element(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_13,plain,
( ~ element(A,sK1)
| element(A,sK2)
| set_equal(sK1,sK2) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_14,plain,
( element(A,sK1)
| ~ element(A,sK2)
| set_equal(sK1,sK2) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_15,plain,
( element(sK0(sK2,sK1),sK1)
| element(sK0(sK2,sK1),sK2)
| ~ set_equal(sK1,sK2) ),
inference(resolve,[status(thm)],[c_8,c_5]) ).
cnf(c_16,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK2,sK1),sK1)
| element(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_15,c_5]) ).
cnf(c_18,plain,
( element(sK0(sK2,sK1),A)
| element(sK0(A,sK2),sK2)
| element(sK0(A,sK2),A)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK2,sK1),sK1) ),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_71,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK2,sK1),sK1) ),
inference(factor,[status(thm)],[c_18]) ).
cnf(c_72,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK2,sK1),sK1) ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_19,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK2,sK1),sK1) ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_20,plain,
( element(sK0(sK2,sK1),A)
| element(sK0(sK1,A),A)
| element(sK0(sK1,A),sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_22,plain,
( ~ element(sK0(sK2,sK1),sK2)
| set_equal(sK2,sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_19,c_6]) ).
cnf(c_73,plain,
( element(sK0(sK2,sK1),sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(factor,[status(thm)],[c_20]) ).
cnf(c_23,plain,
( element(sK0(sK2,sK1),sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_74,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| set_equal(sK2,sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_22,c_23]) ).
cnf(c_75,plain,
( element(sK0(sK1,sK2),sK2)
| set_equal(sK2,sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_27,plain,
( set_equal(sK2,sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_28,plain,
( ~ set_equal(sK1,sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_27,c_8]) ).
cnf(c_76,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_28,c_5]) ).
cnf(c_77,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_36,plain,
( element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_78,plain,
( element(sK0(sK1,sK2),sK1)
| set_equal(sK1,sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_36,c_14]) ).
cnf(c_37,plain,
( set_equal(sK1,sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_41,plain,
( ~ element(A,sK2)
| element(A,sK1)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_37,c_4]) ).
cnf(c_43,plain,
( ~ element(sK0(sK1,sK2),sK2)
| element(sK0(sK1,sK2),sK1) ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_79,plain,
( element(sK0(sK1,sK2),sK1)
| element(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_43,c_36]) ).
cnf(c_44,plain,
element(sK0(sK1,sK2),sK1),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_45,plain,
( element(sK0(sK1,sK2),sK2)
| set_equal(sK1,sK2) ),
inference(resolve,[status(thm)],[c_44,c_13]) ).
cnf(c_48,plain,
( ~ element(sK0(sK1,sK2),sK2)
| set_equal(sK1,sK2) ),
inference(resolve,[status(thm)],[c_44,c_6]) ).
cnf(c_50,plain,
( element(A,sK2)
| ~ element(A,sK1)
| element(sK0(sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_45,c_3]) ).
cnf(c_80,plain,
( ~ element(sK0(sK1,sK2),sK1)
| element(sK0(sK1,sK2),sK2) ),
inference(factor,[status(thm)],[c_50]) ).
cnf(c_51,plain,
element(sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_44,c_80]) ).
cnf(c_52,plain,
set_equal(sK1,sK2),
inference(resolve,[status(thm)],[c_51,c_48]) ).
cnf(c_53,plain,
( element(sK0(sK2,sK1),sK1)
| element(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_52,c_15]) ).
cnf(c_54,negated_conjecture,
~ set_equal(sK2,sK1),
inference(resolve,[status(thm)],[c_52,c_8]) ).
cnf(c_55,plain,
( ~ element(A,sK2)
| element(A,sK1) ),
inference(resolve,[status(thm)],[c_52,c_4]) ).
cnf(c_56,plain,
( element(A,sK2)
| ~ element(A,sK1) ),
inference(resolve,[status(thm)],[c_52,c_3]) ).
cnf(c_81,plain,
( element(sK0(sK2,sK1),sK1)
| element(sK0(sK2,sK1),sK1) ),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_66,plain,
element(sK0(sK2,sK1),sK1),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_67,plain,
element(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_66,c_56]) ).
cnf(c_82,plain,
( ~ element(sK0(sK2,sK1),sK2)
| set_equal(sK2,sK1) ),
inference(resolve,[status(thm)],[c_66,c_6]) ).
cnf(c_83,negated_conjecture,
~ element(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_54,c_82]) ).
cnf(c_70,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_67,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/10.47 % Computer : n016.cluster.edu
% 0.20/10.47 % Model : x86_64 x86_64
% 0.20/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.47 % Memory : 8046.5625MB
% 0.20/10.47 % OS : Linux 6.8.0-71-generic
% 0.20/10.47 % CPULimit : 300
% 0.20/10.47 % WCLimit : 300
% 0.20/10.47 % DateTime : Sat Sep 26 07:04:41 UTC 2026
% 0.20/10.47 % CPUTime :
% 0.20/10.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/10.47 % Process 245084 was started by sandbox2 on n016,
% 0.20/10.47 % Sat Sep 26 07:04:41 2026
% 0.20/10.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/10.48
% 0.20/10.48 % From the command line: assign(max_seconds, 300).
% 0.25/10.50
% 0.25/10.50 % SZS status Theorem for theBenchmark
% 0.25/10.50
% 0.25/10.50 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.25/10.50 % Length of proof is 38.
% 0.25/10.50 % Level of proof is 22.
% 0.25/10.50 % Maximum clause weight is 30.000.
% 0.25/10.50 % Given clauses 33.
% 0.25/10.50
% 0.25/10.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------