%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 09:43:28 AM UTC 2026
% Result : Theorem 0.18s 5.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 88 ( 32 ~; 33 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 41 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ( ? [Z] :
( ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| a_member_of(Z,X) ) )
| eq(X,Y) )
& ( ! [X0] :
( ( ~ a_member_of(X0,Y)
| a_member_of(X0,X) )
& ( a_member_of(X0,Y)
| ~ a_member_of(X0,X) ) )
| ~ eq(X,Y) ) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ~ eq(sK2,sK1)
& eq(sK1,sK2)
& ! [X,Y] :
( ( ( ( ~ a_member_of(sK0(X,Y),Y)
| ~ a_member_of(sK0(X,Y),X) )
& ( a_member_of(sK0(X,Y),Y)
| a_member_of(sK0(X,Y),X) ) )
| eq(X,Y) )
& ( ! [X0] :
( ( ~ a_member_of(X0,Y)
| a_member_of(X0,X) )
& ( a_member_of(X0,Y)
| ~ a_member_of(X0,X) ) )
| ~ eq(X,Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(Z,sK0(X,Y)),skolemize(A,sK1),skolemize(B,sK2)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ~ eq(sK2,sK1)
& eq(sK1,sK2)
& ! [VAR_0,VAR_1] :
( ~ a_member_of(sK0(VAR_0,VAR_1),VAR_1)
| ~ a_member_of(sK0(VAR_0,VAR_1),VAR_0)
| eq(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( a_member_of(sK0(VAR_0,VAR_1),VAR_1)
| a_member_of(sK0(VAR_0,VAR_1),VAR_0)
| eq(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ a_member_of(VAR_2,VAR_1)
| a_member_of(VAR_2,VAR_0)
| ~ eq(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( a_member_of(VAR_2,VAR_1)
| ~ a_member_of(VAR_2,VAR_0)
| ~ eq(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( a_member_of(sK0(A,B),B)
| a_member_of(sK0(A,B),A)
| eq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
( ~ a_member_of(C,B)
| a_member_of(C,A)
| ~ eq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( a_member_of(C,B)
| ~ a_member_of(C,A)
| ~ eq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
( ~ a_member_of(sK0(A,B),B)
| ~ a_member_of(sK0(A,B),A)
| eq(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
eq(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
~ eq(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_8,negated_conjecture,
( a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_9,negated_conjecture,
( ~ a_member_of(sK0(sK2,sK1),sK1)
| ~ a_member_of(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_10,negated_conjecture,
( a_member_of(A,sK2)
| ~ a_member_of(A,sK1) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_11,negated_conjecture,
( ~ a_member_of(A,sK2)
| a_member_of(A,sK1) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_23,negated_conjecture,
( a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_16,negated_conjecture,
a_member_of(sK0(sK2,sK1),sK1),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_17,negated_conjecture,
~ a_member_of(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_16,c_9]) ).
cnf(c_24,negated_conjecture,
a_member_of(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_16,c_10]) ).
cnf(c_22,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n016.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 18:57:06 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.46 % Process 1497334 was started by sandbox on n016,
% 0.18/5.46 % Sat Sep 26 18:57:06 2026
% 0.18/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.47
% 0.18/5.47 % From the command line: assign(max_seconds, 300).
% 0.18/5.48
% 0.18/5.48 % SZS status Theorem for theBenchmark
% 0.18/5.48
% 0.18/5.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.48 % Length of proof is 14.
% 0.18/5.48 % Level of proof is 5.
% 0.18/5.48 % Maximum clause weight is 10.000.
% 0.18/5.48 % Given clauses 9.
% 0.18/5.48
% 0.18/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------