%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 08:36:57 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 1
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 182 ( 48 ~; 111 |; 15 &)
% ( 6 <=>; 2 =>; 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 : 53 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ? [X,Y] :
( ( ~ equalish(Y,X)
| ~ equalish(X,Y) )
& ( equalish(Y,X)
| equalish(X,Y) ) )
& ! [X0,X1] :
( ( ? [Z] :
( ( ~ a_member_of(Z,X1)
| ~ a_member_of(Z,X0) )
& ( a_member_of(Z,X1)
| a_member_of(Z,X0) ) )
| equalish(X0,X1) )
& ( ! [X2] :
( ( ~ a_member_of(X2,X1)
| a_member_of(X2,X0) )
& ( a_member_of(X2,X1)
| ~ a_member_of(X2,X0) ) )
| ~ equalish(X0,X1) ) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ( ~ equalish(sK2,sK1)
| ~ equalish(sK1,sK2) )
& ( equalish(sK2,sK1)
| equalish(sK1,sK2) )
& ! [X0,X1] :
( ( ( ( ~ a_member_of(sK0(X0,X1),X1)
| ~ a_member_of(sK0(X0,X1),X0) )
& ( a_member_of(sK0(X0,X1),X1)
| a_member_of(sK0(X0,X1),X0) ) )
| equalish(X0,X1) )
& ( ! [X2] :
( ( ~ a_member_of(X2,X1)
| a_member_of(X2,X0) )
& ( a_member_of(X2,X1)
| ~ a_member_of(X2,X0) ) )
| ~ equalish(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(Z,sK0(X0,X1)),skolemize(X,sK1),skolemize(Y,sK2)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ( ~ equalish(sK2,sK1)
| ~ equalish(sK1,sK2) )
& ( equalish(sK2,sK1)
| equalish(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)
| equalish(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)
| equalish(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ a_member_of(VAR_2,VAR_1)
| a_member_of(VAR_2,VAR_0)
| ~ equalish(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( a_member_of(VAR_2,VAR_1)
| ~ a_member_of(VAR_2,VAR_0)
| ~ equalish(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
( a_member_of(C,B)
| ~ a_member_of(C,A)
| ~ equalish(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)
| ~ equalish(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( a_member_of(sK0(A,B),B)
| a_member_of(sK0(A,B),A)
| equalish(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)
| equalish(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_6,negated_conjecture,
( equalish(sK2,sK1)
| equalish(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
( ~ equalish(sK2,sK1)
| ~ equalish(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_10,plain,
( ~ a_member_of(C,B)
| a_member_of(C,A)
| a_member_of(sK0(A,B),B)
| a_member_of(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_11,plain,
( a_member_of(C,B)
| ~ a_member_of(C,A)
| a_member_of(sK0(A,B),B)
| a_member_of(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_12,plain,
( ~ a_member_of(A,sK1)
| a_member_of(A,sK2)
| equalish(sK1,sK2) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_13,plain,
( a_member_of(A,sK1)
| ~ a_member_of(A,sK2)
| equalish(sK1,sK2) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_14,plain,
( a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK2)
| ~ equalish(sK1,sK2) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_15,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_14,c_4]) ).
cnf(c_17,plain,
( a_member_of(sK0(sK2,sK1),A)
| a_member_of(sK0(A,sK2),sK2)
| a_member_of(sK0(A,sK2),A)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(resolve,[status(thm)],[c_15,c_10]) ).
cnf(c_70,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(factor,[status(thm)],[c_17]) ).
cnf(c_71,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_18,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_19,plain,
( a_member_of(sK0(sK2,sK1),A)
| a_member_of(sK0(sK1,A),A)
| a_member_of(sK0(sK1,A),sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_21,plain,
( ~ a_member_of(sK0(sK2,sK1),sK2)
| equalish(sK2,sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_18,c_5]) ).
cnf(c_72,plain,
( a_member_of(sK0(sK2,sK1),sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(factor,[status(thm)],[c_19]) ).
cnf(c_22,plain,
( a_member_of(sK0(sK2,sK1),sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| equalish(sK2,sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_74,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| equalish(sK2,sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_26,plain,
( equalish(sK2,sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_27,plain,
( ~ equalish(sK1,sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_26,c_7]) ).
cnf(c_75,negated_conjecture,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_27,c_4]) ).
cnf(c_76,negated_conjecture,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_35,negated_conjecture,
( a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_77,plain,
( a_member_of(sK0(sK1,sK2),sK1)
| equalish(sK1,sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_35,c_13]) ).
cnf(c_36,plain,
( equalish(sK1,sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(copy,[status(thm)],[c_77]) ).
cnf(c_40,plain,
( ~ a_member_of(A,sK2)
| a_member_of(A,sK1)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_36,c_3]) ).
cnf(c_42,plain,
( ~ a_member_of(sK0(sK1,sK2),sK2)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_78,plain,
( a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK1,sK2),sK1) ),
inference(resolve,[status(thm)],[c_42,c_35]) ).
cnf(c_43,plain,
a_member_of(sK0(sK1,sK2),sK1),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_44,plain,
( a_member_of(sK0(sK1,sK2),sK2)
| equalish(sK1,sK2) ),
inference(resolve,[status(thm)],[c_43,c_12]) ).
cnf(c_47,plain,
( ~ a_member_of(sK0(sK1,sK2),sK2)
| equalish(sK1,sK2) ),
inference(resolve,[status(thm)],[c_43,c_5]) ).
cnf(c_49,plain,
( a_member_of(A,sK2)
| ~ a_member_of(A,sK1)
| a_member_of(sK0(sK1,sK2),sK2) ),
inference(resolve,[status(thm)],[c_44,c_2]) ).
cnf(c_79,plain,
( ~ a_member_of(sK0(sK1,sK2),sK1)
| a_member_of(sK0(sK1,sK2),sK2) ),
inference(factor,[status(thm)],[c_49]) ).
cnf(c_50,plain,
a_member_of(sK0(sK1,sK2),sK2),
inference(resolve,[status(thm)],[c_43,c_79]) ).
cnf(c_51,plain,
equalish(sK1,sK2),
inference(resolve,[status(thm)],[c_50,c_47]) ).
cnf(c_52,plain,
( a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK2) ),
inference(resolve,[status(thm)],[c_51,c_14]) ).
cnf(c_53,negated_conjecture,
~ equalish(sK2,sK1),
inference(resolve,[status(thm)],[c_51,c_7]) ).
cnf(c_54,plain,
( ~ a_member_of(A,sK2)
| a_member_of(A,sK1) ),
inference(resolve,[status(thm)],[c_51,c_3]) ).
cnf(c_55,plain,
( a_member_of(A,sK2)
| ~ a_member_of(A,sK1) ),
inference(resolve,[status(thm)],[c_51,c_2]) ).
cnf(c_80,plain,
( a_member_of(sK0(sK2,sK1),sK1)
| a_member_of(sK0(sK2,sK1),sK1) ),
inference(resolve,[status(thm)],[c_52,c_54]) ).
cnf(c_65,plain,
a_member_of(sK0(sK2,sK1),sK1),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_66,plain,
a_member_of(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_65,c_55]) ).
cnf(c_81,negated_conjecture,
( ~ a_member_of(sK0(sK2,sK1),sK2)
| equalish(sK2,sK1) ),
inference(resolve,[status(thm)],[c_65,c_5]) ).
cnf(c_82,negated_conjecture,
~ a_member_of(sK0(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_53,c_81]) ).
cnf(c_69,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 08:15:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2309929 was started by sandbox2 on n013,
% 0.10/0.38 % Sat Sep 26 08:15:07 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.41
% 0.10/0.41 % SZS status Theorem for theBenchmark
% 0.10/0.41
% 0.10/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.41 % Length of proof is 37.
% 0.10/0.41 % Level of proof is 22.
% 0.10/0.41 % Maximum clause weight is 30.000.
% 0.10/0.41 % Given clauses 33.
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------