%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU230+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:45:30 AM UTC 2026
% Result : Theorem 0.22s 5.73s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 24 unt; 0 def)
% Number of atoms : 97 ( 49 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 94 ( 40 ~; 33 |; 16 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 8 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t10_ordinal1,conjecture,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t10_ordinal1_neg,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(assume_negation,[status(cth)],[t10_ordinal1]) ).
fof(nnf_33,plain,
? [A] : ~ in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1_neg]) ).
fof(sk_t10_ordinal1_neg,plain,
~ in(sK0,succ(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_33]) ).
cnf(c_45,negated_conjecture,
~ in(sK0,succ(sK0)),
inference(split_conjunct,[status(thm)],[sk_t10_ordinal1_neg]) ).
cnf(c_47,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_48,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_20,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(sk_rc2_funct_1,plain,
( function(sK1)
& empty(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_20]) ).
cnf(c_57,plain,
empty(sK1),
inference(split_conjunct,[status(thm)],[sk_rc2_funct_1]) ).
cnf(c_63,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_74,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
fof(nnf_7,plain,
! [A,B] :
( ( ? [C] :
( ( C != A
| ~ in(C,B) )
& ( C = A
| in(C,B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(sk_d1_tarski_sk,plain,
! [A,B] :
( ( ( ( sK2(A,B) != A
| ~ in(sK2(A,B),B) )
& ( sK2(A,B) = A
| in(sK2(A,B),B) ) )
| singleton(A) = B )
& ( ! [X0] :
( ( X0 != A
| in(X0,B) )
& ( X0 = A
| ~ in(X0,B) ) )
| singleton(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_7]) ).
fof(sk_d1_tarski,plain,
( ! [VAR_0,VAR_1] :
( sK2(VAR_0,VAR_1) != VAR_0
| ~ in(sK2(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( sK2(VAR_0,VAR_1) = VAR_0
| in(sK2(VAR_0,VAR_1),VAR_1)
| singleton(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 != VAR_0
| in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_0
| ~ in(VAR_2,VAR_1)
| singleton(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_tarski_sk]) ).
cnf(c_77,plain,
( sK2(A,B) = A
| in(sK2(A,B),B)
| singleton(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_78,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(split_conjunct,[status(thm)],[sk_d1_tarski]) ).
cnf(c_80,plain,
succ(A) = set_union2(A,singleton(A)),
inference(clausify,[status(thm)],[d1_ordinal1]) ).
cnf(c_81,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_92,negated_conjecture,
~ in(sK0,set_union2(sK0,singleton(sK0))),
inference(paramod,[status(thm)],[c_80,c_45]) ).
cnf(c_300,plain,
empty_set = sK1,
inference(resolve,[status(thm)],[c_57,c_48]) ).
cnf(c_94,plain,
sK1 = empty_set,
inference(copy,[status(thm)],[c_300]) ).
cnf(c_301,plain,
~ in(A,sK1),
inference(resolve,[status(thm)],[c_57,c_47]) ).
cnf(c_95,plain,
~ in(A,empty_set),
inference(paramod,[status(thm)],[c_94,c_301]) ).
cnf(c_302,plain,
( ~ in(A,C)
| in(A,set_union2(B,C)) ),
inference(resolve,[status(thm)],[c_74,c_81]) ).
cnf(c_252,negated_conjecture,
~ in(sK0,singleton(sK0)),
inference(resolve,[status(thm)],[c_302,c_92]) ).
cnf(c_263,plain,
( sK2(A,empty_set) = A
| singleton(A) = empty_set ),
inference(resolve,[status(thm)],[c_95,c_77]) ).
cnf(c_303,plain,
( B != A
| singleton(A) != empty_set ),
inference(resolve,[status(thm)],[c_78,c_95]) ).
cnf(c_268,plain,
singleton(A) != empty_set,
inference(resolve,[status(thm)],[c_303,c_63]) ).
cnf(c_269,plain,
sK2(A,empty_set) = A,
inference(resolve,[status(thm)],[c_268,c_263]) ).
cnf(c_304,plain,
( sK0 != A
| singleton(A) != singleton(sK0) ),
inference(resolve,[status(thm)],[c_78,c_252]) ).
cnf(c_305,plain,
A = sK2(A,empty_set),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_306,plain,
singleton(sK2(sK0,empty_set)) != singleton(sK0),
inference(resolve,[status(thm)],[c_304,c_305]) ).
cnf(c_307,plain,
singleton(sK0) != singleton(sK0),
inference(paramod,[status(thm)],[c_269,c_306]) ).
cnf(c_299,plain,
$false,
inference(copy,[status(thm)],[c_307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU230+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.65 % Computer : n008.cluster.edu
% 0.17/5.65 % Model : x86_64 x86_64
% 0.17/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.65 % Memory : 8046.5625MB
% 0.17/5.65 % OS : Linux 6.8.0-71-generic
% 0.17/5.65 % CPULimit : 300
% 0.17/5.65 % WCLimit : 300
% 0.17/5.65 % DateTime : Sat Sep 26 08:56:01 UTC 2026
% 0.17/5.66 % CPUTime :
% 0.17/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.66 % Process 3252847 was started by sandbox on n008,
% 0.17/5.66 % Sat Sep 26 08:56:01 2026
% 0.17/5.66 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.68
% 0.17/5.68 % From the command line: assign(max_seconds, 300).
% 0.22/5.73
% 0.22/5.73 % SZS status Theorem for theBenchmark
% 0.22/5.73
% 0.22/5.73 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.22/5.73 % Length of proof is 27.
% 0.22/5.73 % Level of proof is 6.
% 0.22/5.73 % Maximum clause weight is 24.000.
% 0.22/5.73 % Given clauses 60.
% 0.22/5.73
% 0.22/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------