%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:45:09 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 121 ( 66 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 110 ( 34 ~; 62 |; 7 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(l3_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('theBenchmark.p',l3_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(l4_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(l4_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(assume_negation,[status(cth)],[l4_zfmisc_1]) ).
cnf(c_18,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_21,plain,
( ~ in(A,B)
| subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_22,plain,
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[l3_zfmisc_1]) ).
cnf(c_25,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_26,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
cnf(c_28,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
cnf(c_29,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
fof(nnf_14,plain,
? [A,B] :
( ( ( singleton(B) != A
& empty_set != A )
| ~ subset(A,singleton(B)) )
& ( singleton(B) = A
| empty_set = A
| subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1_neg]) ).
fof(sk_l4_zfmisc_1_neg_sk,plain,
( ( ( singleton(sK1) != sK0
& empty_set != sK0 )
| ~ subset(sK0,singleton(sK1)) )
& ( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_14]) ).
fof(sk_l4_zfmisc_1_neg,plain,
( ( singleton(sK1) != sK0
| ~ subset(sK0,singleton(sK1)) )
& ( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) )
& ( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_l4_zfmisc_1_neg_sk]) ).
cnf(c_30,negated_conjecture,
( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_31,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| subset(sK0,singleton(sK1)) ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_32,negated_conjecture,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_33,negated_conjecture,
( sK0 != empty_set
| ~ subset(sK0,singleton(sK1)) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,negated_conjecture,
( singleton(sK1) != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_l4_zfmisc_1_neg]) ).
cnf(c_36,plain,
( subset(B,set_difference(B,singleton(A)))
| in(A,B) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_40,plain,
( set_difference(sK0,singleton(sK1)) = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_31,c_28]) ).
cnf(c_132,negated_conjecture,
( ~ subset(singleton(sK1),sK0)
| sK0 = singleton(sK1)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_31,c_18]) ).
cnf(c_133,negated_conjecture,
( ~ subset(singleton(sK1),sK0)
| singleton(sK1) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_42,negated_conjecture,
( ~ subset(singleton(sK1),sK0)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_45,plain,
( subset(singleton(B),A)
| subset(A,set_difference(A,singleton(B))) ),
inference(resolve,[status(thm)],[c_36,c_21]) ).
cnf(c_68,plain,
( subset(singleton(sK1),sK0)
| subset(sK0,empty_set)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_40,c_45]) ).
cnf(c_134,plain,
( singleton(sK1) = sK0
| sK0 = empty_set
| subset(sK0,empty_set)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_68,c_42]) ).
cnf(c_135,plain,
( singleton(sK1) = sK0
| subset(sK0,empty_set)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_82,plain,
( subset(sK0,empty_set)
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_136,plain,
( empty_set = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_82,c_29]) ).
cnf(c_137,plain,
( sK0 = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_136]) ).
cnf(c_83,plain,
( singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_84,plain,
( ~ subset(sK0,singleton(sK1))
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_83,c_34]) ).
cnf(c_138,plain,
( ~ subset(sK0,sK0)
| sK0 = empty_set
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_83,c_84]) ).
cnf(c_139,plain,
( ~ subset(sK0,sK0)
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_129,plain,
sK0 = empty_set,
inference(resolve,[status(thm)],[c_25,c_139]) ).
cnf(c_140,negated_conjecture,
( sK0 != empty_set
| ~ subset(empty_set,singleton(sK1)) ),
inference(paramod,[status(thm)],[c_129,c_33]) ).
cnf(c_141,negated_conjecture,
( empty_set != empty_set
| ~ subset(empty_set,singleton(sK1)) ),
inference(paramod,[status(thm)],[c_129,c_140]) ).
cnf(c_142,negated_conjecture,
~ subset(empty_set,singleton(sK1)),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_131,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:41:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1114243 was started by sandbox on n020,
% 0.10/0.36 % Sat Sep 26 08:41:18 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 30.
% 0.13/0.39 % Level of proof is 9.
% 0.13/0.39 % Maximum clause weight is 28.000.
% 0.13/0.39 % Given clauses 55.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------