%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET903+1 : 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 : n018.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 08:37:15 AM UTC 2026
% Result : Theorem 0.24s 5.50s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 26 ~; 13 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 3 sgn 9 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t43_zfmisc_1,axiom,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('theBenchmark.p',t43_zfmisc_1) ).
fof(t44_zfmisc_1,conjecture,
! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
file('theBenchmark.p',t44_zfmisc_1) ).
fof(t44_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(assume_negation,[status(cth)],[t44_zfmisc_1]) ).
cnf(c_16,plain,
( empty_set = B
| singleton(A) = B
| singleton(A) != set_union2(B,C) ),
inference(clausify,[status(thm)],[t43_zfmisc_1]) ).
cnf(c_18,plain,
( C = empty_set
| singleton(A) = C
| singleton(A) != set_union2(B,C) ),
inference(clausify,[status(thm)],[t43_zfmisc_1]) ).
cnf(c_19,plain,
( empty_set = C
| singleton(A) = C
| singleton(A) != set_union2(B,C) ),
inference(copy,[status(thm)],[c_18]) ).
fof(nnf_8,plain,
? [A,B,C] :
( C != empty_set
& empty_set != B
& C != B
& singleton(A) = set_union2(B,C) ),
inference(fof_nnf,[status(thm)],[t44_zfmisc_1_neg]) ).
fof(sk_t44_zfmisc_1_neg,plain,
( sK2 != empty_set
& empty_set != sK1
& sK2 != sK1
& singleton(sK0) = set_union2(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_8]) ).
cnf(c_20,negated_conjecture,
singleton(sK0) = set_union2(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t44_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
sK2 != sK1,
inference(split_conjunct,[status(thm)],[sk_t44_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
empty_set != sK1,
inference(split_conjunct,[status(thm)],[sk_t44_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
sK1 != empty_set,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_24,negated_conjecture,
sK2 != empty_set,
inference(split_conjunct,[status(thm)],[sk_t44_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
( empty_set = sK2
| singleton(sK0) = sK2 ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_30,negated_conjecture,
( empty_set = sK2
| set_union2(sK1,sK2) = sK2 ),
inference(paramod,[status(thm)],[c_20,c_29]) ).
cnf(c_31,negated_conjecture,
( sK2 = empty_set
| set_union2(sK1,sK2) = sK2 ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_27,negated_conjecture,
set_union2(sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_24,c_31]) ).
cnf(c_32,negated_conjecture,
( empty_set = sK1
| singleton(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_20,c_16]) ).
cnf(c_33,negated_conjecture,
( empty_set = sK1
| set_union2(sK1,sK2) = sK1 ),
inference(paramod,[status(thm)],[c_20,c_32]) ).
cnf(c_34,negated_conjecture,
( empty_set = sK1
| sK2 = sK1 ),
inference(paramod,[status(thm)],[c_27,c_33]) ).
cnf(c_35,negated_conjecture,
( sK1 = empty_set
| sK2 = sK1 ),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,negated_conjecture,
sK1 = empty_set,
inference(resolve,[status(thm)],[c_21,c_35]) ).
cnf(c_28,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_23,c_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.48 % Computer : n018.cluster.edu
% 0.18/5.48 % Model : x86_64 x86_64
% 0.18/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.48 % Memory : 8046.5625MB
% 0.18/5.48 % OS : Linux 6.8.0-71-generic
% 0.18/5.48 % CPULimit : 300
% 0.18/5.48 % WCLimit : 300
% 0.18/5.48 % DateTime : Sat Sep 26 08:27:12 UTC 2026
% 0.18/5.48 % CPUTime :
% 0.18/5.49 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.49 % Process 4189347 was started by sandbox on n018,
% 0.18/5.49 % Sat Sep 26 08:27:12 2026
% 0.18/5.49 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.49
% 0.18/5.49 % From the command line: assign(max_seconds, 300).
% 0.24/5.50
% 0.24/5.50 % SZS status Theorem for theBenchmark
% 0.24/5.50
% 0.24/5.50 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.24/5.50 % Length of proof is 12.
% 0.24/5.50 % Level of proof is 4.
% 0.24/5.50 % Maximum clause weight is 13.000.
% 0.24/5.50 % Given clauses 11.
% 0.24/5.50
% 0.24/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------