%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET901+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 : n007.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 08:37:14 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 182 ( 148 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 192 ( 58 ~; 110 |; 21 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 8 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',l46_zfmisc_1) ).
fof(t42_zfmisc_1,conjecture,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',t42_zfmisc_1) ).
fof(t42_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(assume_negation,[status(cth)],[t42_zfmisc_1]) ).
cnf(c_7,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_12,plain,
( unordered_pair(B,C) = A
| singleton(C) = A
| singleton(B) = A
| empty_set = A
| ~ subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_13,plain,
( empty_set != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_14,plain,
( singleton(B) != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_15,plain,
( singleton(C) != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_16,plain,
( unordered_pair(B,C) != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B,C] :
( ( ( unordered_pair(B,C) != A
& singleton(C) != A
& singleton(B) != A
& empty_set != A )
| ~ subset(A,unordered_pair(B,C)) )
& ( unordered_pair(B,C) = A
| singleton(C) = A
| singleton(B) = A
| empty_set = A
| subset(A,unordered_pair(B,C)) ) ),
inference(fof_nnf,[status(thm)],[t42_zfmisc_1_neg]) ).
fof(sk_t42_zfmisc_1_neg_sk,plain,
( ( ( unordered_pair(sK1,sK2) != sK0
& singleton(sK2) != sK0
& singleton(sK1) != sK0
& empty_set != sK0 )
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,unordered_pair(sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
fof(sk_t42_zfmisc_1_neg,plain,
( ( unordered_pair(sK1,sK2) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( singleton(sK2) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( singleton(sK1) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( empty_set != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,unordered_pair(sK1,sK2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_t42_zfmisc_1_neg_sk]) ).
cnf(c_17,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,unordered_pair(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t42_zfmisc_1_neg]) ).
cnf(c_18,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| subset(sK0,unordered_pair(sK1,sK2)) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,negated_conjecture,
( empty_set != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t42_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
( sK0 != empty_set
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(copy,[status(thm)],[c_19]) ).
cnf(c_21,negated_conjecture,
( singleton(sK1) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t42_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
( singleton(sK2) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t42_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
( unordered_pair(sK1,sK2) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_t42_zfmisc_1_neg]) ).
cnf(c_26,plain,
subset(empty_set,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_30,plain,
( unordered_pair(C,B) != A
| subset(A,unordered_pair(B,C)) ),
inference(paramod,[status(thm)],[c_7,c_16]) ).
cnf(c_60,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_18,c_12]) ).
cnf(c_61,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_62,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_63,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_64,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_31,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_65,plain,
( subset(sK0,unordered_pair(sK2,sK1))
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_32,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_7,c_65]) ).
cnf(c_66,negated_conjecture,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| unordered_pair(sK1,sK2) != sK0 ),
inference(resolve,[status(thm)],[c_23,c_32]) ).
cnf(c_67,negated_conjecture,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_66,c_31]) ).
cnf(c_68,negated_conjecture,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_69,negated_conjecture,
( singleton(sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_40,negated_conjecture,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_41,plain,
( subset(sK0,unordered_pair(A,sK2))
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_40,c_15]) ).
cnf(c_70,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK2) != sK0 ),
inference(resolve,[status(thm)],[c_22,c_41]) ).
cnf(c_71,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_70,c_40]) ).
cnf(c_72,negated_conjecture,
( singleton(sK1) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_47,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_72]) ).
cnf(c_49,plain,
( subset(sK0,unordered_pair(sK1,A))
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_47,c_14]) ).
cnf(c_73,negated_conjecture,
( sK0 = empty_set
| singleton(sK1) != sK0 ),
inference(resolve,[status(thm)],[c_21,c_49]) ).
cnf(c_74,negated_conjecture,
( sK0 = empty_set
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_73,c_47]) ).
cnf(c_55,negated_conjecture,
sK0 = empty_set,
inference(copy,[status(thm)],[c_74]) ).
cnf(c_75,negated_conjecture,
( sK0 != empty_set
| ~ subset(empty_set,unordered_pair(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_55,c_20]) ).
cnf(c_76,negated_conjecture,
( empty_set != empty_set
| ~ subset(empty_set,unordered_pair(sK1,sK2)) ),
inference(paramod,[status(thm)],[c_55,c_75]) ).
cnf(c_77,negated_conjecture,
~ subset(empty_set,unordered_pair(sK1,sK2)),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:22:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3286658 was started by sandbox on n007,
% 0.09/0.37 % Sat Sep 26 08:22:55 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % Assigning unary symbol singleton kb_weight 0 and highest precedence (11).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 26.
% 0.14/0.39 % Level of proof is 10.
% 0.14/0.39 % Maximum clause weight is 31.000.
% 0.14/0.39 % Given clauses 29.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------