%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:37:19 AM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 14 unt; 0 def)
% Number of atoms : 214 ( 198 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 218 ( 65 ~; 128 |; 21 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 15 sgn 15 !; 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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t75_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',t75_zfmisc_1) ).
fof(t75_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(assume_negation,[status(cth)],[t75_zfmisc_1]) ).
cnf(c_8,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_10,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_11,plain,
( empty_set != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_12,plain,
( singleton(B) != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_13,plain,
( singleton(C) != A
| subset(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[l46_zfmisc_1]) ).
cnf(c_17,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_18,plain,
( subset(A,B)
| set_difference(A,B) != empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
cnf(c_19,plain,
( ~ subset(A,B)
| set_difference(A,B) = empty_set ),
inference(clausify,[status(thm)],[t37_xboole_1]) ).
fof(nnf_7,plain,
? [A,B,C] :
( ( ( unordered_pair(B,C) != A
& singleton(C) != A
& singleton(B) != A
& empty_set != A )
| set_difference(A,unordered_pair(B,C)) != empty_set )
& ( unordered_pair(B,C) = A
| singleton(C) = A
| singleton(B) = A
| empty_set = A
| set_difference(A,unordered_pair(B,C)) = empty_set ) ),
inference(fof_nnf,[status(thm)],[t75_zfmisc_1_neg]) ).
fof(sk_t75_zfmisc_1_neg_sk,plain,
( ( ( unordered_pair(sK1,sK2) != sK0
& singleton(sK2) != sK0
& singleton(sK1) != sK0
& empty_set != sK0 )
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set )
& ( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_7]) ).
fof(sk_t75_zfmisc_1_neg,plain,
( ( unordered_pair(sK1,sK2) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set )
& ( singleton(sK2) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set )
& ( singleton(sK1) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set )
& ( empty_set != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set )
& ( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) = empty_set ) ),
inference(cnf_transformation,[status(thm)],[sk_t75_zfmisc_1_neg_sk]) ).
cnf(c_20,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| empty_set = sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) = empty_set ),
inference(split_conjunct,[status(thm)],[sk_t75_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| set_difference(sK0,unordered_pair(sK1,sK2)) = empty_set ),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
( empty_set != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t75_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
( sK0 != empty_set
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set ),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_24,negated_conjecture,
( singleton(sK1) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t75_zfmisc_1_neg]) ).
cnf(c_25,negated_conjecture,
( singleton(sK2) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t75_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
( unordered_pair(sK1,sK2) != sK0
| set_difference(sK0,unordered_pair(sK1,sK2)) != empty_set ),
inference(split_conjunct,[status(thm)],[sk_t75_zfmisc_1_neg]) ).
cnf(c_28,plain,
( unordered_pair(C,B) = A
| singleton(B) = A
| singleton(C) = A
| empty_set = A
| ~ subset(A,unordered_pair(B,C)) ),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_29,plain,
subset(empty_set,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_30,plain,
subset(singleton(A),unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_12]) ).
cnf(c_31,plain,
subset(singleton(A),unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_34,plain,
set_difference(A,A) = empty_set,
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_35,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_37,plain,
set_difference(empty_set,unordered_pair(A,B)) = empty_set,
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_38,plain,
set_difference(singleton(A),unordered_pair(A,B)) = empty_set,
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_39,plain,
set_difference(singleton(A),unordered_pair(B,A)) = empty_set,
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_82,plain,
( unordered_pair(sK2,sK1) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| empty_set = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_35,c_28]) ).
cnf(c_83,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| empty_set = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_8,c_82]) ).
cnf(c_84,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| sK0 = empty_set
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_85,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_86,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK1) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_87,plain,
( unordered_pair(sK1,sK2) = sK0
| unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_41,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
( unordered_pair(sK1,sK2) != sK0
| set_difference(sK0,sK0) != empty_set
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_41,c_26]) ).
cnf(c_89,plain,
( unordered_pair(sK1,sK2) != sK0
| empty_set != empty_set
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_34,c_88]) ).
cnf(c_45,plain,
( unordered_pair(sK1,sK2) != sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_90,plain,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_91,plain,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_92,plain,
( singleton(sK2) = sK0
| singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_91]) ).
cnf(c_55,plain,
( singleton(sK2) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_61,plain,
( set_difference(sK0,unordered_pair(A,sK2)) = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_55,c_39]) ).
cnf(c_93,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK2) != sK0 ),
inference(resolve,[status(thm)],[c_25,c_61]) ).
cnf(c_94,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_93,c_55]) ).
cnf(c_95,negated_conjecture,
( singleton(sK1) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_66,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_71,plain,
( set_difference(sK0,unordered_pair(sK1,A)) = empty_set
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_66,c_38]) ).
cnf(c_96,negated_conjecture,
( sK0 = empty_set
| singleton(sK1) != sK0 ),
inference(resolve,[status(thm)],[c_24,c_71]) ).
cnf(c_97,negated_conjecture,
( sK0 = empty_set
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_96,c_66]) ).
cnf(c_77,negated_conjecture,
sK0 = empty_set,
inference(copy,[status(thm)],[c_97]) ).
cnf(c_98,negated_conjecture,
( sK0 != empty_set
| set_difference(empty_set,unordered_pair(sK1,sK2)) != empty_set ),
inference(paramod,[status(thm)],[c_77,c_23]) ).
cnf(c_99,negated_conjecture,
( sK0 != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_37,c_98]) ).
cnf(c_100,negated_conjecture,
( empty_set != empty_set
| empty_set != empty_set ),
inference(paramod,[status(thm)],[c_77,c_99]) ).
cnf(c_101,negated_conjecture,
empty_set != empty_set,
inference(copy,[status(thm)],[c_100]) ).
cnf(c_81,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:27:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1083697 was started by sandbox2 on n020,
% 0.08/0.36 % Sat Sep 26 08:27:18 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12).
% 0.08/0.40
% 0.08/0.40 % SZS status Theorem for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.08/0.40 % Length of proof is 37.
% 0.08/0.40 % Level of proof is 11.
% 0.08/0.40 % Maximum clause weight is 38.000.
% 0.08/0.40 % Given clauses 49.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------