%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET909+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 : n012.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 08:37:16 AM UTC 2026
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 45 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 10 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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 : 55 ( 12 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_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(t50_zfmisc_1,conjecture,
! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
file('theBenchmark.p',t50_zfmisc_1) ).
fof(t50_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
inference(assume_negation,[status(cth)],[t50_zfmisc_1]) ).
cnf(c_14,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_15,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_16,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_19,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_26,plain,
( ~ in(D,B)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_33,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(nnf_12,plain,
? [A,B,C] : set_union2(unordered_pair(A,B),C) = empty_set,
inference(fof_nnf,[status(thm)],[t50_zfmisc_1_neg]) ).
fof(sk_t50_zfmisc_1_neg,plain,
set_union2(unordered_pair(sK0,sK1),sK2) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_12]) ).
cnf(c_36,negated_conjecture,
set_union2(unordered_pair(sK0,sK1),sK2) = empty_set,
inference(split_conjunct,[status(thm)],[sk_t50_zfmisc_1_neg]) ).
cnf(c_453,negated_conjecture,
set_union2(sK2,unordered_pair(sK0,sK1)) = empty_set,
inference(paramod,[status(thm)],[c_15,c_36]) ).
cnf(c_37,negated_conjecture,
empty_set = set_union2(sK2,unordered_pair(sK0,sK1)),
inference(copy,[status(thm)],[c_453]) ).
cnf(c_51,plain,
( ~ in(B,A)
| set_union2(sK2,unordered_pair(sK0,sK1)) != A ),
inference(paramod,[status(thm)],[c_37,c_16]) ).
cnf(c_52,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_19,c_14]) ).
cnf(c_454,plain,
~ in(A,set_union2(unordered_pair(sK0,sK1),sK2)),
inference(resolve,[status(thm)],[c_51,c_15]) ).
cnf(c_242,plain,
~ in(A,set_union2(sK2,unordered_pair(sK0,sK1))),
inference(paramod,[status(thm)],[c_15,c_454]) ).
cnf(c_455,plain,
in(set_union2(A,A),unordered_pair(B,A)),
inference(resolve,[status(thm)],[c_52,c_33]) ).
cnf(c_246,plain,
in(A,unordered_pair(B,A)),
inference(paramod,[status(thm)],[c_33,c_455]) ).
cnf(c_277,plain,
( in(C,D)
| set_union2(A,unordered_pair(B,C)) != D ),
inference(resolve,[status(thm)],[c_246,c_26]) ).
cnf(c_456,negated_conjecture,
set_union2(sK2,unordered_pair(sK0,sK1)) = empty_set,
inference(copy,[status(thm)],[c_37]) ).
cnf(c_457,negated_conjecture,
in(sK1,empty_set),
inference(resolve,[status(thm)],[c_277,c_456]) ).
cnf(c_458,negated_conjecture,
in(sK1,set_union2(sK2,unordered_pair(sK0,sK1))),
inference(paramod,[status(thm)],[c_37,c_457]) ).
cnf(c_452,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_242,c_458]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET909+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 08:24:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 132209 was started by sandbox on n012,
% 0.03/0.30 % Sat Sep 26 08:24:51 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.14/0.35
% 0.14/0.35 % SZS status Theorem for theBenchmark
% 0.14/0.35
% 0.14/0.35 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.35 % Length of proof is 21.
% 0.14/0.35 % Level of proof is 5.
% 0.14/0.35 % Maximum clause weight is 11.000.
% 0.14/0.35 % Given clauses 60.
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------