%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET886+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 : n017.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 08:37:13 AM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 22 unt; 0 def)
% Number of atoms : 38 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 7 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t26_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('theBenchmark.p',t26_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t27_zfmisc_1,conjecture,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
file('theBenchmark.p',t27_zfmisc_1) ).
fof(t27_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> unordered_pair(A,B) = singleton(C) ),
inference(assume_negation,[status(cth)],[t27_zfmisc_1]) ).
cnf(c_8,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_11,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_12,plain,
( C = A
| ~ subset(unordered_pair(A,B),singleton(C)) ),
inference(clausify,[status(thm)],[t26_zfmisc_1]) ).
cnf(c_13,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_7,plain,
? [A,B,C] :
( singleton(C) != unordered_pair(A,B)
& subset(unordered_pair(A,B),singleton(C)) ),
inference(fof_nnf,[status(thm)],[t27_zfmisc_1_neg]) ).
fof(sk_t27_zfmisc_1_neg,plain,
( singleton(sK2) != unordered_pair(sK0,sK1)
& subset(unordered_pair(sK0,sK1),singleton(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_7]) ).
cnf(c_14,negated_conjecture,
subset(unordered_pair(sK0,sK1),singleton(sK2)),
inference(split_conjunct,[status(thm)],[sk_t27_zfmisc_1_neg]) ).
cnf(c_15,negated_conjecture,
subset(unordered_pair(sK0,sK1),unordered_pair(sK2,sK2)),
inference(paramod,[status(thm)],[c_13,c_14]) ).
cnf(c_16,negated_conjecture,
singleton(sK2) != unordered_pair(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t27_zfmisc_1_neg]) ).
cnf(c_17,negated_conjecture,
unordered_pair(sK2,sK2) != unordered_pair(sK0,sK1),
inference(paramod,[status(thm)],[c_13,c_16]) ).
cnf(c_18,plain,
( C = A
| ~ subset(unordered_pair(A,B),unordered_pair(C,C)) ),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_19,negated_conjecture,
sK2 = sK0,
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_22,plain,
( C = B
| ~ subset(unordered_pair(A,B),unordered_pair(C,C)) ),
inference(paramod,[status(thm)],[c_8,c_18]) ).
cnf(c_30,negated_conjecture,
unordered_pair(sK0,sK2) != unordered_pair(sK0,sK1),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_31,negated_conjecture,
unordered_pair(sK0,sK0) != unordered_pair(sK0,sK1),
inference(paramod,[status(thm)],[c_19,c_30]) ).
cnf(c_23,negated_conjecture,
unordered_pair(sK0,sK1) != unordered_pair(sK0,sK0),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_32,negated_conjecture,
subset(unordered_pair(sK0,sK1),unordered_pair(sK0,sK2)),
inference(paramod,[status(thm)],[c_19,c_15]) ).
cnf(c_24,negated_conjecture,
subset(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),
inference(paramod,[status(thm)],[c_19,c_32]) ).
cnf(c_33,negated_conjecture,
sK0 = sK1,
inference(resolve,[status(thm)],[c_22,c_24]) ).
cnf(c_27,negated_conjecture,
sK1 = sK0,
inference(copy,[status(thm)],[c_33]) ).
cnf(c_34,negated_conjecture,
~ subset(unordered_pair(A,unordered_pair(sK0,sK0)),unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK1))),
inference(resolve,[status(thm)],[c_22,c_23]) ).
cnf(c_35,negated_conjecture,
~ subset(unordered_pair(A,unordered_pair(sK0,sK0)),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1))),
inference(paramod,[status(thm)],[c_27,c_34]) ).
cnf(c_28,negated_conjecture,
~ subset(unordered_pair(A,unordered_pair(sK0,sK0)),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,sK0))),
inference(paramod,[status(thm)],[c_27,c_35]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_28,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n017.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 08:19:18 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 258472 was started by sandbox on n017,
% 0.15/0.44 % Sat Sep 26 08:19:18 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.45
% 0.15/0.45 % SZS status Theorem for theBenchmark
% 0.15/0.45
% 0.15/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.45 % Length of proof is 21.
% 0.15/0.45 % Level of proof is 7.
% 0.15/0.45 % Maximum clause weight is 13.000.
% 0.15/0.45 % Given clauses 15.
% 0.15/0.45
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------