%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU150+3 : 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 : n004.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 08:45:11 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 2 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 4 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(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ),
file('theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
file('theBenchmark.p',t9_zfmisc_1) ).
fof(t9_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ),
inference(assume_negation,[status(cth)],[t9_zfmisc_1]) ).
cnf(c_6,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_9,plain,
( B = A
| singleton(A) != unordered_pair(B,C) ),
inference(clausify,[status(thm)],[t8_zfmisc_1]) ).
fof(nnf_5,plain,
? [A,B,C] :
( C != B
& singleton(A) = unordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[t9_zfmisc_1_neg]) ).
fof(sk_t9_zfmisc_1_neg,plain,
( sK2 != sK1
& singleton(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_5]) ).
cnf(c_10,negated_conjecture,
singleton(sK0) = unordered_pair(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t9_zfmisc_1_neg]) ).
cnf(c_11,negated_conjecture,
sK2 != sK1,
inference(split_conjunct,[status(thm)],[sk_t9_zfmisc_1_neg]) ).
cnf(c_12,plain,
( C = A
| singleton(A) != unordered_pair(B,C) ),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_13,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_15,negated_conjecture,
sK2 != sK0,
inference(paramod,[status(thm)],[c_13,c_11]) ).
cnf(c_16,negated_conjecture,
singleton(sK0) = unordered_pair(sK0,sK2),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_18,negated_conjecture,
singleton(sK0) != unordered_pair(A,sK2),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_19,negated_conjecture,
unordered_pair(sK0,sK2) != unordered_pair(A,sK2),
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_17,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU150+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:40:36 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 1269857 was started by sandbox on n004,
% 0.09/0.37 % Sat Sep 26 08:40:36 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 12.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 9.000.
% 0.09/0.39 % Given clauses 7.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------