%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU151+3 : 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 : n013.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 08:45:12 AM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 38 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 23 ~; 10 |; 8 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(t10_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_zfmisc_1) ).
fof(t10_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(assume_negation,[status(cth)],[t10_zfmisc_1]) ).
cnf(c_9,plain,
( D = B
| D = A
| ~ in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_10,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
fof(nnf_6,plain,
? [A,B,C,D] :
( D != A
& C != A
& unordered_pair(C,D) = unordered_pair(A,B) ),
inference(fof_nnf,[status(thm)],[t10_zfmisc_1_neg]) ).
fof(sk_t10_zfmisc_1_neg,plain,
( sK1 != sK2
& sK0 != sK2
& unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK0),skolemize(D,sK1)],[nnf_6]) ).
cnf(c_17,negated_conjecture,
unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_18,negated_conjecture,
sK0 != sK2,
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
sK1 != sK2,
inference(split_conjunct,[status(thm)],[sk_t10_zfmisc_1_neg]) ).
cnf(c_26,plain,
( A != B
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_86,negated_conjecture,
( A = sK1
| A = sK0
| ~ in(A,unordered_pair(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_9,c_17]) ).
cnf(c_87,negated_conjecture,
sK2 != sK0,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_88,negated_conjecture,
( sK2 = sK1
| ~ in(sK2,unordered_pair(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_86,c_87]) ).
cnf(c_89,negated_conjecture,
sK2 != sK1,
inference(copy,[status(thm)],[c_19]) ).
cnf(c_61,negated_conjecture,
~ in(sK2,unordered_pair(sK2,sK3)),
inference(resolve,[status(thm)],[c_88,c_89]) ).
cnf(c_84,plain,
in(A,unordered_pair(A,B)),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_85,plain,
$false,
inference(resolve,[status(thm)],[c_84,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:40:58 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2356419 was started by sandbox2 on n013,
% 0.09/5.37 % Sat Sep 26 08:40:58 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.39
% 0.09/5.39 % SZS status Theorem for theBenchmark
% 0.09/5.39
% 0.09/5.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/5.39 % Length of proof is 11.
% 0.09/5.39 % Level of proof is 4.
% 0.09/5.39 % Maximum clause weight is 24.000.
% 0.09/5.39 % Given clauses 18.
% 0.09/5.39
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------