%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET906+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 : n006.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 08:37:15 AM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 43 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 15 ~; 11 |; 2 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 6 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t47_zfmisc_1,conjecture,
! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('theBenchmark.p',t47_zfmisc_1) ).
fof(t47_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
inference(assume_negation,[status(cth)],[t47_zfmisc_1]) ).
cnf(c_15,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
fof(nnf_13,plain,
? [A,B,C] :
( ~ in(A,C)
& subset(set_union2(unordered_pair(A,B),C),C) ),
inference(fof_nnf,[status(thm)],[t47_zfmisc_1_neg]) ).
fof(sk_t47_zfmisc_1_neg,plain,
( ~ in(sK0,sK2)
& subset(set_union2(unordered_pair(sK0,sK1),sK2),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_13]) ).
cnf(c_18,negated_conjecture,
subset(set_union2(unordered_pair(sK0,sK1),sK2),sK2),
inference(split_conjunct,[status(thm)],[sk_t47_zfmisc_1_neg]) ).
cnf(c_19,negated_conjecture,
( in(A,sK2)
| ~ in(A,set_union2(unordered_pair(sK0,sK1),sK2)) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_22,negated_conjecture,
~ in(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t47_zfmisc_1_neg]) ).
cnf(c_32,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_37,plain,
( D != B
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_41,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_54,negated_conjecture,
~ in(sK0,set_union2(unordered_pair(sK0,sK1),sK2)),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_197,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(xxres,[status(thm)],[c_37]) ).
cnf(c_521,plain,
( ~ in(A,B)
| in(A,set_union2(B,C)) ),
inference(xxres,[status(thm)],[c_32]) ).
cnf(c_373,plain,
~ in(sK0,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_521,c_54]) ).
cnf(c_457,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_197]) ).
cnf(c_519,plain,
in(A,unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_41,c_457]) ).
cnf(c_520,plain,
$false,
inference(resolve,[status(thm)],[c_519,c_373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % 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 08:24:42 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 811841 was started by sandbox2 on n006,
% 0.09/0.37 % Sat Sep 26 08:24:42 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.44 % Length of proof is 18.
% 0.09/0.44 % Level of proof is 5.
% 0.09/0.44 % Maximum clause weight is 25.000.
% 0.09/0.44 % Given clauses 44.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------