%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET907+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 : n001.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 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 34 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 4 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 24 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t12_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t38_zfmisc_1,axiom,
! [A,B,C] :
( subset(unordered_pair(A,B),C)
<=> ( in(B,C)
& in(A,C) ) ),
file('theBenchmark.p',t38_zfmisc_1) ).
fof(t48_zfmisc_1,conjecture,
! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
file('theBenchmark.p',t48_zfmisc_1) ).
fof(t48_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( in(C,B)
& in(A,B) )
=> set_union2(unordered_pair(A,C),B) = B ),
inference(assume_negation,[status(cth)],[t48_zfmisc_1]) ).
cnf(c_15,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_22,plain,
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t12_xboole_1]) ).
cnf(c_25,plain,
( ~ in(B,C)
| ~ in(A,C)
| subset(unordered_pair(A,B),C) ),
inference(clausify,[status(thm)],[t38_zfmisc_1]) ).
fof(nnf_12,plain,
? [A,B,C] :
( set_union2(unordered_pair(A,C),B) != B
& in(C,B)
& in(A,B) ),
inference(fof_nnf,[status(thm)],[t48_zfmisc_1_neg]) ).
fof(sk_t48_zfmisc_1_neg,plain,
( set_union2(unordered_pair(sK0,sK2),sK1) != sK1
& in(sK2,sK1)
& in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_12]) ).
cnf(c_26,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t48_zfmisc_1_neg]) ).
cnf(c_27,negated_conjecture,
in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t48_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
set_union2(unordered_pair(sK0,sK2),sK1) != sK1,
inference(split_conjunct,[status(thm)],[sk_t48_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
set_union2(sK1,unordered_pair(sK0,sK2)) != sK1,
inference(paramod,[status(thm)],[c_15,c_28]) ).
cnf(c_55,negated_conjecture,
( ~ in(A,sK1)
| subset(unordered_pair(sK0,A),sK1) ),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_37,negated_conjecture,
subset(unordered_pair(sK0,sK2),sK1),
inference(resolve,[status(thm)],[c_55,c_27]) ).
cnf(c_56,plain,
set_union2(unordered_pair(sK0,sK2),sK1) = sK1,
inference(resolve,[status(thm)],[c_22,c_37]) ).
cnf(c_57,plain,
set_union2(sK1,unordered_pair(sK0,sK2)) = sK1,
inference(paramod,[status(thm)],[c_15,c_56]) ).
cnf(c_54,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_29,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sat Sep 26 08:30:29 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1374757 was started by sandbox on n001,
% 0.16/0.44 % Sat Sep 26 08:30:29 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46
% 0.16/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.46 % Length of proof is 13.
% 0.16/0.46 % Level of proof is 3.
% 0.16/0.46 % Maximum clause weight is 11.000.
% 0.16/0.46 % Given clauses 26.
% 0.16/0.46
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------