%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET914+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 : n002.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 08:37:16 AM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 53 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 21 ~; 13 |; 5 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 6 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
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(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t55_zfmisc_1,conjecture,
! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
file('theBenchmark.p',t55_zfmisc_1) ).
fof(t55_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
inference(assume_negation,[status(cth)],[t55_zfmisc_1]) ).
cnf(c_14,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_16,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_19,plain,
( D != A
| in(D,C)
| unordered_pair(A,B) != C ),
inference(clausify,[status(thm)],[d2_tarski]) ).
cnf(c_26,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_30,plain,
( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[d7_xboole_0]) ).
cnf(c_36,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(nnf_12,plain,
? [A,B,C] :
( in(A,C)
& disjoint(unordered_pair(A,B),C) ),
inference(fof_nnf,[status(thm)],[t55_zfmisc_1_neg]) ).
fof(sk_t55_zfmisc_1_neg,plain,
( in(sK0,sK2)
& disjoint(unordered_pair(sK0,sK1),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_12]) ).
cnf(c_37,negated_conjecture,
disjoint(unordered_pair(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_t55_zfmisc_1_neg]) ).
cnf(c_38,negated_conjecture,
in(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t55_zfmisc_1_neg]) ).
cnf(c_50,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_16]) ).
cnf(c_54,plain,
( A != C
| in(A,unordered_pair(B,C)) ),
inference(resolve,[status(thm)],[c_19,c_14]) ).
cnf(c_211,plain,
disjoint(sK2,unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_37,c_36]) ).
cnf(c_370,plain,
disjoint(sK2,unordered_pair(sK1,sK0)),
inference(paramod,[status(thm)],[c_14,c_211]) ).
cnf(c_408,plain,
in(A,unordered_pair(B,A)),
inference(xxres,[status(thm)],[c_54]) ).
cnf(c_523,plain,
set_intersection2(sK2,unordered_pair(sK1,sK0)) = empty_set,
inference(resolve,[status(thm)],[c_370,c_30]) ).
cnf(c_559,plain,
( ~ in(C,B)
| ~ in(C,A)
| set_intersection2(A,B) != empty_set ),
inference(resolve,[status(thm)],[c_26,c_50]) ).
cnf(c_560,negated_conjecture,
( ~ in(sK0,A)
| set_intersection2(sK2,A) != empty_set ),
inference(resolve,[status(thm)],[c_559,c_38]) ).
cnf(c_557,negated_conjecture,
set_intersection2(sK2,unordered_pair(A,sK0)) != empty_set,
inference(resolve,[status(thm)],[c_560,c_408]) ).
cnf(c_558,plain,
$false,
inference(resolve,[status(thm)],[c_557,c_523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET914+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:28:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1253402 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 08:28:06 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.41 % Length of proof is 23.
% 0.13/0.41 % Level of proof is 5.
% 0.13/0.41 % Maximum clause weight is 24.000.
% 0.13/0.41 % Given clauses 59.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------