%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 08:35:20 AM UTC 2026
% Result : Unsatisfiable 0.14s 10.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 24 unt; 0 def)
% Number of atoms : 48 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 9 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_left_cancellation_3,axiom,
y != z,
file('theBenchmark.p',prove_left_cancellation_3) ).
cnf(c_33,plain,
y != z,
inference(clausify,[status(thm)],[prove_left_cancellation_3]) ).
cnf(c_34,plain,
z != y,
inference(copy,[status(thm)],[c_33]) ).
fof(prove_left_cancellation_2,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_left_cancellation_2) ).
cnf(c_35,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_left_cancellation_2]) ).
fof(prove_left_cancellation_1,axiom,
unordered_pair(x,y) = unordered_pair(x,z),
file('theBenchmark.p',prove_left_cancellation_1) ).
cnf(c_36,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(clausify,[status(thm)],[prove_left_cancellation_1]) ).
cnf(c_37,plain,
unordered_pair(x,z) = unordered_pair(x,y),
inference(copy,[status(thm)],[c_36]) ).
fof(commutativity_of_unordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(VAR_0,VAR_1) = unordered_pair(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(c_43,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_of_unordered_pair]) ).
fof(corollary_2_to_cartesian_product,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,universal_class)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(c_58,plain,
( member(B,universal_class)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[corollary_2_to_cartesian_product]) ).
fof(corollary_1_to_cartesian_product,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,universal_class)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',corollary_1_to_cartesian_product) ).
cnf(c_59,plain,
( member(A,universal_class)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[corollary_1_to_cartesian_product]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_139,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_140,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
cnf(c_174,plain,
unordered_pair(z,x) = unordered_pair(x,y),
inference(paramod,[status(thm)],[c_43,c_37]) ).
cnf(c_1298,plain,
unordered_pair(x,z) = unordered_pair(y,x),
inference(paramod,[status(thm)],[c_43,c_37]) ).
cnf(c_175,plain,
unordered_pair(y,x) = unordered_pair(x,z),
inference(copy,[status(thm)],[c_1298]) ).
cnf(c_196,plain,
member(z,universal_class),
inference(resolve,[status(thm)],[c_58,c_35]) ).
cnf(c_197,plain,
member(y,universal_class),
inference(resolve,[status(thm)],[c_59,c_35]) ).
cnf(c_604,plain,
member(z,unordered_pair(z,A)),
inference(resolve,[status(thm)],[c_196,c_139]) ).
cnf(c_619,plain,
member(y,unordered_pair(y,A)),
inference(resolve,[status(thm)],[c_197,c_139]) ).
cnf(c_918,plain,
member(z,unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_174,c_604]) ).
cnf(c_953,plain,
member(y,unordered_pair(x,z)),
inference(paramod,[status(thm)],[c_175,c_619]) ).
cnf(c_1299,plain,
( z = y
| z = x ),
inference(resolve,[status(thm)],[c_918,c_140]) ).
cnf(c_1005,plain,
z = x,
inference(resolve,[status(thm)],[c_34,c_1299]) ).
cnf(c_1300,plain,
x != y,
inference(paramod,[status(thm)],[c_1005,c_34]) ).
cnf(c_1013,plain,
y != x,
inference(copy,[status(thm)],[c_1300]) ).
cnf(c_1301,plain,
( y = z
| y = x ),
inference(resolve,[status(thm)],[c_953,c_140]) ).
cnf(c_1302,plain,
( z = y
| y = x ),
inference(copy,[status(thm)],[c_1301]) ).
cnf(c_1303,plain,
z = y,
inference(resolve,[status(thm)],[c_1013,c_1302]) ).
cnf(c_1297,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_1303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n004.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sat Sep 26 06:52:18 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.37 % Process 1048438 was started by sandbox on n004,
% 0.10/10.37 % Sat Sep 26 06:52:18 2026
% 0.10/10.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.38
% 0.10/10.38 % From the command line: assign(max_seconds, 300).
% 0.14/10.47
% 0.14/10.47 % SZS status Unsatisfiable for theBenchmark
% 0.14/10.47
% 0.14/10.47 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.14/10.47 % Length of proof is 21.
% 0.14/10.47 % Level of proof is 6.
% 0.14/10.47 % Maximum clause weight is 21.000.
% 0.14/10.47 % Given clauses 192.
% 0.14/10.47
% 0.14/10.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------