%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET072-7 : 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 : n010.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 08:35:37 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.54s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 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 : 15 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_right_cancellation_3,axiom,
x != y,
file('theBenchmark.p',prove_right_cancellation_3) ).
cnf(c_33,plain,
x != y,
inference(clausify,[status(thm)],[prove_right_cancellation_3]) ).
cnf(c_34,plain,
y != x,
inference(copy,[status(thm)],[c_33]) ).
fof(prove_right_cancellation_2,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_right_cancellation_2) ).
cnf(c_35,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_right_cancellation_2]) ).
fof(prove_right_cancellation_1,axiom,
unordered_pair(x,z) = unordered_pair(y,z),
file('theBenchmark.p',prove_right_cancellation_1) ).
cnf(c_36,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(clausify,[status(thm)],[prove_right_cancellation_1]) ).
cnf(c_37,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(copy,[status(thm)],[c_36]) ).
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| ~ member(ordered_pair(VAR_1,VAR_2),cross_product(universal_class,universal_class))
| unordered_pair(VAR_0,VAR_1) != unordered_pair(VAR_0,VAR_2) ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_38,plain,
( B = C
| ~ member(ordered_pair(B,C),cross_product(universal_class,universal_class))
| unordered_pair(A,B) != unordered_pair(A,C) ),
inference(clausify,[status(thm)],[left_cancellation]) ).
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_44,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_of_unordered_pair]) ).
cnf(c_593,plain,
( x = y
| unordered_pair(A,x) != unordered_pair(A,y) ),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_594,plain,
( x = y
| unordered_pair(A,y) != unordered_pair(A,x) ),
inference(copy,[status(thm)],[c_593]) ).
cnf(c_595,plain,
( y = x
| unordered_pair(A,y) != unordered_pair(A,x) ),
inference(copy,[status(thm)],[c_594]) ).
cnf(c_174,plain,
unordered_pair(A,y) != unordered_pair(A,x),
inference(resolve,[status(thm)],[c_34,c_595]) ).
cnf(c_596,plain,
unordered_pair(y,z) = unordered_pair(z,x),
inference(paramod,[status(thm)],[c_44,c_37]) ).
cnf(c_177,plain,
unordered_pair(z,x) = unordered_pair(y,z),
inference(copy,[status(thm)],[c_596]) ).
cnf(c_591,plain,
unordered_pair(y,A) != unordered_pair(A,x),
inference(paramod,[status(thm)],[c_44,c_174]) ).
cnf(c_597,plain,
unordered_pair(y,z) = unordered_pair(z,x),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_592,plain,
$false,
inference(resolve,[status(thm)],[c_591,c_597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET072-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n010.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 07:03:14 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2740724 was started by sandbox on n010,
% 0.15/0.43 % Sat Sep 26 07:03:14 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 0.15/0.54
% 0.15/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.54
% 0.15/0.54 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.15/0.54 % Length of proof is 11.
% 0.15/0.54 % Level of proof is 4.
% 0.15/0.54 % Maximum clause weight is 27.000.
% 0.15/0.54 % Given clauses 123.
% 0.15/0.54
% 0.15/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------