%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:35:49 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_unique_1st_in_pair_of_non_sets,axiom,
first(x) != x,
file('theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
cnf(c_33,plain,
first(x) != x,
inference(clausify,[status(thm)],[prove_unique_1st_in_pair_of_non_sets]) ).
fof(prove_unique_1st_and_2nd_in_pair_of_non_sets1_1,axiom,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets1_1) ).
cnf(c_34,plain,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_non_sets1_1]) ).
fof(existence_of_1st_and_2nd_2,axiom,
! [VAR_0] :
( first(VAR_0) = VAR_0
| member(ordered_pair(first(VAR_0),second(VAR_0)),cross_product(universal_class,universal_class)) ),
file('theBenchmark.p',existence_of_1st_and_2nd_2) ).
cnf(c_40,plain,
( first(A) = A
| member(ordered_pair(first(A),second(A)),cross_product(universal_class,universal_class)) ),
inference(clausify,[status(thm)],[existence_of_1st_and_2nd_2]) ).
cnf(c_235,plain,
first(x) = x,
inference(resolve,[status(thm)],[c_40,c_34]) ).
cnf(c_234,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:10:09 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3039891 was started by sandbox on n008,
% 0.11/0.37 % Sat Sep 26 07:10:09 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.16/0.40
% 0.16/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.40
% 0.16/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/0.40 % Length of proof is 4.
% 0.16/0.40 % Level of proof is 1.
% 0.16/0.40 % Maximum clause weight is 28.000.
% 0.16/0.40 % Given clauses 13.
% 0.16/0.40
% 0.16/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------