%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET075-7 : 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 : n020.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 08:35:38 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 4 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_unordered_pair_axiom3_2,axiom,
unordered_pair(x,y) = null_class,
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
cnf(c_33,plain,
unordered_pair(x,y) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom3_2]) ).
cnf(c_34,plain,
null_class = unordered_pair(x,y),
inference(copy,[status(thm)],[c_33]) ).
fof(prove_corollary_to_unordered_pair_axiom3_1,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
cnf(c_35,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom3_1]) ).
fof(existence_of_null_class,axiom,
! [VAR_0] : ~ member(VAR_0,null_class),
file('theBenchmark.p',existence_of_null_class) ).
cnf(c_50,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[existence_of_null_class]) ).
fof(corollary_2_to_unordered_pair,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,unordered_pair(VAR_0,VAR_1))
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',corollary_2_to_unordered_pair) ).
cnf(c_60,plain,
( member(B,unordered_pair(A,B))
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[corollary_2_to_unordered_pair]) ).
cnf(c_176,plain,
~ member(A,unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_34,c_50]) ).
cnf(c_199,plain,
member(y,unordered_pair(x,y)),
inference(resolve,[status(thm)],[c_60,c_35]) ).
cnf(c_198,plain,
$false,
inference(resolve,[status(thm)],[c_176,c_199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET075-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:04:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 930437 was started by sandbox on n020,
% 0.08/0.35 % Sat Sep 26 07:04:18 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 7.
% 0.13/0.39 % Level of proof is 3.
% 0.13/0.39 % Maximum clause weight is 22.000.
% 0.13/0.39 % Given clauses 30.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------