%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET240-6 : 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 : n007.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 08:36:05 AM UTC 2026
% Result : Unsatisfiable 0.81s 0.50s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 19 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 23 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_restriction_alternate_defn3_2,axiom,
~ member(u,x),
file('theBenchmark.p',prove_restriction_alternate_defn3_2) ).
cnf(c_36,plain,
~ member(u,x),
inference(clausify,[status(thm)],[prove_restriction_alternate_defn3_2]) ).
fof(prove_restriction_alternate_defn3_1,axiom,
member(ordered_pair(u,v),restrict(xr,x,y)),
file('theBenchmark.p',prove_restriction_alternate_defn3_1) ).
cnf(c_37,plain,
member(ordered_pair(u,v),restrict(xr,x,y)),
inference(clausify,[status(thm)],[prove_restriction_alternate_defn3_1]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_111,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_112,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_111]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_123,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(cartesian_product1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_0,VAR_2)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product1) ).
cnf(c_130,plain,
( member(A,C)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product1]) ).
cnf(c_209,plain,
member(ordered_pair(u,v),intersection(cross_product(x,y),xr)),
inference(paramod,[status(thm)],[c_112,c_37]) ).
cnf(c_1088,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(resolve,[status(thm)],[c_209,c_123]) ).
cnf(c_1103,plain,
member(u,x),
inference(resolve,[status(thm)],[c_1088,c_130]) ).
cnf(c_1102,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_1103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET240-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:20:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3116479 was started by sandbox on n007,
% 0.10/0.37 % Sat Sep 26 07:20:10 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.81/0.50
% 0.81/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.81/0.50
% 0.81/0.50 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.81/0.50 % Length of proof is 9.
% 0.81/0.50 % Level of proof is 4.
% 0.81/0.50 % Maximum clause weight is 25.000.
% 0.81/0.50 % Given clauses 204.
% 0.81/0.50
% 0.81/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------