%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET242-6 : 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 : n017.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 08:36:06 AM UTC 2026
% Result : Unsatisfiable 0.24s 0.54s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 17 unt; 0 def)
% Number of atoms : 25 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_restriction_alternate_defn5_3,axiom,
~ member(z,restrict(xr,x,y)),
file('theBenchmark.p',prove_restriction_alternate_defn5_3) ).
cnf(c_36,plain,
~ member(z,restrict(xr,x,y)),
inference(clausify,[status(thm)],[prove_restriction_alternate_defn5_3]) ).
fof(prove_restriction_alternate_defn5_2,axiom,
member(z,cross_product(x,y)),
file('theBenchmark.p',prove_restriction_alternate_defn5_2) ).
cnf(c_37,plain,
member(z,cross_product(x,y)),
inference(clausify,[status(thm)],[prove_restriction_alternate_defn5_2]) ).
fof(prove_restriction_alternate_defn5_1,axiom,
member(z,xr),
file('theBenchmark.p',prove_restriction_alternate_defn5_1) ).
cnf(c_38,plain,
member(z,xr),
inference(clausify,[status(thm)],[prove_restriction_alternate_defn5_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_112,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_113,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_112]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_114,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_276,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_113,c_114]) ).
cnf(c_115,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_276]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_122,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
cnf(c_277,plain,
~ member(z,intersection(cross_product(x,y),xr)),
inference(paramod,[status(thm)],[c_113,c_36]) ).
cnf(c_232,plain,
~ member(z,intersection(xr,cross_product(x,y))),
inference(paramod,[status(thm)],[c_115,c_277]) ).
cnf(c_278,plain,
( member(z,intersection(xr,A))
| ~ member(z,A) ),
inference(resolve,[status(thm)],[c_122,c_38]) ).
cnf(c_279,plain,
member(z,intersection(xr,cross_product(x,y))),
inference(resolve,[status(thm)],[c_278,c_37]) ).
cnf(c_275,plain,
$false,
inference(resolve,[status(thm)],[c_232,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET242-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n017.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 07:18:34 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 136622 was started by sandbox on n017,
% 0.20/0.46 % Sat Sep 26 07:18:34 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.20/0.47
% 0.20/0.47 % From the command line: assign(max_seconds, 300).
% 0.24/0.54
% 0.24/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.54
% 0.24/0.54 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.24/0.54 % Length of proof is 10.
% 0.24/0.54 % Level of proof is 4.
% 0.24/0.54 % Maximum clause weight is 26.000.
% 0.24/0.54 % Given clauses 28.
% 0.24/0.54
% 0.24/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------