%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 06:57:42 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(diamond_strip_lemmaD2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(pair(VAR_2,diamond_strip_lemmaD_sk1(VAR_1,VAR_2,VAR_3,VAR_0)),VAR_0)
| ~ member(pair(VAR_1,VAR_3),VAR_0)
| ~ member(pair(VAR_1,VAR_2),trancl(VAR_0))
| ~ diamond(VAR_0) ),
file('theBenchmark.p',diamond_strip_lemmaD2) ).
cnf(c_3,plain,
( member(pair(C,diamond_strip_lemmaD_sk1(B,C,D,A)),A)
| ~ member(pair(B,D),A)
| ~ member(pair(B,C),trancl(A))
| ~ diamond(A) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD2]) ).
fof(diamond_trancl_1h1,axiom,
diamond(r),
file('theBenchmark.p',diamond_trancl_1h1) ).
cnf(c_4,plain,
diamond(r),
inference(clausify,[status(thm)],[diamond_trancl_1h1]) ).
fof(diamond_strip_lemmaD1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(pair(VAR_3,diamond_strip_lemmaD_sk1(VAR_1,VAR_2,VAR_3,VAR_0)),trancl(VAR_0))
| ~ member(pair(VAR_1,VAR_3),VAR_0)
| ~ member(pair(VAR_1,VAR_2),trancl(VAR_0))
| ~ diamond(VAR_0) ),
file('theBenchmark.p',diamond_strip_lemmaD1) ).
cnf(c_5,plain,
( member(pair(D,diamond_strip_lemmaD_sk1(B,C,D,A)),trancl(A))
| ~ member(pair(B,D),A)
| ~ member(pair(B,C),trancl(A))
| ~ diamond(A) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD1]) ).
cnf(c_6,plain,
( member(pair(C,diamond_strip_lemmaD_sk1(A,B,C,r)),trancl(r))
| ~ member(pair(A,C),r)
| ~ member(pair(A,B),trancl(r)) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
( member(pair(B,diamond_strip_lemmaD_sk1(A,B,C,r)),r)
| ~ member(pair(A,C),r)
| ~ member(pair(A,B),trancl(r)) ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
fof(r_into_trancl,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_0,VAR_1),trancl(VAR_2))
| ~ member(pair(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',r_into_trancl) ).
cnf(c_17,plain,
( member(pair(A,B),trancl(C))
| ~ member(pair(A,B),C) ),
inference(clausify,[status(thm)],[r_into_trancl]) ).
fof(diamond_trancl_1h2,axiom,
member(pair(y,ya),r),
file('theBenchmark.p',diamond_trancl_1h2) ).
cnf(c_18,plain,
member(pair(y,ya),r),
inference(clausify,[status(thm)],[diamond_trancl_1h2]) ).
fof(diamond_trancl_1c1,axiom,
member(pair(y,yp),trancl(r)),
file('theBenchmark.p',diamond_trancl_1c1) ).
cnf(c_19,plain,
member(pair(y,yp),trancl(r)),
inference(clausify,[status(thm)],[diamond_trancl_1c1]) ).
fof(diamond_trancl_1c2,axiom,
! [VAR_0] :
( ~ member(pair(yp,VAR_0),trancl(r))
| ~ member(pair(ya,VAR_0),trancl(r)) ),
file('theBenchmark.p',diamond_trancl_1c2) ).
cnf(c_20,plain,
( ~ member(pair(yp,A),trancl(r))
| ~ member(pair(ya,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_trancl_1c2]) ).
cnf(c_66,plain,
( member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,A,r)),r)
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_7,c_19]) ).
cnf(c_30,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),r),
inference(resolve,[status(thm)],[c_66,c_18]) ).
cnf(c_67,plain,
( member(pair(A,diamond_strip_lemmaD_sk1(y,yp,A,r)),trancl(r))
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_6,c_19]) ).
cnf(c_31,plain,
member(pair(ya,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_67,c_18]) ).
cnf(c_59,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_17,c_30]) ).
cnf(c_68,plain,
~ member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_20,c_31]) ).
cnf(c_65,plain,
$false,
inference(resolve,[status(thm)],[c_59,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 23:17:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2930649 was started by sandbox on n002,
% 0.09/0.37 % Sat Sep 26 23:17:36 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 13.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 21.000.
% 0.09/0.39 % Given clauses 32.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------