%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL099-2 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 44.82s 6.93s
% Output : CNFRefutation 44.82s
% 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_trancl_1h1,axiom,
diamond(r),
file('theBenchmark.p',diamond_trancl_1h1) ).
cnf(c_19,plain,
diamond(r),
inference(clausify,[status(thm)],[diamond_trancl_1h1]) ).
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_20,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_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_21,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_22,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_19,c_21]) ).
cnf(c_23,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_19,c_20]) ).
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_24,plain,
( ~ member(pair(yp,A),trancl(r))
| ~ member(pair(ya,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_trancl_1c2]) ).
fof(diamond_trancl_1c1,axiom,
member(pair(y,yp),trancl(r)),
file('theBenchmark.p',diamond_trancl_1c1) ).
cnf(c_25,plain,
member(pair(y,yp),trancl(r)),
inference(clausify,[status(thm)],[diamond_trancl_1c1]) ).
fof(diamond_trancl_1h2,axiom,
member(pair(y,ya),r),
file('theBenchmark.p',diamond_trancl_1h2) ).
cnf(c_26,plain,
member(pair(y,ya),r),
inference(clausify,[status(thm)],[diamond_trancl_1h2]) ).
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_27,plain,
( member(pair(A,B),trancl(C))
| ~ member(pair(A,B),C) ),
inference(clausify,[status(thm)],[r_into_trancl]) ).
cnf(c_208,plain,
( member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,A,r)),r)
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_25,c_23]) ).
cnf(c_209,plain,
( member(pair(A,diamond_strip_lemmaD_sk1(y,yp,A,r)),trancl(r))
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_651,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),r),
inference(resolve,[status(thm)],[c_208,c_26]) ).
cnf(c_652,plain,
member(pair(ya,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_209,c_26]) ).
cnf(c_19235,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_651,c_27]) ).
cnf(c_19253,plain,
~ member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)),
inference(resolve,[status(thm)],[c_652,c_24]) ).
cnf(c_19252,plain,
$false,
inference(resolve,[status(thm)],[c_19235,c_19253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL099-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n010.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 23:15:00 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 282291 was started by sandbox2 on n010,
% 0.18/0.46 % Sat Sep 26 23:15:00 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 44.82/6.93
% 44.82/6.93 % given #500 (T,wt=20): 5923 ord(union(int(A,eptset))). [resolve(311,b,235,a)].
% 44.82/6.93
% 44.82/6.93 % given #1000 (W,wt=16): 15028 member(int(A,B),pow(B)). [resolve(480,b,156,a),merge(b)].
% 44.82/6.93
% 44.82/6.93 % SZS status Unsatisfiable for theBenchmark
% 44.82/6.93
% 44.82/6.93 % Proof 1 at 4.87 (+ 1.42) seconds.
% 44.82/6.93 % Length of proof is 15.
% 44.82/6.93 % Level of proof is 5.
% 44.82/6.93 % Maximum clause weight is 36.000.
% 44.82/6.93 % Given clauses 1441.
% 44.82/6.93
% 44.82/6.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------