%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL100-1 : 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 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 16 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 39 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 51 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transD,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(pair(VAR_1,VAR_3),VAR_0)
| ~ member(pair(VAR_2,VAR_3),VAR_0)
| ~ member(pair(VAR_1,VAR_2),VAR_0)
| ~ trans(VAR_0) ),
file('theBenchmark.p',transD) ).
cnf(c_1,plain,
( member(pair(B,D),A)
| ~ member(pair(C,D),A)
| ~ member(pair(B,C),A)
| ~ trans(A) ),
inference(clausify,[status(thm)],[transD]) ).
fof(trans_trancl,axiom,
! [VAR_0] : trans(trancl(VAR_0)),
file('theBenchmark.p',trans_trancl) ).
cnf(c_2,plain,
trans(trancl(A)),
inference(clausify,[status(thm)],[trans_trancl]) ).
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_2h1,axiom,
diamond(r),
file('theBenchmark.p',diamond_trancl_2h1) ).
cnf(c_4,plain,
diamond(r),
inference(clausify,[status(thm)],[diamond_trancl_2h1]) ).
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_2h3,axiom,
member(pair(ya,z),r),
file('theBenchmark.p',diamond_trancl_2h3) ).
cnf(c_19,plain,
member(pair(ya,z),r),
inference(clausify,[status(thm)],[diamond_trancl_2h3]) ).
fof(diamond_trancl_2h4,axiom,
! [VAR_0] :
( member(pair(ya,sk1(VAR_0)),trancl(r))
| ~ member(pair(y,VAR_0),trancl(r)) ),
file('theBenchmark.p',diamond_trancl_2h4) ).
cnf(c_20,plain,
( member(pair(ya,sk1(A)),trancl(r))
| ~ member(pair(y,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_trancl_2h4]) ).
fof(diamond_trancl_2h5,axiom,
! [VAR_0] :
( member(pair(VAR_0,sk1(VAR_0)),trancl(r))
| ~ member(pair(y,VAR_0),trancl(r)) ),
file('theBenchmark.p',diamond_trancl_2h5) ).
cnf(c_21,plain,
( member(pair(A,sk1(A)),trancl(r))
| ~ member(pair(y,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_trancl_2h5]) ).
fof(diamond_trancl_2c1,axiom,
member(pair(y,yp),trancl(r)),
file('theBenchmark.p',diamond_trancl_2c1) ).
cnf(c_22,plain,
member(pair(y,yp),trancl(r)),
inference(clausify,[status(thm)],[diamond_trancl_2c1]) ).
fof(diamond_trancl_2c2,axiom,
! [VAR_0] :
( ~ member(pair(yp,VAR_0),trancl(r))
| ~ member(pair(z,VAR_0),trancl(r)) ),
file('theBenchmark.p',diamond_trancl_2c2) ).
cnf(c_23,plain,
( ~ member(pair(yp,A),trancl(r))
| ~ member(pair(z,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_trancl_2c2]) ).
cnf(c_24,plain,
( member(pair(A,D),trancl(C))
| ~ member(pair(B,D),trancl(C))
| ~ member(pair(A,B),trancl(C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_35,plain,
member(pair(yp,sk1(yp)),trancl(r)),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_36,plain,
member(pair(ya,sk1(yp)),trancl(r)),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_399,plain,
( member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),A,r)),r)
| ~ member(pair(ya,A),r) ),
inference(resolve,[status(thm)],[c_7,c_36]) ).
cnf(c_68,plain,
member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),r),
inference(resolve,[status(thm)],[c_399,c_19]) ).
cnf(c_400,plain,
( member(pair(A,diamond_strip_lemmaD_sk1(ya,sk1(yp),A,r)),trancl(r))
| ~ member(pair(ya,A),r) ),
inference(resolve,[status(thm)],[c_6,c_36]) ).
cnf(c_69,plain,
member(pair(z,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[status(thm)],[c_400,c_19]) ).
cnf(c_190,plain,
member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[status(thm)],[c_17,c_68]) ).
cnf(c_200,plain,
~ member(pair(yp,diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[status(thm)],[c_23,c_69]) ).
cnf(c_401,plain,
( member(pair(yp,A),trancl(r))
| ~ member(pair(sk1(yp),A),trancl(r)) ),
inference(resolve,[status(thm)],[c_24,c_35]) ).
cnf(c_402,plain,
~ member(pair(sk1(yp),diamond_strip_lemmaD_sk1(ya,sk1(yp),z,r)),trancl(r)),
inference(resolve,[status(thm)],[c_401,c_200]) ).
cnf(c_398,plain,
$false,
inference(resolve,[status(thm)],[c_190,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL100-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n010.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 23:15:15 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 282694 was started by sandbox2 on n010,
% 0.19/0.45 % Sat Sep 26 23:15:15 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.52
% 0.19/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52
% 0.19/0.52 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.19/0.52 % Length of proof is 21.
% 0.19/0.52 % Level of proof is 4.
% 0.19/0.52 % Maximum clause weight is 36.000.
% 0.19/0.52 % Given clauses 232.
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------