%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL098-1 : 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 : n020.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 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 41 ( 1 sgn 17 !; 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]) ).
cnf(c_3,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]) ).
fof(diamond_strip_lemmaD_2c2,axiom,
! [VAR_0] :
( ~ member(pair(z,VAR_0),r)
| ~ member(pair(sk3,VAR_0),trancl(r)) ),
file('theBenchmark.p',diamond_strip_lemmaD_2c2) ).
cnf(c_4,plain,
( ~ member(pair(z,A),r)
| ~ member(pair(sk3,A),trancl(r)) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2c2]) ).
fof(diamond_strip_lemmaD_2c1,axiom,
member(pair(x,sk3),r),
file('theBenchmark.p',diamond_strip_lemmaD_2c1) ).
cnf(c_5,plain,
member(pair(x,sk3),r),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2c1]) ).
fof(diamond_strip_lemmaD_2h6,axiom,
! [VAR_0] :
( member(pair(y,sk2(VAR_0)),r)
| ~ member(pair(x,VAR_0),r) ),
file('theBenchmark.p',diamond_strip_lemmaD_2h6) ).
cnf(c_6,plain,
( member(pair(y,sk2(A)),r)
| ~ member(pair(x,A),r) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2h6]) ).
fof(diamond_strip_lemmaD_2h5,axiom,
! [VAR_0] :
( member(pair(VAR_0,sk2(VAR_0)),trancl(r))
| ~ member(pair(x,VAR_0),r) ),
file('theBenchmark.p',diamond_strip_lemmaD_2h5) ).
cnf(c_7,plain,
( member(pair(A,sk2(A)),trancl(r))
| ~ member(pair(x,A),r) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2h5]) ).
fof(diamond_strip_lemmaD_2h4,axiom,
member(pair(y,z),r),
file('theBenchmark.p',diamond_strip_lemmaD_2h4) ).
cnf(c_8,plain,
member(pair(y,z),r),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2h4]) ).
fof(diamond_strip_lemmaD_2h2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_2,sk1(VAR_0,VAR_1,VAR_2)),r)
| ~ member(pair(VAR_0,VAR_2),r)
| ~ member(pair(VAR_0,VAR_1),r) ),
file('theBenchmark.p',diamond_strip_lemmaD_2h2) ).
cnf(c_10,plain,
( member(pair(C,sk1(A,B,C)),r)
| ~ member(pair(A,C),r)
| ~ member(pair(A,B),r) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2h2]) ).
fof(diamond_strip_lemmaD_2h1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_1,sk1(VAR_0,VAR_1,VAR_2)),r)
| ~ member(pair(VAR_0,VAR_2),r)
| ~ member(pair(VAR_0,VAR_1),r) ),
file('theBenchmark.p',diamond_strip_lemmaD_2h1) ).
cnf(c_11,plain,
( member(pair(B,sk1(A,B,C)),r)
| ~ member(pair(A,C),r)
| ~ member(pair(A,B),r) ),
inference(clausify,[status(thm)],[diamond_strip_lemmaD_2h1]) ).
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_12,plain,
( member(pair(A,B),trancl(C))
| ~ member(pair(A,B),C) ),
inference(clausify,[status(thm)],[r_into_trancl]) ).
cnf(c_22,plain,
member(pair(y,sk2(sk3)),r),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_23,plain,
member(pair(sk3,sk2(sk3)),trancl(r)),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_102,plain,
( member(pair(z,sk1(y,z,A)),r)
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_37,plain,
member(pair(z,sk1(y,z,sk2(sk3))),r),
inference(resolve,[status(thm)],[c_102,c_22]) ).
cnf(c_103,plain,
( member(pair(A,sk1(y,z,A)),r)
| ~ member(pair(y,A),r) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_39,plain,
member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),r),
inference(resolve,[status(thm)],[c_103,c_22]) ).
cnf(c_98,plain,
~ member(pair(sk3,sk1(y,z,sk2(sk3))),trancl(r)),
inference(resolve,[status(thm)],[c_4,c_37]) ).
cnf(c_104,plain,
( member(pair(sk3,A),trancl(r))
| ~ member(pair(sk2(sk3),A),trancl(r)) ),
inference(resolve,[status(thm)],[c_3,c_23]) ).
cnf(c_100,plain,
~ member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),trancl(r)),
inference(resolve,[status(thm)],[c_104,c_98]) ).
cnf(c_105,plain,
~ member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),r),
inference(resolve,[status(thm)],[c_12,c_100]) ).
cnf(c_101,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n020.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 23:15:04 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 2765310 was started by sandbox on n020,
% 0.19/0.45 % Sat Sep 26 23:15:04 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.49
% 0.19/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.19/0.49 % Length of proof is 18.
% 0.19/0.49 % Level of proof is 5.
% 0.19/0.49 % Maximum clause weight is 18.000.
% 0.19/0.49 % Given clauses 56.
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------