%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT028-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:28:24 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 28 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 19 ( 7 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
! [VAR_0] :
( ~ c_in(VAR_0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),VAR_0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_86,plain,
( ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),A,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_in(v_R____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_87,plain,
c_in(v_R____,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_assms_0,axiom,
v_a != v_b,
file('theBenchmark.p',cls_assms_0) ).
cnf(c_92,plain,
v_a != v_b,
inference(clausify,[status(thm)],[cls_assms_0]) ).
cnf(c_93,plain,
v_b != v_a,
inference(copy,[status(thm)],[c_92]) ).
fof(cls_mktop__Lin_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_in(VAR_0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(VAR_0,VAR_1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('theBenchmark.p',cls_mktop__Lin_0) ).
cnf(c_151,plain,
( ~ c_in(A,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(A,B),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
inference(clausify,[status(thm)],[cls_mktop__Lin_0]) ).
fof(cls_in__mktop_4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_in(c_Pair(VAR_0,VAR_1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(VAR_2,VAR_1),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| VAR_0 = VAR_1
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_in__mktop_4) ).
cnf(c_153,plain,
( c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(C,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| A = B
| A = B ),
inference(clausify,[status(thm)],[cls_in__mktop_4]) ).
cnf(c_154,plain,
( c_in(c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(C,B),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| A = B ),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_746,plain,
c_in(c_Arrow__Order__Mirabelle_Omktop(v_R____,A),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(resolve,[status(thm)],[c_151,c_87]) ).
cnf(c_778,plain,
( ~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_a = v_b ),
inference(resolve,[status(thm)],[c_154,c_86]) ).
cnf(c_779,plain,
( ~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| v_b = v_a ),
inference(copy,[status(thm)],[c_778]) ).
cnf(c_776,plain,
~ c_in(c_Arrow__Order__Mirabelle_Omktop(A,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(resolve,[status(thm)],[c_93,c_779]) ).
cnf(c_777,plain,
$false,
inference(resolve,[status(thm)],[c_776,c_746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT028-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 06:18:24 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.15/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.38 % Process 2977471 was started by sandbox on n007,
% 0.15/0.38 % Sat Sep 26 06:18:24 2026
% 0.15/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 0.15/0.52
% 0.15/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.52
% 0.15/0.52 % Proof 1 at 0.09 (+ 0.02) seconds.
% 0.15/0.52 % Length of proof is 10.
% 0.15/0.52 % Level of proof is 3.
% 0.15/0.52 % Maximum clause weight is 18.000.
% 0.15/0.52 % Given clauses 90.
% 0.15/0.52
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------