%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT026-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:28:23 AM UTC 2026
% Result : Unsatisfiable 1.16s 0.58s
% Output : CNFRefutation 1.16s
% 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_assms_0,axiom,
v_a != v_b,
file('theBenchmark.p',cls_assms_0) ).
cnf(c_91,plain,
v_a != v_b,
inference(clausify,[status(thm)],[cls_assms_0]) ).
cnf(c_92,plain,
v_b != v_a,
inference(copy,[status(thm)],[c_91]) ).
fof(cls_linear__alt_0,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__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_linear__alt_0) ).
cnf(c_147,plain,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,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_linear__alt_0]) ).
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_150,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_152,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_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 ),
inference(copy,[status(thm)],[c_152]) ).
cnf(c_694,plain,
c_in(c_Arrow__Order__Mirabelle_Omktop(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,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_150,c_147]) ).
cnf(c_726,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_153,c_86]) ).
cnf(c_727,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_726]) ).
cnf(c_724,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_92,c_727]) ).
cnf(c_725,plain,
$false,
inference(resolve,[status(thm)],[c_724,c_694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT026-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 06:19:47 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.40 % Process 1406739 was started by sandbox2 on n005,
% 0.13/0.40 % Sat Sep 26 06:19:47 2026
% 0.13/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.42
% 0.18/0.42 % From the command line: assign(max_seconds, 300).
% 1.16/0.58
% 1.16/0.58 % SZS status Unsatisfiable for theBenchmark
% 1.16/0.58
% 1.16/0.58 % Proof 1 at 0.12 (+ 0.03) seconds.
% 1.16/0.58 % Length of proof is 10.
% 1.16/0.58 % Level of proof is 3.
% 1.16/0.58 % Maximum clause weight is 18.000.
% 1.16/0.58 % Given clauses 89.
% 1.16/0.58
% 1.16/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------