%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT031-1 : 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 : 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 08:28:24 AM UTC 2026
% Result : Unsatisfiable 3.25s 0.94s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 11 unt; 0 def)
% Number of atoms : 19 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 23 ( 3 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_143,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_144,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_145,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_F),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),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_PiE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(VAR_0,VAR_3)),VAR_4),c_FuncSet_OPi(VAR_2,VAR_5,VAR_0,VAR_3)))
| hBOOL(hAPP(hAPP(c_in(VAR_3),hAPP(VAR_4,VAR_1)),hAPP(VAR_5,VAR_1)))
| ~ hBOOL(hAPP(hAPP(c_in(VAR_0),VAR_1),VAR_2)) ),
file('theBenchmark.p',cls_PiE_0) ).
cnf(c_158,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(A,D)),E),c_FuncSet_OPi(C,F,A,D)))
| hBOOL(hAPP(hAPP(c_in(D),hAPP(E,B)),hAPP(F,B)))
| ~ hBOOL(hAPP(hAPP(c_in(A),B),C)) ),
inference(clausify,[status(thm)],[cls_PiE_0]) ).
fof(cls_COMBK__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : hAPP(c_COMBK(VAR_0,VAR_1,VAR_2),VAR_3) = VAR_0,
file('theBenchmark.p',cls_COMBK__def_0) ).
cnf(c_519,plain,
hAPP(c_COMBK(A,B,C),D) = A,
inference(clausify,[status(thm)],[cls_COMBK__def_0]) ).
cnf(c_1081,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),A)),B),c_FuncSet_OPi(c_Arrow__Order__Mirabelle_OProf,C,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),A)))
| hBOOL(hAPP(hAPP(c_in(A),hAPP(B,v_Q____)),hAPP(C,v_Q____))) ),
inference(resolve,[status(thm)],[c_158,c_144]) ).
cnf(c_1082,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),hAPP(c_COMBK(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Q____))),
inference(resolve,[status(thm)],[c_1081,c_145]) ).
cnf(c_1083,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(paramod,[status(thm)],[c_519,c_1082]) ).
cnf(c_1080,plain,
$false,
inference(resolve,[status(thm)],[c_143,c_1083]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT031-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 06:20:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1411438 was started by sandbox on n005,
% 0.08/0.36 % Sat Sep 26 06:20:32 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 3.25/0.94
% 3.25/0.94 % SZS status Unsatisfiable for theBenchmark
% 3.25/0.94
% 3.25/0.94 % Proof 1 at 0.40 (+ 0.04) seconds.
% 3.25/0.94 % Length of proof is 6.
% 3.25/0.94 % Level of proof is 1.
% 3.25/0.94 % Maximum clause weight is 123.000.
% 3.25/0.94 % Given clauses 93.
% 3.25/0.94
% 3.25/0.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------