%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT007-1 : 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 : n016.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 08:28:22 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.72s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 3 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
! [VAR_0] : ~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),VAR_0)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_102,plain,
~ hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),A)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_0,axiom,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_104,plain,
hBOOL(c_Order__Relation_Olinear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),v_r,tc_Arrow__Order__Mirabelle_Oalt)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_strict__linear__order__on__diff__Id_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(c_Order__Relation_Olinear__order__on(VAR_0,VAR_2,VAR_1))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(VAR_0,VAR_1),c_HOL_Ominus__class_Ominus(VAR_2,c_Relation_OId(VAR_1),tc_fun(tc_prod(VAR_1,VAR_1),tc_bool)))) ),
file('theBenchmark.p',cls_strict__linear__order__on__diff__Id_0) ).
cnf(c_105,plain,
( ~ hBOOL(c_Order__Relation_Olinear__order__on(A,C,B))
| hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(A,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)))) ),
inference(clausify,[status(thm)],[cls_strict__linear__order__on__diff__Id_0]) ).
fof(cls_Lin__def_0,axiom,
c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('theBenchmark.p',cls_Lin__def_0) ).
cnf(c_110,plain,
c_Arrow__Order__Mirabelle_OLin = c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
inference(clausify,[status(thm)],[cls_Lin__def_0]) ).
cnf(c_111,plain,
c_Collect(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) = c_Arrow__Order__Mirabelle_OLin,
inference(copy,[status(thm)],[c_110]) ).
fof(cls_Collect__def_0,axiom,
! [VAR_0,VAR_1] : c_Collect(VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Collect__def_0) ).
cnf(c_633,plain,
c_Collect(A,B) = A,
inference(clausify,[status(thm)],[cls_Collect__def_0]) ).
cnf(c_707,plain,
c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt) = c_Arrow__Order__Mirabelle_OLin,
inference(paramod,[status(thm)],[c_633,c_111]) ).
cnf(c_709,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,A)),
inference(paramod,[status(thm)],[c_707,c_102]) ).
cnf(c_746,plain,
hBOOL(hAPP(c_Order__Relation_Ostrict__linear__order__on(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_bool)),tc_Arrow__Order__Mirabelle_Oalt),c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(resolve,[status(thm)],[c_105,c_104]) ).
cnf(c_747,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_HOL_Ominus__class_Ominus(v_r,c_Relation_OId(tc_Arrow__Order__Mirabelle_Oalt),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),
inference(paramod,[status(thm)],[c_707,c_746]) ).
cnf(c_745,plain,
$false,
inference(resolve,[status(thm)],[c_709,c_747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT007-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.59 % Computer : n016.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.59 % WCLimit : 300
% 0.09/5.59 % DateTime : Sat Sep 26 06:22:52 UTC 2026
% 0.09/5.59 % CPUTime :
% 0.09/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.59 % Process 187429 was started by sandbox2 on n016,
% 0.09/5.59 % Sat Sep 26 06:22:52 2026
% 0.09/5.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.62
% 0.14/5.62 % From the command line: assign(max_seconds, 300).
% 0.14/5.72
% 0.14/5.72 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.72
% 0.14/5.72 % Proof 1 at 0.09 (+ 0.01) seconds.
% 0.14/5.72 % Length of proof is 9.
% 0.14/5.72 % Level of proof is 4.
% 0.14/5.72 % Maximum clause weight is 44.000.
% 0.14/5.72 % Given clauses 60.
% 0.14/5.72
% 0.14/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------