%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG350-1 : 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 : 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 06:50:03 AM UTC 2026
% Result : Unsatisfiable 0.23s 5.81s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(c_10,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(cls_less__le__not__le_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ c_HOL_Oord__class_Oless(VAR_2,VAR_1,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Opreorder(VAR_0) ),
file('theBenchmark.p',cls_less__le__not__le_1) ).
cnf(c_12,plain,
( ~ c_HOL_Oord__class_Oless(C,B,A)
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Opreorder(A) ),
inference(clausify,[status(thm)],[cls_less__le__not__le_1]) ).
cnf(c_456,plain,
( ~ c_HOL_Oord__class_Oless(B,A,tc_RealDef_Oreal)
| ~ c_lessequals(A,B,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
fof(cls_Y_0,axiom,
! [VAR_0] :
( ~ hBOOL(hAPP(v_P,VAR_0))
| c_HOL_Oord__class_Oless(VAR_0,v_Y____,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_Y_0) ).
cnf(c_480,plain,
( ~ hBOOL(hAPP(v_P,A))
| c_HOL_Oord__class_Oless(A,v_Y____,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_Y_0]) ).
fof(cls_real__le__linear_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_0,tc_RealDef_Oreal)
| c_lessequals(VAR_0,VAR_1,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__le__linear_0) ).
cnf(c_481,plain,
( c_lessequals(B,A,tc_RealDef_Oreal)
| c_lessequals(A,B,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__le__linear_0]) ).
fof(cls_conjecture_0,axiom,
hBOOL(hAPP(v_P,v_xa)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_484,plain,
hBOOL(hAPP(v_P,v_xa)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_485,plain,
~ c_lessequals(v_xa,v_Y____,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_1036,plain,
c_HOL_Oord__class_Oless(v_xa,v_Y____,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_484,c_480]) ).
cnf(c_1038,plain,
c_lessequals(v_Y____,v_xa,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_485,c_481]) ).
cnf(c_2137,plain,
~ c_lessequals(v_Y____,v_xa,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_1036,c_456]) ).
cnf(c_2136,plain,
$false,
inference(resolve,[status(thm)],[c_1038,c_2137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG350-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n020.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Sat Sep 26 21:54:56 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.46 % Process 2591338 was started by sandbox on n020,
% 0.16/5.46 % Sat Sep 26 21:54:56 2026
% 0.16/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.48
% 0.16/5.48 % From the command line: assign(max_seconds, 300).
% 0.23/5.81
% 0.23/5.81 % SZS status Unsatisfiable for theBenchmark
% 0.23/5.81
% 0.23/5.81 % Proof 1 at 0.26 (+ 0.05) seconds.
% 0.23/5.81 % Length of proof is 10.
% 0.23/5.81 % Level of proof is 2.
% 0.23/5.81 % Maximum clause weight is 8.000.
% 0.23/5.81 % Given clauses 198.
% 0.23/5.81
% 0.23/5.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------