%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG339-1 : 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 06:50:02 AM UTC 2026
% Result : Unsatisfiable 102.16s 14.15s
% Output : CNFRefutation 102.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 44 ( 24 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(VAR_0,v_d1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(VAR_0,v_d2,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_680,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(A,v_d1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(A,v_d2,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_681,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d2,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1,tc_RealDef_Oreal),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_682,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_d1,tc_RealDef_Oreal),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_real__lbound__gt__zero_1,axiom,
! [VAR_0,VAR_1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(VAR_0,VAR_1),VAR_0,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__lbound__gt__zero_1) ).
cnf(c_690,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,B),A,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__lbound__gt__zero_1]) ).
fof(cls_real__lbound__gt__zero_2,axiom,
! [VAR_0,VAR_1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(VAR_0,VAR_1),VAR_1,tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__lbound__gt__zero_2) ).
cnf(c_691,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,B),B,tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__lbound__gt__zero_2]) ).
fof(cls_real__lbound__gt__zero_0,axiom,
! [VAR_0,VAR_1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),VAR_1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(VAR_0,VAR_1),tc_RealDef_Oreal) ),
file('theBenchmark.p',cls_real__lbound__gt__zero_0) ).
cnf(c_705,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,B),tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[cls_real__lbound__gt__zero_0]) ).
cnf(c_12442,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,v_d1),A,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_690,c_682]) ).
cnf(c_2008,plain,
c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),v_d2,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_12442,c_681]) ).
cnf(c_12443,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,v_d1),v_d1,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_691,c_682]) ).
cnf(c_2175,plain,
c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),v_d1,tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_12443,c_681]) ).
cnf(c_12444,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),A,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(A,v_d1),tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_705,c_682]) ).
cnf(c_3063,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_12444,c_681]) ).
cnf(c_12445,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),v_d1,tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_2008,c_680]) ).
cnf(c_12446,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(v_d2,v_d1),tc_RealDef_Oreal),
inference(resolve,[status(thm)],[c_2175,c_12445]) ).
cnf(c_12441,plain,
$false,
inference(resolve,[status(thm)],[c_3063,c_12446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG339-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 21:52:47 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3178408 was started by sandbox on n005,
% 0.18/0.45 % Sat Sep 26 21:52:47 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 102.16/14.15
% 102.16/14.15 % SZS status Unsatisfiable for theBenchmark
% 102.16/14.15
% 102.16/14.15 % Proof 1 at 4.71 (+ 0.83) seconds.
% 102.16/14.15 % Length of proof is 10.
% 102.16/14.15 % Level of proof is 2.
% 102.16/14.15 % Maximum clause weight is 21.000.
% 102.16/14.15 % Given clauses 431.
% 102.16/14.15
% 102.16/14.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------