%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV824-1 : 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 : n026.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 09:09:11 AM UTC 2026
% Result : Unsatisfiable 7.83s 6.50s
% Output : CNFRefutation 7.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(c_81,plain,
class_Orderings_Olinorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Olinorder]) ).
fof(cls_linorder__not__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_2,VAR_1,VAR_0)
| c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_linorder__not__le_0) ).
cnf(c_117,plain,
( c_lessequals(C,B,A)
| c_HOL_Oord__class_Oless(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_linorder__not__le_0]) ).
fof(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
cnf(c_181,plain,
class_Orderings_Opreorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat__Orderings_Opreorder]) ).
fof(cls_order__less__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_HOL_Oord__class_Oless(VAR_1,VAR_3,VAR_0)
| ~ c_HOL_Oord__class_Oless(VAR_3,VAR_2,VAR_0)
| c_HOL_Oord__class_Oless(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Opreorder(VAR_0) ),
file('theBenchmark.p',cls_order__less__trans_0) ).
cnf(c_192,plain,
( ~ c_HOL_Oord__class_Oless(B,D,A)
| ~ c_HOL_Oord__class_Oless(D,C,A)
| c_HOL_Oord__class_Oless(B,C,A)
| ~ class_Orderings_Opreorder(A) ),
inference(clausify,[status(thm)],[cls_order__less__trans_0]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ v_fun1(VAR_0,VAR_2)
| ~ c_Natural_Oevaln(v_com,VAR_2,c_Suc(v_n),VAR_1)
| v_fun2(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_261,plain,
( ~ v_fun1(A,C)
| ~ c_Natural_Oevaln(v_com,C,c_Suc(v_n),B)
| v_fun2(A,B) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_0,axiom,
v_fun1(v_x,v_xa),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_262,plain,
v_fun1(v_x,v_xa),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_263,plain,
( ~ c_Natural_Oevaln(v_com,v_xa,c_Suc(v_n),A)
| v_fun2(v_x,A) ),
inference(resolve,[status(thm)],[c_261,c_262]) ).
cnf(c_281,plain,
( ~ c_HOL_Oord__class_Oless(A,C,tc_nat)
| ~ c_HOL_Oord__class_Oless(C,B,tc_nat)
| c_HOL_Oord__class_Oless(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_181,c_192]) ).
fof(cls_conjecture_2,axiom,
~ v_fun2(v_x,v_xb),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_313,plain,
~ v_fun2(v_x,v_xb),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_1,axiom,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_314,plain,
c_Natural_Oevaln(v_com,v_xa,v_n,v_xb),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_not__less__eq_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oord__class_Oless(VAR_1,VAR_0,tc_nat)
| c_HOL_Oord__class_Oless(VAR_0,c_Suc(VAR_1),tc_nat) ),
file('theBenchmark.p',cls_not__less__eq_0) ).
cnf(c_319,plain,
( c_HOL_Oord__class_Oless(B,A,tc_nat)
| c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq_0]) ).
fof(cls_evaln__nonstrict_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Natural_Oevaln(VAR_0,VAR_1,VAR_4,VAR_3)
| ~ c_lessequals(VAR_4,VAR_2,tc_nat)
| c_Natural_Oevaln(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',cls_evaln__nonstrict_0) ).
cnf(c_357,plain,
( ~ c_Natural_Oevaln(A,B,E,D)
| ~ c_lessequals(E,C,tc_nat)
| c_Natural_Oevaln(A,B,C,D) ),
inference(clausify,[status(thm)],[cls_evaln__nonstrict_0]) ).
fof(cls_less__not__refl_0,axiom,
! [VAR_0] : ~ c_HOL_Oord__class_Oless(VAR_0,VAR_0,tc_nat),
file('theBenchmark.p',cls_less__not__refl_0) ).
cnf(c_473,plain,
~ c_HOL_Oord__class_Oless(A,A,tc_nat),
inference(clausify,[status(thm)],[cls_less__not__refl_0]) ).
cnf(c_658,plain,
( c_lessequals(B,A,tc_nat)
| c_HOL_Oord__class_Oless(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_117,c_81]) ).
cnf(c_996,plain,
( ~ c_HOL_Oord__class_Oless(c_Suc(A),C,tc_nat)
| c_HOL_Oord__class_Oless(B,C,tc_nat)
| c_HOL_Oord__class_Oless(A,B,tc_nat) ),
inference(resolve,[status(thm)],[c_319,c_281]) ).
cnf(c_6968,plain,
( ~ c_HOL_Oord__class_Oless(c_Suc(A),A,tc_nat)
| c_HOL_Oord__class_Oless(A,A,tc_nat) ),
inference(factor,[status(thm)],[c_996]) ).
cnf(c_1013,plain,
~ c_HOL_Oord__class_Oless(c_Suc(A),A,tc_nat),
inference(resolve,[status(thm)],[c_473,c_6968]) ).
cnf(c_1143,plain,
( ~ c_lessequals(v_n,A,tc_nat)
| c_Natural_Oevaln(v_com,v_xa,A,v_xb) ),
inference(resolve,[status(thm)],[c_357,c_314]) ).
cnf(c_6956,plain,
( c_HOL_Oord__class_Oless(A,v_n,tc_nat)
| c_Natural_Oevaln(v_com,v_xa,A,v_xb) ),
inference(resolve,[status(thm)],[c_1143,c_658]) ).
cnf(c_6969,plain,
( v_fun2(v_x,v_xb)
| c_HOL_Oord__class_Oless(c_Suc(v_n),v_n,tc_nat) ),
inference(resolve,[status(thm)],[c_6956,c_263]) ).
cnf(c_6970,plain,
v_fun2(v_x,v_xb),
inference(resolve,[status(thm)],[c_1013,c_6969]) ).
cnf(c_6967,plain,
$false,
inference(resolve,[status(thm)],[c_313,c_6970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV824-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 15:04:00 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.39 % Process 1306900 was started by sandbox on n026,
% 0.10/5.39 % Sat Sep 26 15:04:00 2026
% 0.10/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/5.43
% 0.17/5.43 % From the command line: assign(max_seconds, 300).
% 7.83/6.50
% 7.83/6.50 % SZS status Unsatisfiable for theBenchmark
% 7.83/6.50
% 7.83/6.50 % Proof 1 at 0.89 (+ 0.16) seconds.
% 7.83/6.50 % Length of proof is 19.
% 7.83/6.50 % Level of proof is 4.
% 7.83/6.50 % Maximum clause weight is 23.000.
% 7.83/6.50 % Given clauses 385.
% 7.83/6.50
% 7.83/6.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------