%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 09:07:09 AM UTC 2026
% Result : Unsatisfiable 39.13s 6.08s
% Output : CNFRefutation 39.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 31 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 10 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Wellfounded__Recursion_Owellorder_1,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_Wellfounded__Recursion_Owellorder(VAR_0) ),
file('theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
cnf(c_1,plain,
( class_Orderings_Oorder(A)
| ~ class_Wellfounded__Recursion_Owellorder(A) ),
inference(clausify,[status(thm)],[clsrel_Wellfounded__Recursion_Owellorder_1]) ).
fof(cls_SetInterval_OatLeastLessThan__empty_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_SetInterval_OatLeastLessThan(VAR_2,VAR_1,VAR_0) = c_emptyset
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
cnf(c_5,plain,
( c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_SetInterval_OatLeastLessThan__empty_0]) ).
cnf(c_1375,plain,
( c_SetInterval_OatLeastLessThan(C,B,A) = c_emptyset
| ~ c_lessequals(B,C,A)
| ~ class_Wellfounded__Recursion_Owellorder(A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
fof(clsarity_nat_8,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('theBenchmark.p',clsarity_nat_8) ).
cnf(c_1605,plain,
class_Wellfounded__Recursion_Owellorder(tc_nat),
inference(clausify,[status(thm)],[clsarity_nat_8]) ).
fof(cls_SetInterval_OatLeastLessThan__singleton_0,axiom,
! [VAR_0] : c_SetInterval_OatLeastLessThan(VAR_0,c_Suc(VAR_0),tc_nat) = c_insert(VAR_0,c_emptyset,tc_nat),
file('theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
cnf(c_3545,plain,
c_SetInterval_OatLeastLessThan(A,c_Suc(A),tc_nat) = c_insert(A,c_emptyset,tc_nat),
inference(clausify,[status(thm)],[cls_SetInterval_OatLeastLessThan__singleton_0]) ).
fof(cls_Set_Oempty__not__insert_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_emptyset != c_insert(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
cnf(c_3705,plain,
c_emptyset != c_insert(A,B,C),
inference(clausify,[status(thm)],[cls_Set_Oempty__not__insert_0]) ).
cnf(c_3706,plain,
c_insert(A,B,C) != c_emptyset,
inference(copy,[status(thm)],[c_3705]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : c_lessequals(VAR_0,v_x(VAR_0),tc_nat),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3834,plain,
c_lessequals(A,v_x(A),tc_nat),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : v_x(VAR_0) = v_nat,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3835,plain,
v_x(A) = v_nat,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_13039,plain,
c_lessequals(A,v_nat,tc_nat),
inference(paramod,[status(thm)],[c_3835,c_3834]) ).
cnf(c_17248,plain,
( c_SetInterval_OatLeastLessThan(v_nat,A,tc_nat) = c_emptyset
| ~ class_Wellfounded__Recursion_Owellorder(tc_nat) ),
inference(resolve,[status(thm)],[c_13039,c_1375]) ).
cnf(c_13745,plain,
c_SetInterval_OatLeastLessThan(v_nat,A,tc_nat) = c_emptyset,
inference(resolve,[status(thm)],[c_1605,c_17248]) ).
cnf(c_17249,plain,
c_emptyset = c_insert(v_nat,c_emptyset,tc_nat),
inference(paramod,[status(thm)],[c_13745,c_3545]) ).
cnf(c_17250,plain,
c_insert(v_nat,c_emptyset,tc_nat) = c_emptyset,
inference(copy,[status(thm)],[c_17249]) ).
cnf(c_17247,plain,
$false,
inference(resolve,[status(thm)],[c_3706,c_17250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV254-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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 13:22:32 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 3250091 was started by sandbox on n014,
% 0.08/0.36 % Sat Sep 26 13:22:32 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.43
% 0.14/0.43 % From the command line: assign(max_seconds, 300).
% 39.13/6.08
% 39.13/6.08 % given #500 (I,wt=26): 934 -class_Ring__and__Field_Ocomm__semiring__1__cancel(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_lessequals(c_1,c_uminus(B,A),A) | c_lessequals(B,c_uminus(c_1,A),A). [resolve(61,b,46,a)].
% 39.13/6.08
% 39.13/6.08 % given #1000 (I,wt=27): 1467 -c_in(c_Pair(A,B,C,D),E,tc_prod(C,D)) | c_in(B,c_Relation_ORange(E,C,D),D) # tptp_name(cls_Relation_ORangeI_0) # clausal_fof(1). [assumption].
% 39.13/6.08
% 39.13/6.08 % given #1500 (I,wt=9): 1974 -class_Ring__and__Field_Opordered__ring(A) | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) # tptp_name(clsrel_Ring__and__Field_Opordered__ring_20) # clausal_fof(1). [assumption].
% 39.13/6.08
% 39.13/6.08 % given #2000 (I,wt=31): 2607 c_List_Onibble_Onibble__rec(A,B,C,D,E,F,V6,V7,V8,V9,V10,V11,V12,V13,V14,V15,c_List_Onibble_ONibbleE,V16) = V14 # tptp_name(cls_List_Onibble_Orecs__15_0) # clausal_fof(1). [assumption].
% 39.13/6.08
% 39.13/6.08 % given #2500 (I,wt=22): 3212 -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(B,c_0,A) | c_less(c_0,c_uminus(B,A),A) # tptp_name(cls_OrderedGroup_Oneg__0__less__iff__less_1) # clausal_fof(1). [assumption].
% 39.13/6.08
% 39.13/6.08 % given #3000 (I,wt=33): 3822 c_insert(c_Message_Omsg_OKey(A),c_Message_Oparts(B),tc_Message_Omsg) = c_Message_Oparts(c_insert(c_Message_Omsg_OKey(A),B,tc_Message_Omsg)). [copy(3821),flip(a)].
% 39.13/6.08
% 39.13/6.08 % given #3500 (F,wt=23): 16626 -c_less(c_Binomial_Obinomial(c_Suc(A),c_Suc(c_1)),A,tc_nat). [para(8251(a,1),8897(a,2))].
% 39.13/6.08
% 39.13/6.08 % SZS status Unsatisfiable for theBenchmark
% 39.13/6.08
% 39.13/6.08 % Proof 1 at 5.12 (+ 0.40) seconds.
% 39.13/6.08 % Length of proof is 12.
% 39.13/6.08 % Level of proof is 3.
% 39.13/6.08 % Maximum clause weight is 25.000.
% 39.13/6.08 % Given clauses 3527.
% 39.13/6.08
% 39.13/6.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------