%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA024-1 : 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 : n007.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 06:51:09 AM UTC 2026
% Result : Unsatisfiable 49.08s 7.58s
% Output : CNFRefutation 49.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 33 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_711,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_712,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(v_k(VAR_0),v_f(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_714,plain,
c_lessequals(v_k(A),v_f(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_minus(VAR_1,VAR_2,VAR_0) = c_plus(VAR_1,c_uminus(VAR_2,VAR_0),VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0) ).
cnf(c_720,plain,
( c_minus(B,C,A) = c_plus(B,c_uminus(C,A),A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oab__group__add__class_Odiff__minus_0]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
! [VAR_0] :
( class_OrderedGroup_Oab__group__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(c_895,plain,
( class_OrderedGroup_Oab__group__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
cnf(c_898,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
fof(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_plus(VAR_1,VAR_3,VAR_0),c_plus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
cnf(c_2078,plain,
( c_lessequals(c_plus(B,D,A),c_plus(C,D,A),A)
| ~ c_lessequals(B,C,A)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oadd__le__cancel__right_1]) ).
cnf(c_3755,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolve,[status(thm)],[c_895,c_711]) ).
cnf(c_3758,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolve,[status(thm)],[c_898,c_711]) ).
cnf(c_11691,plain,
( c_lessequals(c_plus(v_k(A),B,t_b),c_plus(v_f(A),B,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
inference(resolve,[status(thm)],[c_2078,c_714]) ).
cnf(c_5427,plain,
c_lessequals(c_plus(v_k(A),B,t_b),c_plus(v_f(A),B,t_b),t_b),
inference(resolve,[status(thm)],[c_3758,c_11691]) ).
cnf(c_11629,plain,
c_minus(A,B,t_b) = c_plus(A,c_uminus(B,t_b),t_b),
inference(resolve,[status(thm)],[c_3755,c_720]) ).
cnf(c_11692,plain,
~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(paramod,[status(thm)],[c_11629,c_712]) ).
cnf(c_11693,plain,
~ c_lessequals(c_plus(v_k(v_x),c_uminus(v_g(v_x),t_b),t_b),c_plus(v_f(v_x),c_uminus(v_g(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_11629,c_11692]) ).
cnf(c_11690,plain,
$false,
inference(resolve,[status(thm)],[c_5427,c_11693]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA024-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 22:04:24 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.34 % Process 583609 was started by sandbox on n007,
% 0.09/0.34 % Sat Sep 26 22:04:24 2026
% 0.09/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.42
% 0.13/0.42 % From the command line: assign(max_seconds, 300).
% 49.08/7.58
% 49.08/7.58 % given #500 (I,wt=4): 839 -class_Ring__and__Field_Oordered__semidom(A) | class_LOrder_Olorder(A) # tptp_name(clsrel_Ring__and__Field_Oordered__semidom_28) # clausal_fof(1). [assumption].
% 49.08/7.58
% 49.08/7.58 % given #1000 (I,wt=13): 1348 -c_in(A,c_Main_OInterI__1(A,B,C),C) | c_in(A,c_Inter(B,C),C) # tptp_name(cls_Set_OInterI_1) # clausal_fof(1). [assumption].
% 49.08/7.58
% 49.08/7.58 % given #1500 (I,wt=8): 2071 -class_OrderedGroup_Oab__group__add(A) | c_minus(B,c_0,A) = B # tptp_name(cls_OrderedGroup_Odiff__0__right_0) # clausal_fof(1). [assumption].
% 49.08/7.58
% 49.08/7.58 % given #2000 (I,wt=17): 2829 c_List_Oreplicate(c_Nat_Osize(c_List_Oupt(A,B),tc_List_Olist(tc_nat)),C,D) = c_List_Odrop(A,c_List_Oreplicate(B,C,D),D). [copy(2828),rewrite([2777(4)]),flip(a)].
% 49.08/7.58
% 49.08/7.58 % given #2500 (I,wt=9): 3544 -c_Parity_Oeven(c_times(A,A,tc_nat),tc_nat) | c_Parity_Oeven(A,tc_nat). [factor(1980,b,c)].
% 49.08/7.58
% 49.08/7.58 % SZS status Unsatisfiable for theBenchmark
% 49.08/7.58
% 49.08/7.58 % Proof 1 at 6.51 (+ 0.51) seconds.
% 49.08/7.58 % Length of proof is 12.
% 49.08/7.58 % Level of proof is 3.
% 49.08/7.58 % Maximum clause weight is 16.000.
% 49.08/7.58 % Given clauses 2712.
% 49.08/7.58
% 49.08/7.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------