%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 06:51:10 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 41 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 5 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
! [VAR_0] :
( class_Orderings_Olinorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
cnf(c_1,plain,
( class_Orderings_Olinorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_2,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
! [VAR_0] :
( class_OrderedGroup_Olordered__ab__group__abs(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_3,plain,
( class_OrderedGroup_Olordered__ab__group__abs(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__group__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c_4,plain,
( class_OrderedGroup_Opordered__ab__group__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_54]) ).
fof(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(c_0,c_HOL_Oabs(VAR_1,VAR_0),VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(c_5,plain,
( c_lessequals(c_0,c_HOL_Oabs(B,A),A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c_6,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_7,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(clsrel_OrderedGroup_Opordered__ab__group__add_10,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
cnf(c_8,plain,
( class_Orderings_Oorder(A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Opordered__ab__group__add_10]) ).
fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_Orderings_Omax(VAR_3,VAR_1,VAR_0),VAR_2,VAR_0)
| ~ c_lessequals(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(c_11,plain,
( c_lessequals(c_Orderings_Omax(D,B,A),C,A)
| ~ c_lessequals(D,C,A)
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2]) ).
cnf(c_12,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_Orderings_Olinorder__not__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_2,VAR_1,VAR_0)
| c_less(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
cnf(c_13,plain,
( c_lessequals(C,B,A)
| c_less(B,C,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Olinorder__not__le_0]) ).
fof(cls_Orderings_Oorder__less__imp__le_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ c_less(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(c_14,plain,
( c_lessequals(B,C,A)
| ~ c_less(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c_15,plain,
( c_lessequals(B,A,t_b)
| c_less(A,B,t_b) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_16,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_17,plain,
( c_lessequals(B,A,t_b)
| c_lessequals(A,B,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
fof(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_3,VAR_2,VAR_0)
| ~ c_lessequals(VAR_3,VAR_1,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(c_18,plain,
( c_lessequals(D,C,A)
| ~ c_lessequals(D,B,A)
| ~ c_lessequals(B,C,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c_19,plain,
( c_lessequals(C,B,t_b)
| ~ c_lessequals(C,A,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_20,plain,
( c_lessequals(B,A,t_b)
| c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_21,plain,
( c_lessequals(c_Orderings_Omax(C,A,t_b),B,t_b)
| ~ c_lessequals(C,B,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_22,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(cls_conjecture_2,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_23,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_24,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_56,plain,
( c_lessequals(c_0,B,t_b)
| ~ c_lessequals(c_HOL_Oabs(A,t_b),B,t_b) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_37,plain,
~ c_lessequals(c_HOL_Oabs(A,t_b),c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(resolve,[status(thm)],[c_56,c_23]) ).
cnf(c_57,plain,
( c_lessequals(c_Orderings_Omax(A,c_0,t_b),c_HOL_Oabs(B,t_b),t_b)
| ~ c_lessequals(A,c_HOL_Oabs(B,t_b),t_b) ),
inference(resolve,[status(thm)],[c_21,c_22]) ).
cnf(c_39,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_57,c_24]) ).
cnf(c_54,plain,
c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(A,t_b),t_b),
inference(resolve,[status(thm)],[c_37,c_20]) ).
cnf(c_55,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 22:13:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2788026 was started by sandbox2 on n001,
% 0.11/0.37 % Sat Sep 26 22:13:28 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 26.
% 0.11/0.38 % Level of proof is 6.
% 0.11/0.38 % Maximum clause weight is 19.000.
% 0.11/0.38 % Given clauses 12.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------