%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA028-2 : 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 : n016.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 29 unt; 0 def)
% Number of atoms : 97 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 45 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 134 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
! [VAR_0] :
( class_OrderedGroup_Ocomm__monoid__add(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(c_1,plain,
( class_OrderedGroup_Ocomm__monoid__add(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
fof(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
! [VAR_0,VAR_1] :
( c_plus(c_0,VAR_1,VAR_0) = VAR_1
| ~ class_OrderedGroup_Ocomm__monoid__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(c_2,plain,
( c_plus(c_0,B,A) = B
| ~ class_OrderedGroup_Ocomm__monoid__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
fof(cls_OrderedGroup_Odiff__self_0,axiom,
! [VAR_0,VAR_1] :
( c_minus(VAR_1,VAR_1,VAR_0) = c_0
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
cnf(c_3,plain,
( c_minus(B,B,A) = c_0
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Odiff__self_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_4,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(cls_OrderedGroup_Ocompare__rls__5_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_minus(VAR_1,c_minus(VAR_2,VAR_3,VAR_0),VAR_0) = c_minus(c_plus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
cnf(c_5,plain,
( c_minus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,D,A),C,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__5_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_plus(c_minus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_minus(c_plus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
cnf(c_6,plain,
( c_plus(c_minus(B,C,A),D,A) = c_minus(c_plus(B,D,A),C,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__3_0]) ).
fof(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_plus(VAR_1,c_minus(VAR_2,VAR_3,VAR_0),VAR_0) = c_minus(c_plus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(c_7,plain,
( c_plus(B,c_minus(C,D,A),A) = c_minus(c_plus(B,C,A),D,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__2_0]) ).
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_8,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_Ocompare__rls__9_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,c_minus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(c_plus(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(c_9,plain,
( c_lessequals(B,c_minus(D,C,A),A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
fof(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_minus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,c_plus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
cnf(c_10,plain,
( c_lessequals(c_minus(B,D,A),C,A)
| ~ c_lessequals(B,c_plus(C,D,A),A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__8_1]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_11,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
cnf(c_12,plain,
( c_plus(c_0,B,A) = B
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_13,plain,
( c_lessequals(B,c_minus(D,C,A),A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_14,plain,
( c_lessequals(c_minus(B,D,A),C,A)
| ~ c_lessequals(B,c_plus(C,D,A),A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_15,plain,
( ~ class_Ring__and__Field_Oordered__idom(B)
| c_minus(A,A,B) = c_0 ),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_16,plain,
( ~ class_Ring__and__Field_Oordered__idom(D)
| c_minus(A,c_minus(B,C,D),D) = c_minus(c_plus(A,C,D),B,D) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_17,plain,
( ~ class_Ring__and__Field_Oordered__idom(C)
| c_plus(c_minus(A,B,C),D,C) = c_minus(c_plus(A,D,C),B,C) ),
inference(resolve,[status(thm)],[c_6,c_4]) ).
cnf(c_18,plain,
( ~ class_Ring__and__Field_Oordered__idom(D)
| c_plus(A,c_minus(B,C,D),D) = c_minus(c_plus(A,B,D),C,D) ),
inference(resolve,[status(thm)],[c_7,c_4]) ).
cnf(c_19,plain,
c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,B,t_b),C,t_b),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_20,plain,
c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(c_plus(A,C,t_b),B,t_b),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_21,plain,
c_minus(A,c_minus(B,C,t_b),t_b) = c_minus(c_plus(A,C,t_b),B,t_b),
inference(resolve,[status(thm)],[c_16,c_11]) ).
cnf(c_22,plain,
c_minus(c_plus(A,B,t_b),C,t_b) = c_minus(A,c_minus(C,B,t_b),t_b),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_23,plain,
c_minus(A,A,t_b) = c_0,
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_24,plain,
( c_lessequals(c_minus(A,C,t_b),B,t_b)
| ~ c_lessequals(A,c_plus(B,C,t_b),t_b) ),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_25,plain,
( c_lessequals(A,c_minus(C,B,t_b),t_b)
| ~ c_lessequals(c_plus(A,B,t_b),C,t_b) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_26,plain,
c_plus(c_0,A,t_b) = A,
inference(resolve,[status(thm)],[c_11,c_12]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(v_g(VAR_0),v_k(VAR_0),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_27,plain,
c_lessequals(v_g(A),v_k(A),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_minus(v_f(v_x),v_k(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_28,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(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]) ).
cnf(c_29,plain,
c_plus(c_minus(A,B,t_b),C,t_b) = c_minus(A,c_minus(B,C,t_b),t_b),
inference(paramod,[status(thm)],[c_22,c_20]) ).
cnf(c_30,plain,
c_plus(A,c_minus(B,C,t_b),t_b) = c_minus(A,c_minus(C,B,t_b),t_b),
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_81,plain,
c_plus(c_0,A,t_b) = c_minus(B,c_minus(B,A,t_b),t_b),
inference(paramod,[status(thm)],[c_23,c_29]) ).
cnf(c_82,plain,
A = c_minus(B,c_minus(B,A,t_b),t_b),
inference(paramod,[status(thm)],[c_26,c_81]) ).
cnf(c_40,plain,
c_minus(A,c_minus(A,B,t_b),t_b) = B,
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
c_plus(A,c_minus(B,c_minus(C,D,t_b),t_b),t_b) = c_minus(A,c_minus(C,c_plus(B,D,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_22,c_30]) ).
cnf(c_44,plain,
c_minus(A,c_minus(c_minus(B,C,t_b),D,t_b),t_b) = c_minus(A,c_minus(B,c_plus(D,C,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_30,c_83]) ).
cnf(c_84,plain,
c_plus(A,B,t_b) = c_minus(C,c_minus(c_minus(C,A,t_b),B,t_b),t_b),
inference(paramod,[status(thm)],[c_40,c_29]) ).
cnf(c_85,plain,
c_plus(A,B,t_b) = c_minus(C,c_minus(C,c_plus(B,A,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_44,c_84]) ).
cnf(c_56,plain,
c_plus(A,B,t_b) = c_plus(B,A,t_b),
inference(paramod,[status(thm)],[c_40,c_85]) ).
cnf(c_59,plain,
( c_lessequals(c_minus(A,B,t_b),C,t_b)
| ~ c_lessequals(A,c_plus(B,C,t_b),t_b) ),
inference(paramod,[status(thm)],[c_56,c_24]) ).
cnf(c_60,plain,
( c_lessequals(B,c_minus(C,A,t_b),t_b)
| ~ c_lessequals(c_plus(A,B,t_b),C,t_b) ),
inference(paramod,[status(thm)],[c_56,c_25]) ).
cnf(c_86,plain,
~ c_lessequals(v_f(v_x),c_plus(v_k(v_x),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_59,c_28]) ).
cnf(c_63,plain,
~ c_lessequals(v_f(v_x),c_minus(v_k(v_x),c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_30,c_86]) ).
cnf(c_87,plain,
~ c_lessequals(c_plus(c_minus(v_g(v_x),v_f(v_x),t_b),v_f(v_x),t_b),v_k(v_x),t_b),
inference(resolve,[status(thm)],[c_60,c_63]) ).
cnf(c_88,plain,
~ c_lessequals(c_plus(v_f(v_x),c_minus(v_g(v_x),v_f(v_x),t_b),t_b),v_k(v_x),t_b),
inference(paramod,[status(thm)],[c_56,c_87]) ).
cnf(c_89,plain,
~ c_lessequals(c_minus(v_f(v_x),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),v_k(v_x),t_b),
inference(paramod,[status(thm)],[c_30,c_88]) ).
cnf(c_90,plain,
~ c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(paramod,[status(thm)],[c_40,c_89]) ).
cnf(c_80,plain,
$false,
inference(resolve,[status(thm)],[c_27,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA028-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:11:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1815332 was started by sandbox2 on n016,
% 0.10/0.37 % Sat Sep 26 22:11:47 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 37.
% 0.10/0.40 % Level of proof is 9.
% 0.10/0.40 % Maximum clause weight is 41.000.
% 0.10/0.40 % Given clauses 27.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------