%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA027-2 : 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 : n010.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 0.12s 0.61s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 84 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 46 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 19 !; 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(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(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_4,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]) ).
cnf(c_5,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
! [VAR_0] :
( class_OrderedGroup_Opordered__ab__group__add(VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
cnf(c_6,plain,
( class_OrderedGroup_Opordered__ab__group__add(A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_1]) ).
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_7,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__9_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_plus(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ c_lessequals(VAR_1,c_minus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Opordered__ab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(c_8,plain,
( c_lessequals(c_plus(B,D,A),C,A)
| ~ c_lessequals(B,c_minus(C,D,A),A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
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_9,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]) ).
fof(clsrel_LOrder_Ojoin__semilorder_1,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_LOrder_Ojoin__semilorder(VAR_0) ),
file('theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(c_10,plain,
( class_Orderings_Oorder(A)
| ~ class_LOrder_Ojoin__semilorder(A) ),
inference(clausify,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
fof(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
! [VAR_0] :
( class_LOrder_Ojoin__semilorder(VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
cnf(c_11,plain,
( class_LOrder_Ojoin__semilorder(A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_15]) ).
cnf(c_12,plain,
( ~ class_LOrder_Ojoin__semilorder(C)
| c_lessequals(D,B,C)
| ~ c_lessequals(D,A,C)
| ~ c_lessequals(A,B,C) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_14,plain,
( c_lessequals(B,c_minus(D,C,A),A)
| ~ c_lessequals(c_plus(B,C,A),D,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_15,plain,
( c_lessequals(c_plus(B,D,A),C,A)
| ~ c_lessequals(B,c_minus(C,D,A),A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_16,plain,
( c_lessequals(D,C,A)
| ~ c_lessequals(D,B,A)
| ~ c_lessequals(B,C,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_17,plain,
( c_lessequals(C,B,t_b)
| ~ c_lessequals(C,A,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_13,c_16]) ).
cnf(c_18,plain,
( c_lessequals(c_plus(A,C,t_b),B,t_b)
| ~ c_lessequals(A,c_minus(B,C,t_b),t_b) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_19,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_13,c_14]) ).
cnf(c_20,plain,
c_plus(c_0,A,t_b) = A,
inference(resolve,[status(thm)],[c_4,c_5]) ).
fof(cls_conjecture_1,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_21,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_1]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_22,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_23,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_32,plain,
c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b),
inference(resolve,[status(thm)],[c_18,c_21]) ).
cnf(c_25,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_20,c_32]) ).
cnf(c_33,plain,
~ c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_f(v_x),t_b),
inference(resolve,[status(thm)],[c_19,c_23]) ).
cnf(c_26,plain,
~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(paramod,[status(thm)],[c_20,c_33]) ).
cnf(c_34,plain,
( c_lessequals(v_g(v_x),A,t_b)
| ~ c_lessequals(v_k(v_x),A,t_b) ),
inference(resolve,[status(thm)],[c_17,c_22]) ).
cnf(c_30,plain,
~ c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(resolve,[status(thm)],[c_34,c_26]) ).
cnf(c_31,plain,
$false,
inference(resolve,[status(thm)],[c_30,c_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.59 % Computer : n010.cluster.edu
% 0.12/0.59 % Model : x86_64 x86_64
% 0.12/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.59 % Memory : 8046.5625MB
% 0.12/0.59 % OS : Linux 6.8.0-71-generic
% 0.12/0.59 % CPULimit : 300
% 0.12/0.59 % WCLimit : 300
% 0.12/0.59 % DateTime : Sat Sep 26 22:07:32 UTC 2026
% 0.12/0.59 % CPUTime :
% 0.12/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.59 % Process 123381 was started by sandbox2 on n010,
% 0.12/0.59 % Sat Sep 26 22:07:32 2026
% 0.12/0.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.60
% 0.12/0.60 % From the command line: assign(max_seconds, 300).
% 0.12/0.61
% 0.12/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.61
% 0.12/0.61 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.61 % Length of proof is 27.
% 0.12/0.61 % Level of proof is 5.
% 0.12/0.61 % Maximum clause weight is 14.000.
% 0.12/0.61 % Given clauses 9.
% 0.12/0.61
% 0.12/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------