%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA030-2 : 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 : n011.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 29 unt; 0 def)
% Number of atoms : 91 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 42 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 5 sgn 30 !; 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_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_3,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_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_4,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_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_5,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]) ).
cnf(c_6,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oabs(VAR_1,VAR_0) = VAR_1
| ~ c_lessequals(c_0,VAR_1,VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
cnf(c_7,plain,
( c_HOL_Oabs(B,A) = B
| ~ c_lessequals(c_0,B,A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c_8,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(cls_OrderedGroup_Ominus__minus_0,axiom,
! [VAR_0,VAR_1] :
( c_uminus(c_uminus(VAR_1,VAR_0),VAR_0) = VAR_1
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
cnf(c_9,plain,
( c_uminus(c_uminus(B,A),A) = B
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ominus__minus_0]) ).
fof(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_uminus(c_minus(VAR_1,VAR_2,VAR_0),VAR_0) = c_minus(VAR_2,VAR_1,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
cnf(c_10,plain,
( c_uminus(c_minus(B,C,A),A) = c_minus(C,B,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ominus__diff__eq_0]) ).
fof(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_uminus(c_plus(VAR_1,VAR_2,VAR_0),VAR_0) = c_plus(c_uminus(VAR_1,VAR_0),c_uminus(VAR_2,VAR_0),VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
cnf(c_11,plain,
( c_uminus(c_plus(B,C,A),A) = c_plus(c_uminus(B,A),c_uminus(C,A),A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ominus__add__distrib_0]) ).
fof(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_minus(VAR_1,c_uminus(VAR_2,VAR_0),VAR_0) = c_plus(VAR_1,VAR_2,VAR_0)
| ~ class_OrderedGroup_Oab__group__add(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
cnf(c_12,plain,
( c_minus(B,c_uminus(C,A),A) = c_plus(B,C,A)
| ~ class_OrderedGroup_Oab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Odiff__minus__eq__add_0]) ).
cnf(c_14,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolve,[status(thm)],[c_5,c_6]) ).
fof(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,c_plus(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(c_minus(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__8_0) ).
cnf(c_15,plain,
( c_lessequals(B,c_plus(D,C,A),A)
| ~ c_lessequals(c_minus(B,C,A),D,A)
| ~ class_OrderedGroup_Opordered__ab__group__add(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Ocompare__rls__8_0]) ).
cnf(c_16,plain,
class_Orderings_Olinorder(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(VAR_1,VAR_3,VAR_0)
| ~ c_lessequals(c_Orderings_Omax(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
cnf(c_17,plain,
( c_lessequals(B,D,A)
| ~ c_lessequals(c_Orderings_Omax(B,C,A),D,A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0]) ).
fof(cls_Orderings_Ole__maxI2_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_1,c_Orderings_Omax(VAR_2,VAR_1,VAR_0),VAR_0)
| ~ class_Orderings_Olinorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).
cnf(c_18,plain,
( c_lessequals(B,c_Orderings_Omax(C,B,A),A)
| ~ class_Orderings_Olinorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Ole__maxI2_0]) ).
cnf(c_19,plain,
c_lessequals(A,c_Orderings_Omax(B,A,t_b),t_b),
inference(resolve,[status(thm)],[c_16,c_18]) ).
cnf(c_20,plain,
( c_lessequals(A,C,t_b)
| ~ c_lessequals(c_Orderings_Omax(A,B,t_b),C,t_b) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_22,plain,
c_minus(A,c_uminus(B,t_b),t_b) = c_plus(A,B,t_b),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_23,plain,
c_plus(A,B,t_b) = c_minus(A,c_uminus(B,t_b),t_b),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_24,plain,
c_uminus(c_plus(A,B,t_b),t_b) = c_plus(c_uminus(A,t_b),c_uminus(B,t_b),t_b),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_60,plain,
c_uminus(c_minus(A,c_uminus(B,t_b),t_b),t_b) = c_plus(c_uminus(A,t_b),c_uminus(B,t_b),t_b),
inference(paramod,[status(thm)],[c_23,c_24]) ).
cnf(c_61,plain,
c_uminus(c_minus(A,c_uminus(B,t_b),t_b),t_b) = c_minus(c_uminus(A,t_b),c_uminus(c_uminus(B,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_23,c_60]) ).
cnf(c_25,plain,
c_minus(c_uminus(A,t_b),c_uminus(c_uminus(B,t_b),t_b),t_b) = c_uminus(c_minus(A,c_uminus(B,t_b),t_b),t_b),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_26,plain,
c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_27,plain,
c_uminus(c_uminus(A,t_b),t_b) = A,
inference(resolve,[status(thm)],[c_8,c_9]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] : ~ c_lessequals(v_f(v_x(VAR_0)),c_plus(v_g(v_x(VAR_0)),c_times(VAR_0,c_HOL_Oabs(v_h(v_x(VAR_0)),t_b),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_28,plain,
~ c_lessequals(v_f(v_x(A)),c_plus(v_g(v_x(A)),c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_29,plain,
~ c_lessequals(v_f(v_x(A)),c_minus(v_g(v_x(A)),c_uminus(c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_23,c_28]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(VAR_0),v_g(VAR_0),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(VAR_0),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_30,plain,
c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(A),v_g(A),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_31,plain,
( c_HOL_Oabs(A,t_b) = A
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_7,c_6]) ).
cnf(c_32,plain,
( c_lessequals(A,c_plus(C,B,t_b),t_b)
| ~ c_lessequals(c_minus(A,B,t_b),C,t_b) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_33,plain,
( c_lessequals(A,c_minus(C,c_uminus(B,t_b),t_b),t_b)
| ~ c_lessequals(c_minus(A,B,t_b),C,t_b) ),
inference(paramod,[status(thm)],[c_23,c_32]) ).
cnf(c_34,plain,
c_minus(c_uminus(A,t_b),B,t_b) = c_uminus(c_minus(A,c_uminus(B,t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_27,c_25]) ).
cnf(c_62,plain,
~ c_lessequals(v_f(v_x(A)),c_uminus(c_minus(c_uminus(c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),v_g(v_x(A)),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_26,c_29]) ).
cnf(c_63,plain,
~ c_lessequals(v_f(v_x(A)),c_uminus(c_uminus(c_minus(c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),c_uminus(v_g(v_x(A)),t_b),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_34,c_62]) ).
cnf(c_39,plain,
~ c_lessequals(v_f(v_x(A)),c_minus(c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),c_uminus(v_g(v_x(A)),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_27,c_63]) ).
cnf(c_41,plain,
c_HOL_Oabs(c_Orderings_Omax(A,c_0,t_b),t_b) = c_Orderings_Omax(A,c_0,t_b),
inference(resolve,[status(thm)],[c_31,c_19]) ).
cnf(c_43,plain,
c_lessequals(c_Orderings_Omax(c_minus(v_f(A),v_g(A),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_41,c_30]) ).
cnf(c_56,plain,
~ c_lessequals(c_minus(v_f(v_x(A)),v_g(v_x(A)),t_b),c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_33,c_39]) ).
cnf(c_58,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x(A)),v_g(v_x(A)),t_b),B,t_b),c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_20,c_56]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 22:07:44 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1654110 was started by sandbox on n011,
% 0.09/0.36 % Sat Sep 26 22:07:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 38.
% 0.12/0.37 % Level of proof is 9.
% 0.12/0.37 % Maximum clause weight is 21.000.
% 0.12/0.37 % Given clauses 14.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------