%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA018-2 : 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 : n008.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 06:51:07 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 74 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 37 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_1,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]) ).
fof(cls_conjecture_2,axiom,
c_less(c_0,v_ca,t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_2,plain,
c_less(c_0,v_ca,t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_3,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
! [VAR_0] :
( class_OrderedGroup_Osemigroup__mult(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(c_4,plain,
( class_OrderedGroup_Osemigroup__mult(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_21]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
! [VAR_0] :
( class_LOrder_Ojoin__semilorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
cnf(c_5,plain,
( class_LOrder_Ojoin__semilorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_35]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
! [VAR_0] :
( class_Ring__and__Field_Opordered__semiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(c_6,plain,
( class_Ring__and__Field_Opordered__semiring(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
fof(cls_OrderedGroup_Omult__ac__1_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_times(c_times(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_times(VAR_1,c_times(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_OrderedGroup_Osemigroup__mult(VAR_0) ),
file('theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(c_7,plain,
( c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A)
| ~ class_OrderedGroup_Osemigroup__mult(A) ),
inference(clausify,[status(thm)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(c_8,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_9,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolve,[status(thm)],[c_3,c_6]) ).
fof(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_lessequals(c_times(VAR_3,VAR_1,VAR_0),c_times(VAR_3,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(c_0,VAR_3,VAR_0)
| ~ c_lessequals(VAR_1,VAR_2,VAR_0)
| ~ class_Ring__and__Field_Opordered__semiring(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(c_10,plain,
( c_lessequals(c_times(D,B,A),c_times(D,C,A),A)
| ~ c_lessequals(c_0,D,A)
| ~ c_lessequals(B,C,A)
| ~ class_Ring__and__Field_Opordered__semiring(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_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_11,plain,
( class_Orderings_Oorder(A)
| ~ class_LOrder_Ojoin__semilorder(A) ),
inference(clausify,[status(thm)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c_12,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolve,[status(thm)],[c_3,c_5]) ).
cnf(c_13,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_14,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(B,C,t_b),t_b),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_15,plain,
( c_lessequals(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_16,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(cls_conjecture_4,axiom,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_17,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_18,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_14,c_17]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(v_x(VAR_0),t_b),c_times(v_ca,c_HOL_Oabs(v_f(VAR_0),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_19,plain,
c_lessequals(c_HOL_Oabs(v_x(A),t_b),c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_lessequals(c_HOL_Oabs(v_f(VAR_0),t_b),c_times(v_c,c_HOL_Oabs(v_g(VAR_0),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_20,plain,
c_lessequals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_21,plain,
( c_lessequals(c_times(C,A,t_b),c_times(C,B,t_b),t_b)
| ~ c_lessequals(c_0,C,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
cnf(c_22,plain,
c_lessequals(c_0,v_ca,t_b),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_27,plain,
( c_lessequals(C,B,t_b)
| ~ c_lessequals(C,A,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_28,plain,
( c_lessequals(c_HOL_Oabs(v_x(A),t_b),B,t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),B,t_b) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_23,plain,
~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(v_xa),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_28,c_18]) ).
cnf(c_29,plain,
( c_lessequals(c_times(A,c_HOL_Oabs(v_f(B),t_b),t_b),c_times(A,c_times(v_c,c_HOL_Oabs(v_g(B),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_25,plain,
c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_29,c_22]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.58 % Computer : n008.cluster.edu
% 0.12/5.58 % Model : x86_64 x86_64
% 0.12/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.58 % Memory : 8046.5625MB
% 0.12/5.58 % OS : Linux 6.8.0-71-generic
% 0.12/5.58 % CPULimit : 300
% 0.12/5.58 % WCLimit : 300
% 0.12/5.58 % DateTime : Sat Sep 26 22:06:02 UTC 2026
% 0.12/5.58 % CPUTime :
% 0.12/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.58 % Process 459191 was started by sandbox on n008,
% 0.12/5.58 % Sat Sep 26 22:06:02 2026
% 0.12/5.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.59
% 0.12/5.59 % From the command line: assign(max_seconds, 300).
% 0.15/5.60
% 0.15/5.60 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.60
% 0.15/5.60 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.60 % Length of proof is 25.
% 0.15/5.60 % Level of proof is 5.
% 0.15/5.60 % Maximum clause weight is 19.000.
% 0.15/5.60 % Given clauses 9.
% 0.15/5.60
% 0.15/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------