%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA034-2 : 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 : n018.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 06:51:11 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 25 unt; 0 def)
% Number of atoms : 99 ( 7 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 98 ( 50 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_1,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(cls_Ring__and__Field_Oabs__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_HOL_Oabs(c_times(VAR_1,VAR_2,VAR_0),VAR_0) = c_times(c_HOL_Oabs(VAR_1,VAR_0),c_HOL_Oabs(VAR_2,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(c_2,plain,
( c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Oabs__mult_0]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
! [VAR_0] :
( class_Ring__and__Field_Opordered__cancel__semiring(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(c_3,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
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_4,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(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_5,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_Ring__and__Field_Omult__mono_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_lessequals(c_times(VAR_3,VAR_1,VAR_0),c_times(VAR_4,VAR_2,VAR_0),VAR_0)
| ~ c_lessequals(c_0,VAR_4,VAR_0)
| ~ c_lessequals(c_0,VAR_1,VAR_0)
| ~ c_lessequals(VAR_3,VAR_4,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_Omult__mono_0) ).
cnf(c_6,plain,
( c_lessequals(c_times(D,B,A),c_times(E,C,A),A)
| ~ c_lessequals(c_0,E,A)
| ~ c_lessequals(c_0,B,A)
| ~ c_lessequals(D,E,A)
| ~ c_lessequals(B,C,A)
| ~ class_Ring__and__Field_Opordered__semiring(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__mono_0]) ).
cnf(c_7,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_8,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolve,[status(thm)],[c_3,c_1]) ).
fof(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(c_0,c_times(VAR_2,VAR_1,VAR_0),VAR_0)
| ~ c_lessequals(c_0,VAR_2,VAR_0)
| ~ c_lessequals(c_0,VAR_1,VAR_0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(VAR_0) ),
file('theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(c_9,plain,
( c_lessequals(c_0,c_times(C,B,A),A)
| ~ c_lessequals(c_0,C,A)
| ~ c_lessequals(c_0,B,A)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(A) ),
inference(clausify,[status(thm)],[cls_Ring__and__Field_Omult__nonneg__nonneg_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_10,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(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(VAR_0) ),
file('theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(c_11,plain,
( class_Orderings_Oorder(A)
| ~ class_OrderedGroup_Olordered__ab__group__abs(A) ),
inference(clausify,[status(thm)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]) ).
fof(cls_conjecture_0,axiom,
c_less(c_0,v_c,t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_12,plain,
c_less(c_0,v_c,t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_13,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(C)
| c_lessequals(A,B,C)
| ~ c_less(A,B,C) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_14,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_lessequals(c_0,v_c,t_b) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_15,plain,
( c_lessequals(c_0,c_times(B,A,t_b),t_b)
| ~ c_lessequals(c_0,B,t_b)
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_16,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_17,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_18,plain,
c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b) = c_HOL_Oabs(c_times(A,B,t_b),t_b),
inference(copy,[status(thm)],[c_17]) ).
fof(cls_conjecture_5,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_19,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_4,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_20,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_21,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(copy,[status(thm)],[c_20]) ).
fof(cls_conjecture_3,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_22,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_2,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_23,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
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_24,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_25,plain,
( c_lessequals(c_times(C,A,t_b),c_times(D,B,t_b),t_b)
| ~ c_lessequals(c_0,D,t_b)
| ~ c_lessequals(c_0,A,t_b)
| ~ c_lessequals(C,D,t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_26,plain,
c_lessequals(c_0,v_c,t_b),
inference(resolve,[status(thm)],[c_14,c_16]) ).
cnf(c_27,plain,
c_lessequals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_56,plain,
( c_lessequals(c_0,c_times(A,c_HOL_Oabs(B,t_b),t_b),t_b)
| ~ c_lessequals(c_0,A,t_b) ),
inference(resolve,[status(thm)],[c_15,c_27]) ).
cnf(c_34,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(A,t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_56,c_26]) ).
cnf(c_57,plain,
( c_lessequals(c_times(A,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(B,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,B,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(A,B,t_b) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_58,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(resolve,[status(thm)],[c_57,c_23]) ).
cnf(c_59,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
inference(resolve,[status(thm)],[c_58,c_27]) ).
cnf(c_60,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(resolve,[status(thm)],[c_59,c_34]) ).
cnf(c_61,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_18,c_60]) ).
cnf(c_54,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(paramod,[status(thm)],[c_21,c_61]) ).
cnf(c_55,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n018.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 22:10:28 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 1517767 was started by sandbox2 on n018,
% 0.11/5.38 % Sat Sep 26 22:10:28 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 30.
% 0.14/5.40 % Level of proof is 6.
% 0.14/5.40 % Maximum clause weight is 31.000.
% 0.14/5.40 % Given clauses 15.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------