TSTP Solution File: ANA034-10 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:08:54 EDT 2023
% Result : Unsatisfiable 3.56s 1.88s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 38
% Syntax : Number of formulae : 56 ( 35 unt; 21 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 452 ( 2 ~; 0 |; 0 &; 450 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-4 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_less_type,type,
c_less: $i > $i > $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(v_c_type,type,
v_c: $i ).
thf(t_b_type,type,
t_b: $i ).
thf(true_type,type,
true: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $i ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_a_type,type,
v_a: $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(v_b_type,type,
v_b: $i > $i ).
thf(v_ca_type,type,
v_ca: $i ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $i ).
thf(ifeq2_type,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $i ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_type,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $i ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( c_lessequals @ c_0 @ A @ B ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ C @ B ) @ true @ ( ifeq @ ( c_lessequals @ D @ A @ B ) @ true @ ( ifeq @ ( c_lessequals @ C @ E @ B ) @ true @ ( ifeq @ ( class_Ring__and__Field_Opordered__semiring @ B ) @ true @ ( c_lessequals @ ( c_times @ D @ C @ B ) @ ( c_times @ A @ E @ B ) @ B ) @ true ) @ true ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
thf(37,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ifeq @ ( c_lessequals @ c_0 @ A @ B ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ C @ B ) @ true @ ( ifeq @ ( c_lessequals @ D @ A @ B ) @ true @ ( ifeq @ ( c_lessequals @ C @ E @ B ) @ true @ ( ifeq @ ( class_Ring__and__Field_Opordered__semiring @ B ) @ true @ ( c_lessequals @ ( c_times @ D @ C @ B ) @ ( c_times @ A @ E @ B ) @ B ) @ true ) @ true ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(20,plain,
( ( class_Ring__and__Field_Oordered__idom @ t_b )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( c_less @ A @ B @ C ) @ true @ ( ifeq @ ( class_Orderings_Oorder @ C ) @ true @ ( c_lessequals @ A @ B @ C ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( c_less @ A @ B @ C ) @ true @ ( ifeq @ ( class_Orderings_Oorder @ C ) @ true @ ( c_lessequals @ A @ B @ C ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( ifeq @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true @ ( class_Orderings_Oorder @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(45,plain,
! [A: $i] :
( ( ifeq @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true @ ( class_Orderings_Oorder @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
( ( 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 )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(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 )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Ring__and__Field_Opordered__semiring @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(49,plain,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Ring__and__Field_Opordered__semiring @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ B @ A ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ C @ A ) @ true @ ( c_lessequals @ c_0 @ ( c_times @ B @ C @ A ) @ A ) @ true ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ B @ A ) @ true @ ( ifeq @ ( c_lessequals @ c_0 @ C @ A ) @ true @ ( c_lessequals @ c_0 @ ( c_times @ B @ C @ A ) @ A ) @ true ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A ) )
= ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( c_times @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A ) )
= ( c_HOL_Oabs @ ( c_times @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ( 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 )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(18,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 )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq2 @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true @ ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true @ ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,negated_conjecture,
( ( 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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(23,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(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(47,plain,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_Ring__and__Field_Opordered__cancel__semiring @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2,negated_conjecture,
( ( 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 )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(21,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 )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(51,plain,
! [A: $i] :
( ( ifeq @ ( class_Ring__and__Field_Oordered__idom @ A ) @ true @ ( class_OrderedGroup_Olordered__ab__group__abs @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
( ( c_less @ c_0 @ v_c @ t_b )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(19,plain,
( ( c_less @ c_0 @ v_c @ t_b )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(57,plain,
$false,
inference(e,[status(thm)],[37,20,41,45,22,49,39,35,18,31,43,23,47,21,33,51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 18:22:27 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.00/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.00 % [INFO] Parsing done (128ms).
% 1.27/1.00 % [INFO] Running in sequential loop mode.
% 1.72/1.22 % [INFO] eprover registered as external prover.
% 1.72/1.22 % [INFO] cvc4 registered as external prover.
% 1.72/1.22 % [INFO] Scanning for conjecture ...
% 1.89/1.29 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 2.05/1.32 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.05/1.34 % [INFO] Problem is propositional (TPTP CNF).
% 2.05/1.34 % [INFO] Type checking passed.
% 2.05/1.35 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.56/1.88 % External prover 'e' found a proof!
% 3.56/1.88 % [INFO] Killing All external provers ...
% 3.56/1.88 % Time passed: 1342ms (effective reasoning time: 873ms)
% 3.56/1.88 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.56/1.88 % Axioms used in derivation (11): ifeq_axiom, cls_Ring__and__Field_Omult__mono_0, clsrel_Ring__and__Field_Oordered__idom_42, cls_Orderings_Oorder__less__imp__le_0, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_Ring__and__Field_Oordered__idom_40, cls_Ring__and__Field_Omult__nonneg__nonneg_0, clsrel_OrderedGroup_Olordered__ab__group__abs_17, cls_Ring__and__Field_Oabs__mult_0, ifeq_axiom_001, cls_OrderedGroup_Oabs__ge__zero_0
% 3.56/1.88 % No. of inferences in proof: 35
% 3.56/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1342 ms resp. 873 ms w/o parsing
% 3.84/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.84/1.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------