TSTP Solution File: ANA039-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA039-2 : TPTP v8.1.2. Released v3.2.0.
% 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 10:08:57 EDT 2023
% Result : Unsatisfiable 2.61s 1.53s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 34 ( 7 unt; 13 typ; 0 def)
% Number of atoms : 43 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 188 ( 24 ~; 22 |; 0 &; 142 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_h_type,type,
v_h: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(v_c_type,type,
v_c: $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_0_type,type,
c_0: $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(9,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oorder @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
thf(25,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Orderings_Oorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ c_0 @ D @ A )
| ( c_lessequals @ ( c_times @ B @ D @ A ) @ ( c_times @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ c_0 @ D @ A )
| ( c_lessequals @ ( c_times @ B @ D @ A ) @ ( c_times @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(13,plain,
class_Ring__and__Field_Oordered__idom @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(27,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,plain,
~ ( c_lessequals @ ( c_HOL_Oabs @ ( v_h @ v_x ) @ t_a ) @ ( c_times @ ( c_HOL_Oabs @ v_c @ t_a ) @ ( c_HOL_Oabs @ ( v_f @ v_x ) @ t_a ) @ t_a ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_h @ A ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs @ ( v_h @ A ) @ t_a ) @ ( c_times @ v_c @ ( c_HOL_Oabs @ ( v_f @ A ) @ t_a ) @ t_a ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(23,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(19,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ B @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
$false,
inference(e,[status(thm)],[25,21,13,17,27,12,11,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA039-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 18:24:58 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.96 % [INFO] Parsing done (111ms).
% 1.16/0.97 % [INFO] Running in sequential loop mode.
% 1.54/1.16 % [INFO] eprover registered as external prover.
% 1.54/1.16 % [INFO] cvc4 registered as external prover.
% 1.54/1.16 % [INFO] Scanning for conjecture ...
% 1.83/1.22 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.86/1.24 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.86/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.86/1.25 % [INFO] Type checking passed.
% 1.86/1.25 % [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 ...
% 2.61/1.52 % External prover 'e' found a proof!
% 2.61/1.52 % [INFO] Killing All external provers ...
% 2.61/1.52 % Time passed: 998ms (effective reasoning time: 550ms)
% 2.61/1.52 % 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)>
% 2.61/1.53 % Axioms used in derivation (7): cls_Orderings_Oorder__class_Oorder__trans_0, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0, clsrel_Ring__and__Field_Oordered__idom_44, cls_OrderedGroup_Oabs__ge__self_0, clsrel_Ring__and__Field_Oordered__idom_42
% 2.61/1.53 % No. of inferences in proof: 21
% 2.61/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 998 ms resp. 550 ms w/o parsing
% 2.76/1.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.76/1.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------