%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 06:50:15 AM UTC 2026
% Result : Unsatisfiable 4.04s 7.18s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 100 ( 12 ~; 10 |; 0 &; 78 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_lb_decl,type,
v_lb: $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_decl,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(10,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_uminus ) @ ( B @ c_plus ) ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_lb @ c_uminus ) @ ( v_x @ v_f @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_lb @ c_uminus ) @ ( v_x @ v_f @ c_plus ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(17,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( C @ c_plus ) ) @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_lb @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_lb @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(19,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[10,14,9,17,12,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.17/5.42 % Computer : n015.cluster.edu
% 0.17/5.42 % Model : x86_64 x86_64
% 0.17/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.42 % Memory : 8046.5625MB
% 0.17/5.42 % OS : Linux 6.8.0-71-generic
% 0.17/5.42 % CPULimit : 300
% 0.17/5.42 % WCLimit : 300
% 0.17/5.42 % DateTime : Sat Sep 26 22:07:20 UTC 2026
% 0.17/5.42 % CPUTime :
% 0.17/5.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/5.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/6.11 % [INFO] Parsing done (154ms).
% 1.33/6.12 % [INFO] Running in sequential loop mode.
% 2.11/6.46 % [INFO] eprover registered as external prover.
% 2.11/6.47 % [INFO] Scanning for conjecture ...
% 2.21/6.54 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.21/6.58 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.21/6.59 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/6.59 % [INFO] Type checking passed.
% 2.21/6.60 % [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 ...
% 4.04/7.17 % External prover 'e' found a proof!
% 4.04/7.17 % [INFO] Killing All external provers ...
% 4.04/7.17 % Time passed: 1582ms (effective reasoning time: 1044ms)
% 4.04/7.18 % Axioms used in derivation (4): cls_OrderedGroup_Oright__minus_0, clsrel_Ring__and__Field_Oordered__idom_37, cls_OrderedGroup_Oadd__le__cancel__right_1, clsrel_Ring__and__Field_Oordered__idom_4
% 4.04/7.18 % No. of inferences in proof: 15
% 4.04/7.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1582 ms resp. 1044 ms w/o parsing
% 4.14/7.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.14/7.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------