%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 06:50:18 AM UTC 2026
% Result : Unsatisfiable 3.06s 2.25s
% Output : Refutation 3.06s
% 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 : 108 ( 12 ~; 10 |; 0 &; 86 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_k_decl,type,
v_k: $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/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(2,negated_conjecture,
~ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,plain,
~ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(17,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__group__add )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ ( C @ ( A @ ( C @ ( B @ c_minus ) ) @ c_plus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
! [A: $i] : ( t_b @ ( A @ v_f @ ( A @ v_k @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(19,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Opordered__ab__group__add )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_minus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_minus ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[10,9,17,12,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 22:06:44 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.16 % [INFO] Parsing done (181ms).
% 1.21/1.18 % [INFO] Running in sequential loop mode.
% 1.78/1.57 % [INFO] eprover registered as external prover.
% 1.78/1.57 % [INFO] Scanning for conjecture ...
% 1.96/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.11/1.71 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.11/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.11/1.73 % [INFO] Type checking passed.
% 2.11/1.73 % [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 ...
% 3.06/2.24 % External prover 'e' found a proof!
% 3.06/2.24 % [INFO] Killing All external provers ...
% 3.06/2.24 % Time passed: 1712ms (effective reasoning time: 1059ms)
% 3.06/2.25 % Axioms used in derivation (4): clsrel_OrderedGroup_Opordered__ab__group__add_0, cls_OrderedGroup_Ocompare__rls__10_0, clsrel_Ring__and__Field_Oordered__idom_54, cls_OrderedGroup_Ocompare__rls__9_1
% 3.06/2.25 % No. of inferences in proof: 15
% 3.06/2.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1712 ms resp. 1059 ms w/o parsing
% 3.06/2.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/2.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------