%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n001.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 4.62s 2.65s
% Output : Refutation 4.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 254 ( 2 ~; 0 |; 0 &; 252 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(v_k_decl,type,
v_k: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(true_decl,type,
true: $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Ocomm__monoid__add_decl,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $i ).
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 > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $i ).
thf(4,negated_conjecture,
( ( t_b @ class_Ring__and__Field_Oordered__idom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(18,plain,
( ( t_b @ class_Ring__and__Field_Oordered__idom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
( ( t_b @ ( v_x @ v_f @ ( v_x @ v_k @ c_lessequals ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(16,plain,
( ( t_b @ ( v_x @ v_f @ ( v_x @ v_k @ c_lessequals ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
( ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,plain,
( ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(42,plain,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( c_0 @ c_plus ) ) @ ( true @ ( A @ class_OrderedGroup_Ocomm__monoid__add @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( c_0 @ c_plus ) ) @ ( true @ ( A @ class_OrderedGroup_Ocomm__monoid__add @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Ocomm__monoid__add @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(38,plain,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Ocomm__monoid__add @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
( ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(17,plain,
( ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( A @ ( C @ ( D @ c_minus ) ) @ ( B @ c_lessequals ) ) @ ( true @ ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( A @ ( C @ ( D @ c_minus ) ) @ ( B @ c_lessequals ) ) @ ( true @ ( A @ ( D @ ( A @ ( C @ ( B @ c_plus ) ) @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( D @ ( B @ c_lessequals ) ) @ ( true @ ( A @ ( D @ ( C @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_Orderings_Oorder @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( D @ ( B @ c_lessequals ) ) @ ( true @ ( A @ ( D @ ( C @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ ( C @ ( B @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_Orderings_Oorder @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Olinorder @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(40,plain,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Olinorder @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Oorder @ ( true @ ( A @ class_Orderings_Olinorder @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(36,plain,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Oorder @ ( true @ ( A @ class_Orderings_Olinorder @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) @ ( true @ ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( C @ ( A @ ( D @ ( B @ c_plus ) ) @ c_lessequals ) ) @ ( true @ ( A @ ( A @ ( D @ ( C @ c_minus ) ) @ ( B @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_OrderedGroup_Opordered__ab__group__add @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[18,16,15,42,24,28,38,17,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n001.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:11:59 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.25/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.70/1.48 % [INFO] Parsing done (286ms).
% 1.94/1.50 % [INFO] Running in sequential loop mode.
% 2.43/1.89 % [INFO] eprover registered as external prover.
% 2.43/1.90 % [INFO] Scanning for conjecture ...
% 2.66/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.66/2.01 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.66/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 2.66/2.04 % [INFO] Type checking passed.
% 2.66/2.04 % [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 ...
% 4.62/2.65 % External prover 'e' found a proof!
% 4.62/2.65 % [INFO] Killing All external provers ...
% 4.62/2.65 % Time passed: 2039ms (effective reasoning time: 1137ms)
% 4.62/2.65 % Axioms used in derivation (10): ifeq_axiom, cls_OrderedGroup_Ocompare__rls__9_1, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Ocompare__rls__9_0, clsrel_Ring__and__Field_Oordered__idom_23, cls_Orderings_Oorder__class_Oorder__trans_0, ifeq_axiom_001, clsrel_Orderings_Olinorder_4, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_Ring__and__Field_Oordered__idom_33
% 4.62/2.65 % No. of inferences in proof: 29
% 4.62/2.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2039 ms resp. 1137 ms w/o parsing
% 4.86/2.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.86/2.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------