%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 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 : n007.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 06:50:20 AM UTC 2026
% Result : Unsatisfiable 6.25s 3.55s
% Output : Refutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 17
% Syntax : Number of formulae : 35 ( 35 unt; 0 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 : 0 ( 0 >; 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_decl,type,
c_less: $i > $i > $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(true_decl,type,
true: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $i ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_f_decl,type,
v_f: $i > $i ).
thf(v_b_decl,type,
v_b: $i > $i ).
thf(v_ca_decl,type,
v_ca: $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 > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $i ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $i ).
thf(10,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( true @ ( B @ ( B @ ( E @ ( A @ c_times ) ) @ ( B @ ( C @ ( D @ c_times ) ) @ c_lessequals ) ) @ ( true @ ( B @ class_Ring__and__Field_Opordered__semiring @ ifeq ) ) ) @ ( true @ ( B @ ( E @ ( C @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( A @ ( D @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( A @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
thf(37,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( true @ ( true @ ( B @ ( B @ ( E @ ( A @ c_times ) ) @ ( B @ ( C @ ( D @ c_times ) ) @ c_lessequals ) ) @ ( true @ ( B @ class_Ring__and__Field_Opordered__semiring @ ifeq ) ) ) @ ( true @ ( B @ ( E @ ( C @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( A @ ( D @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( C @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( B @ ( A @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( t_b @ class_Ring__and__Field_Oordered__idom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(20,plain,
( ( t_b @ class_Ring__and__Field_Oordered__idom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ ( A @ c_lessequals ) ) @ ( true @ ( C @ class_Orderings_Oorder @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ c_less ) ) @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( B @ ( A @ c_lessequals ) ) @ ( true @ ( C @ class_Orderings_Oorder @ ifeq ) ) ) @ ( true @ ( C @ ( B @ ( A @ c_less ) ) @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Oorder @ ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(45,plain,
! [A: $i] :
( ( true @ ( A @ class_Orderings_Oorder @ ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_ca @ c_times ) ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(22,plain,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_ca @ c_times ) ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( true @ ( A @ class_Ring__and__Field_Opordered__semiring @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(49,plain,
! [A: $i] :
( ( true @ ( A @ class_Ring__and__Field_Opordered__semiring @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( C @ ( B @ c_times ) ) @ ( c_0 @ c_lessequals ) ) @ ( true @ ( A @ ( C @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_Ring__and__Field_Opordered__cancel__semiring @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( C @ ( B @ c_times ) ) @ ( c_0 @ c_lessequals ) ) @ ( true @ ( A @ ( C @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( c_0 @ c_lessequals ) ) @ ifeq ) ) ) @ ( true @ ( A @ class_Ring__and__Field_Opordered__cancel__semiring @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_times ) ) @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq2 ) ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oabs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oabs ) @ ( A @ ( A @ ( C @ c_HOL_Oabs ) @ ( A @ ( B @ c_HOL_Oabs ) @ c_times ) ) @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq2 ) ) ) )
= ( A @ ( A @ ( C @ ( B @ c_times ) ) @ c_HOL_Oabs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_times ) ) @ c_HOL_Oabs ) @ ( t_b @ ( v_ca @ ( v_c @ c_times ) ) @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_b @ ( v_x @ v_a @ c_times ) ) @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(18,plain,
( ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_times ) ) @ c_HOL_Oabs ) @ ( t_b @ ( v_ca @ ( v_c @ c_times ) ) @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_b @ ( v_x @ v_a @ c_times ) ) @ c_HOL_Oabs ) @ c_lessequals ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) @ ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) @ ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,negated_conjecture,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_times ) ) @ c_HOL_Oabs ) @ ( t_b @ ( v_ca @ ( v_c @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_ca @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(23,plain,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_times ) ) @ c_HOL_Oabs ) @ ( t_b @ ( v_ca @ ( v_c @ c_times ) ) @ c_times ) ) )
= ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_ca @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ c_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i] :
( ( true @ ( A @ class_Ring__and__Field_Opordered__cancel__semiring @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(47,plain,
! [A: $i] :
( ( true @ ( A @ class_Ring__and__Field_Opordered__cancel__semiring @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(2,negated_conjecture,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( v_x @ v_a @ c_HOL_Oabs ) @ c_lessequals ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(21,plain,
( ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( v_x @ v_a @ c_HOL_Oabs ) @ c_lessequals ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(51,plain,
! [A: $i] :
( ( true @ ( A @ class_OrderedGroup_Olordered__ab__group__abs @ ( true @ ( A @ class_Ring__and__Field_Oordered__idom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
( ( t_b @ ( v_c @ ( c_0 @ c_less ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(19,plain,
( ( t_b @ ( v_c @ ( c_0 @ c_less ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(53,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
% 0.00/0.04 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.12 % 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
% 0.25/0.50 % Computer : n007.cluster.edu
% 0.25/0.50 % Model : x86_64 x86_64
% 0.25/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.50 % Memory : 8046.5625MB
% 0.25/0.50 % OS : Linux 6.8.0-71-generic
% 0.25/0.50 % CPULimit : 300
% 0.25/0.50 % WCLimit : 300
% 0.25/0.50 % DateTime : Sat Sep 26 22:06:09 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.11/0.51 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
% 1.37/1.24 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.50 % [INFO] Parsing done (258ms).
% 1.96/1.53 % [INFO] Running in sequential loop mode.
% 3.16/2.18 % [INFO] eprover registered as external prover.
% 3.16/2.19 % [INFO] Scanning for conjecture ...
% 3.42/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.66/2.44 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.66/2.48 % [INFO] Problem is propositional (TPTP CNF).
% 3.66/2.49 % [INFO] Type checking passed.
% 3.66/2.50 % [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 ...
% 6.25/3.54 % External prover 'e' found a proof!
% 6.25/3.54 % [INFO] Killing All external provers ...
% 6.25/3.54 % Time passed: 2886ms (effective reasoning time: 2004ms)
% 6.25/3.55 % 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
% 6.25/3.55 % No. of inferences in proof: 35
% 6.25/3.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2886 ms resp. 2004 ms w/o parsing
% 6.49/3.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.49/3.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------