%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA032-2 : 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 : n017.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 5.20s 7.72s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 216 ( 22 ~; 20 |; 0 &; 174 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $i > $i ).
thf(v_b_decl,type,
v_b: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_g_decl,type,
v_g: $i > $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 > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_decl,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(14,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 @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( v_c @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_times ) ) @ ( v_c @ c_times ) ) @ ( t_b @ ( t_b @ ( v_x @ v_f @ c_HOL_Oabs ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_times ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(32,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,negated_conjecture,
t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_b @ ( v_x @ v_b @ c_HOL_Oabs ) @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_times ) ) @ c_times ) ) )
= ( A @ ( A @ ( D @ ( C @ c_times ) ) @ ( B @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Osemigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_HOL_Oabs ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(26,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Oab__semigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(30,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
thf(28,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_times ) ) )
= ( A @ ( B @ ( C @ c_times ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[24,14,13,32,12,18,16,26,30,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.16/5.44 % Computer : n017.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 22:03:54 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 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
% 0.19/6.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/6.19 % [INFO] Parsing done (182ms).
% 1.38/6.21 % [INFO] Running in sequential loop mode.
% 2.02/6.60 % [INFO] eprover registered as external prover.
% 2.02/6.61 % [INFO] Scanning for conjecture ...
% 2.20/6.71 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.20/6.74 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.20/6.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.20/6.76 % [INFO] Type checking passed.
% 2.20/6.77 % [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 ...
% 5.20/7.72 % External prover 'e' found a proof!
% 5.20/7.72 % [INFO] Killing All external provers ...
% 5.20/7.72 % Time passed: 2143ms (effective reasoning time: 1508ms)
% 5.20/7.72 % Axioms used in derivation (8): cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_17, cls_OrderedGroup_Omult__ac__2_0, clsrel_Ring__and__Field_Oordered__idom_21, clsrel_Ring__and__Field_Oordered__idom_42, cls_OrderedGroup_Omult__ac__1_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0
% 5.20/7.72 % No. of inferences in proof: 23
% 5.20/7.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2143 ms resp. 1508 ms w/o parsing
% 5.20/7.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/7.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------