%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA014-2 : 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 : n013.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 06:50:16 AM UTC 2026
% Result : Unsatisfiable 5.02s 2.96s
% Output : Refutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 186 ( 24 ~; 22 |; 0 &; 140 @)
% ( 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 : 18 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_c_decl,type,
v_c: $i ).
thf(c_0_decl,type,
c_0: $i ).
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_f_decl,type,
v_f: $i > $i ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__field_decl,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(class_OrderedGroup_Omonoid__mult_decl,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(c_1_decl,type,
c_1: $i ).
thf(class_OrderedGroup_Osemigroup__mult_decl,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Ring__and__Field_Ofield_decl,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(c_HOL_Oinverse_decl,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(13,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(42,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
v_c != c_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( c_1 @ c_times ) ) )
= B )
| ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
thf(34,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Omonoid__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
thf(36,plain,
! [A: $i] :
( ( A @ class_OrderedGroup_Osemigroup__mult )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( A @ c_times ) ) @ ( t_a @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,plain,
! [A: $i] :
~ ( t_a @ ( t_a @ ( t_a @ ( t_a @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ ( t_a @ ( v_c @ c_HOL_Oabs ) @ c_times ) ) @ ( A @ c_times ) ) @ ( t_a @ ( A @ v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,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 ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
thf(28,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 ) ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
thf(38,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Ofield )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
t_a @ class_Ring__and__Field_Oordered__field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(16,plain,
t_a @ class_Ring__and__Field_Oordered__field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse ) @ c_times ) ) )
= c_1 )
| ( B = c_0 )
| ~ ( A @ class_Ring__and__Field_Ofield ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
thf(40,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Oordered__idom )
| ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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_Osemigroup__mult__class_Omult__assoc_0) ).
thf(23,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(44,plain,
$false,
inference(e,[status(thm)],[42,14,20,34,36,15,28,38,16,31,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.24/0.48 % Computer : n013.cluster.edu
% 0.24/0.48 % Model : x86_64 x86_64
% 0.24/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.48 % Memory : 8046.5625MB
% 0.24/0.48 % OS : Linux 6.8.0-71-generic
% 0.24/0.48 % CPULimit : 300
% 0.24/0.48 % WCLimit : 300
% 0.24/0.48 % DateTime : Sat Sep 26 22:04:06 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 0.98/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.21 % [INFO] Parsing done (184ms).
% 1.59/1.23 % [INFO] Running in sequential loop mode.
% 2.60/1.85 % [INFO] eprover registered as external prover.
% 2.60/1.86 % [INFO] Scanning for conjecture ...
% 2.80/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.80/2.05 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.10/2.08 % [INFO] Problem is propositional (TPTP CNF).
% 3.10/2.09 % [INFO] Type checking passed.
% 3.10/2.10 % [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 ...
% 5.02/2.95 % External prover 'e' found a proof!
% 5.02/2.95 % [INFO] Killing All external provers ...
% 5.02/2.96 % Time passed: 2320ms (effective reasoning time: 1712ms)
% 5.02/2.96 % Axioms used in derivation (10): cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0, clsrel_Ring__and__Field_Oordered__field_58, clsrel_Ring__and__Field_Oordered__field_34, cls_Ring__and__Field_Ofield__class_Oaxioms__1_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Ring__and__Field_Oabs__mult_0, cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0, clsrel_Ring__and__Field_Ofield_12, clsrel_Ring__and__Field_Ofield_21, clsrel_Ring__and__Field_Oordered__field_0
% 5.02/2.96 % No. of inferences in proof: 27
% 5.02/2.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2320 ms resp. 1712 ms w/o parsing
% 5.02/3.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.02/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------