%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 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 06:50:17 AM UTC 2026
% Result : Unsatisfiable 4.14s 2.61s
% Output : Refutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 222 ( 28 ~; 28 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_f_decl,type,
v_f: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(t_a_decl,type,
t_a: $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(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(v_xa_decl,type,
v_xa: $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_1_decl,type,
c_1: $i ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(14,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(42,plain,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(38,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ class_OrderedGroup_Olordered__ab__group__abs )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(44,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)],[15]) ).
thf(2,negated_conjecture,
t_a @ ( v_x @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
t_a @ ( v_x @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,negated_conjecture,
t_a @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(16,plain,
t_a @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( t_a @ ( t_a @ ( t_a @ ( A @ v_xa @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( t_a @ ( A @ v_xa @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(20,plain,
! [A: $i] :
( ~ ( t_a @ ( A @ ( c_0 @ c_less ) ) )
| ~ ( t_a @ ( t_a @ ( t_a @ ( A @ v_xa @ v_h @ c_HOL_Oabs ) @ ( A @ c_times ) ) @ ( t_a @ ( A @ v_xa @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(29,plain,
! [A: $i] :
( ( ( A @ ( c_0 @ c_HOL_Oabs ) )
= c_0 )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( c_0 @ v_f )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
( ( c_0 @ v_f )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(32,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)],[9]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(40,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(26,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ ( c_1 @ ( A @ c_minus ) ) @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
thf(23,plain,
! [A: $i] :
( ( A
= ( tc_nat @ ( c_1 @ ( A @ c_minus ) ) @ c_Suc ) )
| ~ ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_times ) ) @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_x @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(19,plain,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_x @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[42,38,44,18,16,20,29,17,32,34,40,26,23,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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 22:02:55 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 1.28/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.44 % [INFO] Parsing done (189ms).
% 1.61/1.46 % [INFO] Running in sequential loop mode.
% 2.27/1.86 % [INFO] eprover registered as external prover.
% 2.27/1.86 % [INFO] Scanning for conjecture ...
% 2.49/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.49/2.01 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.72/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 2.72/2.04 % [INFO] Type checking passed.
% 2.72/2.05 % [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 ...
% 4.14/2.61 % External prover 'e' found a proof!
% 4.14/2.61 % [INFO] Killing All external provers ...
% 4.14/2.61 % Time passed: 1896ms (effective reasoning time: 1148ms)
% 4.14/2.61 % Axioms used in derivation (10): cls_OrderedGroup_Oabs__ge__zero_0, cls_Orderings_Oorder__less__imp__le_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_OrderedGroup_Oabs__eq__0_1, clsrel_Ring__and__Field_Oordered__idom_40, cls_Ring__and__Field_Omult__nonneg__nonneg_0, cls_Nat_Onot__gr0_0, cls_NatBin_OSuc__pred_H_0, clsrel_LOrder_Ojoin__semilorder_1, clsrel_Ring__and__Field_Oordered__idom_35
% 4.14/2.61 % No. of inferences in proof: 31
% 4.14/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1896 ms resp. 1148 ms w/o parsing
% 4.14/2.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.14/2.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------