%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA034-2 : 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 : n026.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 3.14s 6.93s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 362 ( 34 ~; 32 |; 0 &; 296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
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(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
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 > $o ).
thf(class_Ring__and__Field_Opordered__semiring_decl,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_Ring__and__Field_Opordered__cancel__semiring_decl,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_decl,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(15,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(41,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(1,negated_conjecture,
t_b @ ( v_c @ ( c_0 @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
t_b @ ( v_c @ ( c_0 @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( E @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ 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_Omult__mono_0) ).
thf(27,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( E @ c_times ) ) @ ( A @ ( B @ ( D @ c_times ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( c_0 @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,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(39,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)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
thf(35,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(18,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(19,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 ) ),
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(24,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(13,axiom,
! [A: $i] :
( ( A @ class_Ring__and__Field_Opordered__cancel__semiring )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
thf(37,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)],[13]) ).
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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(20,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
thf(29,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)],[9]) ).
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/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(21,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(11,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(33,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)],[11]) ).
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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(16,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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
thf(31,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(43,plain,
$false,
inference(e,[status(thm)],[41,17,27,39,35,18,19,24,37,20,29,21,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.13/5.61 % Computer : n026.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Sat Sep 26 22:11:02 UTC 2026
% 0.13/5.62 % CPUTime :
% 0.13/5.62 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
% 0.18/5.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/6.03 % [INFO] Parsing done (104ms).
% 1.02/6.04 % [INFO] Running in sequential loop mode.
% 1.44/6.27 % [INFO] eprover registered as external prover.
% 1.44/6.28 % [INFO] Scanning for conjecture ...
% 1.65/6.39 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.65/6.43 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.88/6.45 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/6.45 % [INFO] Type checking passed.
% 1.88/6.46 % [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 ...
% 3.14/6.93 % External prover 'e' found a proof!
% 3.14/6.93 % [INFO] Killing All external provers ...
% 3.14/6.93 % Time passed: 1219ms (effective reasoning time: 890ms)
% 3.14/6.93 % Axioms used in derivation (9): cls_OrderedGroup_Oabs__ge__zero_0, 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
% 3.14/6.93 % No. of inferences in proof: 31
% 3.14/6.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1219 ms resp. 890 ms w/o parsing
% 3.14/6.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.14/6.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------