%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA025-2 : 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 : n012.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 06:50:18 AM UTC 2026
% Result : Unsatisfiable 1.97s 1.31s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 218 ( 32 ~; 30 |; 0 &; 156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(v_k_decl,type,
v_k: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_g_decl,type,
v_g: $i > $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(c_Orderings_Omax_decl,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_HOL_Oabs_decl,type,
c_HOL_Oabs: $i > $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(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_decl,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(14,plain,
~ ( t_b @ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_f @ c_minus ) ) @ c_HOL_Oabs ) @ ( t_b @ ( c_0 @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ c_Orderings_Omax ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
thf(28,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_LOrder_Ojoin__semilorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
~ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,plain,
~ ( t_b @ ( t_b @ ( v_x @ v_g @ ( v_x @ v_k @ c_minus ) ) @ ( c_0 @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(18,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,
! [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(26,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)],[8]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(30,plain,
! [A: $i] :
( ( A @ class_LOrder_Ojoin__semilorder )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__abs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,negated_conjecture,
t_b @ class_Ring__and__Field_Oordered__idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(15,plain,
t_b @ class_Ring__and__Field_Oordered__idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
thf(32,plain,
! [A: $i] :
( ( A @ class_Orderings_Olinorder )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,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(34,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)],[12]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,13,22,18,26,30,15,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA025-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % 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
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Sat Sep 26 22:06:19 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 0.52/0.64 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.65/0.74 % [INFO] Parsing done (93ms).
% 0.65/0.75 % [INFO] Running in sequential loop mode.
% 1.01/0.94 % [INFO] eprover registered as external prover.
% 1.01/0.95 % [INFO] Scanning for conjecture ...
% 1.01/1.00 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.01/1.01 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.01/1.02 % [INFO] Problem is propositional (TPTP CNF).
% 1.01/1.02 % [INFO] Type checking passed.
% 1.27/1.03 % [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 ...
% 1.97/1.31 % External prover 'e' found a proof!
% 1.97/1.31 % [INFO] Killing All external provers ...
% 1.97/1.31 % Time passed: 910ms (effective reasoning time: 563ms)
% 1.97/1.31 % Axioms used in derivation (9): cls_OrderedGroup_Oabs__ge__zero_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_Orderings_Oorder__less__imp__le_0, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_LOrder_Ojoin__semilorder_1, clsrel_Ring__and__Field_Oordered__idom_50, clsrel_Ring__and__Field_Oordered__idom_33, cls_Orderings_Olinorder__not__le_0, cls_Orderings_Oorder__class_Oorder__trans_0
% 1.97/1.31 % No. of inferences in proof: 25
% 1.97/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 910 ms resp. 563 ms w/o parsing
% 1.97/1.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.97/1.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------