%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ANA021-2 : 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 : n020.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 3.12s 2.21s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 82 ( 6 ~; 4 |; 0 &; 72 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% 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_f_decl,type,
v_f: $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_times_decl,type,
c_times: $i > $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_h_decl,type,
v_h: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_less_decl,type,
c_less: $i > $i > $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(1,negated_conjecture,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ 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(6,plain,
! [A: $i] : ( t_a @ ( t_a @ ( t_a @ ( A @ c_Suc @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( A @ c_Suc @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,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(12,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)],[4]) ).
thf(2,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(7,plain,
v_x != c_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,negated_conjecture,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(8,plain,
~ ( t_a @ ( t_a @ ( t_a @ ( v_x @ v_h @ c_HOL_Oabs ) @ ( v_c @ c_times ) ) @ ( t_a @ ( v_x @ v_f @ c_HOL_Oabs ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,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(15,plain,
! [A: $i] :
( ( A = c_0 )
| ( tc_nat @ ( A @ ( c_0 @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[6,12,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.11/0.40 % Computer : n020.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 22:06:50 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.16 % [INFO] Parsing done (170ms).
% 1.24/1.17 % [INFO] Running in sequential loop mode.
% 1.75/1.57 % [INFO] eprover registered as external prover.
% 1.75/1.58 % [INFO] Scanning for conjecture ...
% 1.94/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.08/1.71 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.08/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.73 % [INFO] Type checking passed.
% 2.08/1.73 % [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 ...
% 3.12/2.20 % External prover 'e' found a proof!
% 3.12/2.20 % [INFO] Killing All external provers ...
% 3.12/2.21 % Time passed: 1664ms (effective reasoning time: 1030ms)
% 3.12/2.21 % Axioms used in derivation (2): cls_NatBin_OSuc__pred_H_0, cls_Nat_Onot__gr0_0
% 3.12/2.21 % No. of inferences in proof: 11
% 3.12/2.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1664 ms resp. 1030 ms w/o parsing
% 3.12/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.12/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------