%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 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 : n002.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 08:18:47 AM UTC 2026
% Result : Unsatisfiable 3.86s 2.41s
% Output : Refutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 160 ( 2 ~; 0 |; 0 &; 158 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(perfectp_decl,type,
perfectp: $i > $i ).
thf(true_decl,type,
true: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(s_decl,type,
s: $i > $i ).
thf('<=_decl',type,
'<=': $i > $i > $i ).
thf(false_decl,type,
false: $i ).
thf(if_decl,type,
if: $i > $i > $i > $i ).
thf(f_decl,type,
f: $i > $i > $i > $i > $i ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ minus ) )
= ( B @ ( A @ minus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule2) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ minus ) )
= ( B @ ( A @ minus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( zero @ '<=' ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule3) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( zero @ '<=' ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( zero @ ( A @ minus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule1) ).
thf(18,plain,
! [A: $i] :
( ( zero @ ( A @ minus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ perfectp )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(15,plain,
! [A: $i] :
( ( A @ perfectp )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ s @ ( A @ s @ f ) ) ) )
= ( D @ ( C @ ( D @ ( A @ f ) ) ) @ ( D @ ( C @ ( A @ ( B @ minus ) @ ( A @ s @ f ) ) ) @ ( B @ ( A @ '<=' ) @ if ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule13) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ s @ ( A @ s @ f ) ) ) )
= ( D @ ( C @ ( D @ ( A @ f ) ) ) @ ( D @ ( C @ ( A @ ( B @ minus ) @ ( A @ s @ f ) ) ) @ ( B @ ( A @ '<=' ) @ if ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( zero @ ( A @ s @ '<=' ) )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule4) ).
thf(24,plain,
! [A: $i] :
( ( zero @ ( A @ s @ '<=' ) )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( true @ if ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule6) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( true @ if ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ s @ ( A @ ( zero @ f ) ) ) )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule11) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ s @ ( A @ ( zero @ f ) ) ) )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( ( zero @ perfectp )
= false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule8) ).
thf(32,plain,
( ( zero @ perfectp )
= false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ s @ perfectp )
= ( A @ s @ ( A @ s @ ( zero @ s @ ( A @ f ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule9) ).
thf(34,plain,
! [A: $i] :
( ( A @ s @ perfectp )
= ( A @ s @ ( A @ s @ ( zero @ s @ ( A @ f ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( zero @ ( A @ s @ f ) ) ) )
= ( C @ ( A @ s @ ( B @ minus ) @ ( C @ ( A @ f ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule12) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( zero @ ( A @ s @ f ) ) ) )
= ( C @ ( A @ s @ ( B @ minus ) @ ( C @ ( A @ f ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ '<=' ) )
= ( B @ ( A @ '<=' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule5) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ '<=' ) )
= ( B @ ( A @ '<=' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( zero @ ( A @ ( zero @ f ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule10) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( zero @ ( A @ ( zero @ f ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( false @ if ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule7) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( false @ if ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[20,22,18,15,42,24,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN135-1.006 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.12/0.41 % Computer : n002.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sat Sep 26 04:39:35 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 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
% 0.84/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.19 % [INFO] Parsing done (191ms).
% 1.38/1.20 % [INFO] Running in sequential loop mode.
% 1.98/1.61 % [INFO] eprover registered as external prover.
% 1.98/1.62 % [INFO] Scanning for conjecture ...
% 2.16/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.16/1.74 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.16/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.76 % [INFO] Type checking passed.
% 2.16/1.77 % [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 ...
% 3.86/2.41 % External prover 'e' found a proof!
% 3.86/2.41 % [INFO] Killing All external provers ...
% 3.86/2.41 % Time passed: 1850ms (effective reasoning time: 1198ms)
% 3.86/2.41 % Axioms used in derivation (13): rule11, rule4, rule5, rule8, rule1, rule2, rule10, rule3, rule6, rule7, rule13, rule9, rule12
% 3.86/2.41 % No. of inferences in proof: 29
% 3.86/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1850 ms resp. 1198 ms w/o parsing
% 3.86/2.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.86/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------