%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n011.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 08:08:06 AM UTC 2026
% Result : Unsatisfiable 4.31s 2.74s
% Output : Refutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 146 ( 14 ~; 10 |; 0 &; 122 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(n0_decl,type,
n0: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(n1_decl,type,
n1: $i ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(25,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(2,negated_conjecture,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).
thf(14,plain,
! [A: $i] :
~ ( n0 @ ( A @ successor @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times) ).
thf(20,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ multiply ) @ add ) @ ( B @ successor @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
~ ( a @ successor @ ( n0 @ successor @ ( a @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deny_addition_lemma) ).
thf(13,plain,
~ ( a @ successor @ ( n0 @ successor @ ( a @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,axiom,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
thf(17,plain,
! [A: $i] : ( A @ ( n0 @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition) ).
thf(18,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ successor @ ( B @ successor @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_equality1) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equalish ) )
| ~ ( B @ successor @ ( A @ successor @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ successor @ ( A @ successor @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
n0 @ successor @ ( n1 @ equalish ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_succeeds_zero) ).
thf(30,plain,
n0 @ successor @ ( n1 @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_zero) ).
thf(19,plain,
! [A: $i] : ( n0 @ ( n0 @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[25,14,20,13,17,18,28,21,26,23,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.09 % 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
% 0.21/0.46 % Computer : n011.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sat Sep 26 01:54:00 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 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
% 1.47/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.82/1.59 % [INFO] Parsing done (253ms).
% 2.01/1.60 % [INFO] Running in sequential loop mode.
% 2.48/2.02 % [INFO] eprover registered as external prover.
% 2.48/2.03 % [INFO] Scanning for conjecture ...
% 2.74/2.12 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.92/2.16 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.92/2.17 % [INFO] Problem is propositional (TPTP CNF).
% 2.92/2.17 % [INFO] Type checking passed.
% 2.92/2.18 % [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 ...
% 4.31/2.74 % External prover 'e' found a proof!
% 4.31/2.74 % [INFO] Killing All external provers ...
% 4.31/2.74 % Time passed: 2062ms (effective reasoning time: 1131ms)
% 4.31/2.74 % Axioms used in derivation (10): successor_equality1, successor_substitution, reflexivity, addition, times_zero, times, adding_zero, transitivity, one_succeeds_zero, symmetry
% 4.31/2.74 % No. of inferences in proof: 25
% 4.31/2.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2062 ms resp. 1131 ms w/o parsing
% 4.31/2.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------