%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n005.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 08:26:47 AM UTC 2026
% Result : Unsatisfiable 4.80s 3.01s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 18 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 166 ( 10 ~; 8 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(negate_decl,type,
negate: $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(e_decl,type,
e: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(k_decl,type,
k: $i ).
thf(d_decl,type,
d: $i ).
thf(one_decl,type,
one: $i ).
thf(positive_integer_decl,type,
positive_integer: $i > $o ).
thf(successor_decl,type,
successor: $i > $i ).
thf(9,axiom,
( ( e @ ( d @ add ) @ negate )
= ( e @ negate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(29,plain,
( ( e @ ( d @ add ) @ negate )
= ( e @ negate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_times_x) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',next_integer) ).
thf(27,plain,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_result) ).
thf(12,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ multiply ) @ ( e @ add ) @ negate )
!= ( e @ negate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
k @ positive_integer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
thf(31,plain,
k @ positive_integer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',robbins_axiom) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ negate @ ( B @ add ) @ negate @ ( B @ add ) @ ( C @ multiply ) @ ( A @ add ) @ negate )
= ( A @ negate ) )
| ~ ( C @ positive_integer )
| ( ( A @ negate @ ( B @ add ) @ negate @ ( A @ negate @ add ) @ negate )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_6) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ negate @ ( B @ add ) @ negate @ ( B @ add ) @ ( C @ multiply ) @ ( A @ add ) @ negate )
= ( A @ negate ) )
| ~ ( C @ positive_integer )
| ( ( A @ negate @ ( B @ add ) @ negate @ ( A @ negate @ add ) @ negate )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
one @ positive_integer,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one) ).
thf(26,plain,
one @ positive_integer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_by_adding) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[29,21,27,12,31,19,15,32,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.14/0.42 % Computer : n005.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 06:15:02 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 1.19/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.78/1.40 % [INFO] Parsing done (290ms).
% 1.78/1.43 % [INFO] Running in sequential loop mode.
% 2.61/2.04 % [INFO] eprover registered as external prover.
% 2.61/2.05 % [INFO] Scanning for conjecture ...
% 3.05/2.18 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.14/2.23 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.14/2.27 % [INFO] Problem is propositional (TPTP CNF).
% 3.14/2.28 % [INFO] Type checking passed.
% 3.14/2.28 % [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 ...
% 4.80/3.00 % External prover 'e' found a proof!
% 4.80/3.00 % [INFO] Killing All external provers ...
% 4.80/3.00 % Time passed: 2432ms (effective reasoning time: 1567ms)
% 4.80/3.00 % Axioms used in derivation (10): k_positive, one_times_x, next_integer, times_by_adding, condition, one, robbins_axiom, lemma_3_6, associativity_of_add, commutativity_of_add
% 4.80/3.01 % No. of inferences in proof: 23
% 4.80/3.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2432 ms resp. 1567 ms w/o parsing
% 5.29/3.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.29/3.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------