%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% 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 08:26:46 AM UTC 2026
% Result : Unsatisfiable 6.45s 2.42s
% Output : Refutation 6.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 290 ( 2 ~; 0 |; 0 &; 288 @)
% ( 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 : 18 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 60 ( 0 ^; 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ifeq3_decl,type,
ifeq3: $i > $i > $i > $i > $i ).
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(successor_decl,type,
successor: $i > $i ).
thf(k_decl,type,
k: $i ).
thf(d_decl,type,
d: $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(positive_integer_decl,type,
positive_integer: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq4_decl,type,
ifeq4: $i > $i > $i > $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(17,axiom,
! [A: $i] :
( ( true @ ( A @ successor @ positive_integer @ ( true @ ( A @ positive_integer @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',next_integer) ).
thf(52,plain,
! [A: $i] :
( ( true @ ( A @ successor @ positive_integer @ ( true @ ( A @ positive_integer @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_times_x) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,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(54,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)],[18]) ).
thf(15,axiom,
( ( b @ ( a @ ( e @ negate @ ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ multiply ) @ ( e @ add ) @ negate @ ifeq3 ) ) ) )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',base_step) ).
thf(48,plain,
( ( b @ ( a @ ( e @ negate @ ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ multiply ) @ ( e @ add ) @ negate @ ifeq3 ) ) ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
thf(42,plain,
( ( e @ negate @ ( d @ add ) @ negate @ ( e @ negate @ add ) @ negate )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
( ( one @ positive_integer )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one) ).
thf(24,plain,
( ( one @ positive_integer )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(20,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate @ ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate @ ifeq4 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_2) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( A @ add ) @ negate @ ( B @ add ) @ negate @ ( C @ ( B @ add ) @ negate @ ( A @ add ) @ negate @ ifeq4 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_003) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,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(38,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)],[10]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( B @ add ) @ ( A @ multiply ) @ ( C @ add ) @ negate @ ( B @ add ) @ negate @ ( D @ ( C @ negate @ ( B @ add ) @ negate @ ifeq4 ) ) ) @ ( true @ ( A @ positive_integer @ ifeq2 ) ) ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_4) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( B @ add ) @ ( A @ multiply ) @ ( C @ add ) @ negate @ ( B @ add ) @ negate @ ( D @ ( C @ negate @ ( B @ add ) @ negate @ ifeq4 ) ) ) @ ( true @ ( A @ positive_integer @ ifeq2 ) ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
( ( k @ positive_integer )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
thf(34,plain,
( ( k @ positive_integer )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ successor @ multiply ) @ ( A @ ( B @ multiply ) @ ( A @ add ) @ ( true @ ( A @ positive_integer @ ifeq2 ) ) ) )
= ( A @ ( B @ successor @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_by_adding) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ successor @ multiply ) @ ( A @ ( B @ multiply ) @ ( A @ add ) @ ( true @ ( A @ positive_integer @ ifeq2 ) ) ) )
= ( A @ ( B @ successor @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq4 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq4 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq3 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( b @ ( a @ ( e @ negate @ ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ successor @ multiply ) @ ( e @ add ) @ negate @ ifeq3 ) ) ) )
= b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_induction_step) ).
thf(19,plain,
( ( b @ ( a @ ( e @ negate @ ( e @ negate @ ( d @ add ) @ negate @ ( d @ add ) @ ( k @ successor @ multiply ) @ ( e @ add ) @ negate @ ifeq3 ) ) ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(464,plain,
$false,
inference(e,[status(thm)],[52,44,54,48,50,42,24,20,46,28,38,32,34,40,26,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ROB015-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.15/0.63 % Computer : n005.cluster.edu
% 0.15/0.63 % Model : x86_64 x86_64
% 0.15/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.63 % Memory : 8046.5625MB
% 0.15/0.63 % OS : Linux 6.8.0-71-generic
% 0.15/0.63 % CPULimit : 300
% 0.15/0.63 % WCLimit : 300
% 0.15/0.63 % DateTime : Sat Sep 26 06:14:48 UTC 2026
% 0.15/0.64 % CPUTime :
% 0.15/0.64 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
% 0.18/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/1.03 % [INFO] Parsing done (97ms).
% 0.93/1.04 % [INFO] Running in sequential loop mode.
% 1.27/1.22 % [INFO] eprover registered as external prover.
% 1.27/1.23 % [INFO] Scanning for conjecture ...
% 1.27/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 1.53/1.31 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.53/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 1.53/1.33 % [INFO] Type checking passed.
% 1.53/1.33 % [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 ...
% 6.45/2.41 % External prover 'e' found a proof!
% 6.45/2.41 % [INFO] Killing All external provers ...
% 6.45/2.41 % Time passed: 1678ms (effective reasoning time: 1369ms)
% 6.45/2.41 % Axioms used in derivation (16): k_positive, ifeq_axiom, next_integer, times_by_adding, condition, ifeq_axiom_003, lemma_3_4, ifeq_axiom_002, one, ifeq_axiom_001, one_times_x, lemma_3_2, associativity_of_add, commutativity_of_add, base_step, robbins_axiom
% 6.45/2.41 % No. of inferences in proof: 37
% 6.45/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1678 ms resp. 1369 ms w/o parsing
% 6.45/2.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.45/2.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------