%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ROB011-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n007.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 3.28s 2.58s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 110 ( 6 ~; 4 |; 0 &; 100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(negate_decl,type,
negate: $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(c_decl,type,
c: $i ).
thf(positive_integer_decl,type,
positive_integer: $i > $o ).
thf(successor_decl,type,
successor: $i > $i ).
thf(1,negated_conjecture,
( ( c @ ( a @ add ) @ ( one @ multiply ) @ ( b @ add ) @ negate @ ( a @ add ) @ negate )
!= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_base_step) ).
thf(10,plain,
( ( c @ ( a @ add ) @ ( one @ multiply ) @ ( b @ add ) @ negate @ ( a @ add ) @ negate )
!= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ successor @ multiply ) )
= ( A @ ( B @ multiply ) @ ( A @ add ) ) )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_by_adding) ).
thf(21,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(2,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ add ) )
= ( A @ ( B @ add ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ negate @ ( A @ add ) @ negate @ ( B @ ( A @ add ) @ negate @ add ) @ negate )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',robbins_axiom) ).
thf(17,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(9,axiom,
( ( b @ negate @ ( a @ add ) @ negate )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condition) ).
thf(27,plain,
( ( b @ negate @ ( a @ add ) @ negate )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_times_x) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( one @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ add ) @ add ) )
= ( C @ ( B @ add ) @ ( A @ add ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',one) ).
thf(24,plain,
one @ positive_integer,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',next_integer) ).
thf(25,plain,
! [A: $i] :
( ( A @ successor @ positive_integer )
| ~ ( A @ positive_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[10,21,13,17,27,19,15,24,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ROB011-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 06:12:40 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.87/1.18 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.42 % [INFO] Parsing done (238ms).
% 1.22/1.44 % [INFO] Running in sequential loop mode.
% 1.77/1.86 % [INFO] eprover registered as external prover.
% 1.77/1.87 % [INFO] Scanning for conjecture ...
% 1.97/1.96 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.97/1.99 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.97/2.01 % [INFO] Problem is propositional (TPTP CNF).
% 1.97/2.01 % [INFO] Type checking passed.
% 1.97/2.02 % [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 ...
% 3.28/2.58 % External prover 'e' found a proof!
% 3.28/2.58 % [INFO] Killing All external provers ...
% 3.28/2.58 % Time passed: 1932ms (effective reasoning time: 1124ms)
% 3.28/2.58 % Axioms used in derivation (8): one_times_x, next_integer, times_by_adding, condition, one, robbins_axiom, associativity_of_add, commutativity_of_add
% 3.28/2.58 % No. of inferences in proof: 19
% 3.28/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1932 ms resp. 1124 ms w/o parsing
% 3.62/2.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------