%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM002_2 : TPTP v9.3.1. Released v5.0.0.
% 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 : n008.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 06:57:49 AM UTC 2026
% Result : Theorem 6.40s 3.75s
% Output : Refutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 167 ( 11 ~; 2 |; 8 &; 144 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 26 usr; 17 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(state_type,type,
state: $tType ).
thf(label_type,type,
label: $tType ).
thf(statement_type,type,
statement: $tType ).
thf(register_type,type,
register: $tType ).
thf(number_type,type,
number: $tType ).
thf(boolean_type,type,
boolean: $tType ).
thf(p1_decl,type,
p1: state ).
thf(p2_decl,type,
p2: state ).
thf(p3_decl,type,
p3: state ).
thf(p4_decl,type,
p4: state ).
thf(p5_decl,type,
p5: state ).
thf(p6_decl,type,
p6: state ).
thf(p7_decl,type,
p7: state ).
thf(p8_decl,type,
p8: state ).
thf(n_decl,type,
n: number ).
thf(n0_decl,type,
n0: number ).
thf(n1_decl,type,
n1: number ).
thf(n2_decl,type,
n2: number ).
thf(register_j_decl,type,
register_j: register ).
thf(register_k_decl,type,
register_k: register ).
thf(out_decl,type,
out: label ).
thf(loop_decl,type,
loop: label ).
thf(equal_function_decl,type,
equal_function: register > number > boolean ).
thf(assign_decl,type,
assign: register > number > statement ).
thf(goto_decl,type,
goto: label > statement ).
thf(ifthen_decl,type,
ifthen: boolean > state > statement ).
thf(plus_decl,type,
plus: register > number > number ).
thf(times_decl,type,
times: number > register > number ).
thf(follows_decl,type,
follows: state > state > $o ).
thf(fails_decl,type,
fails: state > state > $o ).
thf(labels_decl,type,
labels: label > state > $o ).
thf(has_decl,type,
has: state > statement > $o ).
thf(17,axiom,
p4 @ ( n @ ( register_j @ equal_function ) @ ifthen ) @ ( p3 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_3) ).
thf(41,plain,
p4 @ ( n @ ( register_j @ equal_function ) @ ifthen ) @ ( p3 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
n0 @ ( register_j @ assign ) @ ( p1 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_1) ).
thf(27,plain,
n0 @ ( register_j @ assign ) @ ( p1 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
p6 @ ( p7 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_6_to_7) ).
thf(31,plain,
p6 @ ( p7 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: state,B: state] :
~ ( ( A @ ( B @ follows ) )
& ( A @ ( B @ fails ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',direct_success) ).
thf(42,plain,
! [A: state,B: state] :
~ ( ( A @ ( B @ follows ) )
& ( A @ ( B @ fails ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
p7 @ ( p8 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_7_to_8) ).
thf(24,plain,
p7 @ ( p8 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
p3 @ ( loop @ labels ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',label_state_3) ).
thf(37,plain,
p3 @ ( loop @ labels ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
n1 @ ( register_k @ assign ) @ ( p2 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_2) ).
thf(25,plain,
n1 @ ( register_k @ assign ) @ ( p2 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,axiom,
! [A: state,B: state,C: state] :
( ( B @ ( C @ fails ) )
=> ( ( B @ ( A @ fails ) )
| ( A @ ( C @ fails ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_success) ).
thf(46,plain,
! [A: state,B: state,C: state] :
( ( B @ ( C @ fails ) )
=> ( ( B @ ( A @ fails ) )
| ( A @ ( C @ fails ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
n1 @ ( register_j @ plus ) @ ( register_j @ assign ) @ ( p7 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_7) ).
thf(29,plain,
n1 @ ( register_j @ plus ) @ ( register_j @ assign ) @ ( p7 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
~ ( p3 @ ( p3 @ fails ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_loop_through_p3) ).
thf(2,negated_conjecture,
~ ~ ( p3 @ ( p3 @ fails ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ~ ( p3 @ ( p3 @ fails ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: boolean,B: state,C: state] :
~ ( ( C @ ( A @ ifthen ) @ ( B @ has ) )
& ( B @ ( C @ fails ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conditional_success) ).
thf(33,plain,
! [A: boolean,B: state,C: state] :
~ ( ( C @ ( A @ ifthen ) @ ( B @ has ) )
& ( B @ ( C @ fails ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
p4 @ ( p5 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_4_to_5) ).
thf(28,plain,
p4 @ ( p5 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: label,B: state,C: state] :
~ ( ( C @ ( A @ labels ) )
& ( A @ goto @ ( B @ has ) )
& ( B @ ( C @ fails ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goto_success) ).
thf(38,plain,
! [A: label,B: state,C: state] :
~ ( ( C @ ( A @ labels ) )
& ( A @ goto @ ( B @ has ) )
& ( B @ ( C @ fails ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
out @ goto @ ( p4 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_4) ).
thf(32,plain,
out @ goto @ ( p4 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
p3 @ ( p6 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_3_to_6) ).
thf(45,plain,
p3 @ ( p6 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
register_k @ ( n2 @ times ) @ ( register_k @ assign ) @ ( p6 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_6) ).
thf(26,plain,
register_k @ ( n2 @ times ) @ ( register_k @ assign ) @ ( p6 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
p1 @ ( p2 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_1_to_2) ).
thf(23,plain,
p1 @ ( p2 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
p2 @ ( p3 @ follows ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transition_2_to_3) ).
thf(36,plain,
p2 @ ( p3 @ follows ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
loop @ goto @ ( p8 @ has ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_8) ).
thf(30,plain,
loop @ goto @ ( p8 @ has ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
$false,
inference(e,[status(thm)],[41,27,31,42,24,37,25,46,29,21,33,28,38,32,45,26,23,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM002_2 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.13 % 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
% 0.26/0.53 % Computer : n008.cluster.edu
% 0.26/0.53 % Model : x86_64 x86_64
% 0.26/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.53 % Memory : 8046.5625MB
% 0.26/0.53 % OS : Linux 6.8.0-71-generic
% 0.26/0.53 % CPULimit : 300
% 0.26/0.53 % WCLimit : 300
% 0.26/0.53 % DateTime : Sat Sep 26 23:20:40 UTC 2026
% 0.26/0.53 % CPUTime :
% 0.26/0.53 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
% 1.57/1.44 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.10/1.78 % [INFO] Parsing done (335ms).
% 2.38/1.80 % [INFO] Running in sequential loop mode.
% 3.39/2.46 % [INFO] eprover registered as external prover.
% 3.39/2.47 % [INFO] Scanning for conjecture ...
% 3.80/2.63 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.98/2.72 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.98/2.79 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.98/2.80 % [INFO] Type checking passed.
% 4.17/2.80 % [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 ...
% 6.40/3.74 % External prover 'e' found a proof!
% 6.40/3.74 % [INFO] Killing All external provers ...
% 6.40/3.74 % Time passed: 2979ms (effective reasoning time: 1927ms)
% 6.40/3.74 % Solved by 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)>
% 6.40/3.74 % Axioms used in derivation (18): transition_3_to_6, state_4, transition_2_to_3, state_8, label_state_3, state_3, state_2, goto_success, state_1, transitivity_of_success, state_7, transition_4_to_5, transition_1_to_2, transition_6_to_7, conditional_success, direct_success, transition_7_to_8, state_6
% 6.40/3.74 % No. of inferences in proof: 40
% 6.40/3.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2979 ms resp. 1927 ms w/o parsing
% 6.86/3.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.86/3.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------