%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% 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 : n002.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 09:10:12 AM UTC 2026
% Result : Theorem 2.99s 2.44s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 42 ( 10 ~; 0 |; 7 &; 16 @)
% ( 1 <=>; 8 =>; 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 : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 6 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_state_decl,type,
is_state: $i > $o ).
thf(undefined_state_decl,type,
undefined_state: $i > $i ).
thf(state_decl,type,
state: $i ).
thf(hoare_165779456gleton_decl,type,
hoare_165779456gleton: $o ).
thf(induct_false_decl,type,
induct_false: $o ).
thf(induct_true_decl,type,
induct_true: $o ).
thf(5,axiom,
~ induct_false,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_induct__false__def) ).
thf(24,plain,
~ induct_false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
state @ undefined_state @ is_state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Ostate) ).
thf(14,plain,
state @ undefined_state @ is_state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
hoare_165779456gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(28,plain,
hoare_165779456gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ is_state )
=> ~ ! [B: $i] :
( ( B @ is_state )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ is_state )
=> ~ ! [B: $i] :
( ( B @ is_state )
=> ( B = A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i] :
( ( A @ is_state )
=> ~ ! [B: $i] :
( ( B @ is_state )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_induct__true__def) ).
thf(27,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_induct__trueI) ).
thf(26,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
( hoare_165779456gleton
<=> ? [A: $i,B: $i] :
( ( A != B )
& ( B @ is_state )
& ( A @ is_state ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(15,plain,
( ( ? [A: $i,B: $i] :
( ( A != B )
& ( B @ is_state )
& ( A @ is_state ) )
=> hoare_165779456gleton )
& ( hoare_165779456gleton
=> ? [A: $i,B: $i] :
( ( A != B )
& ( B @ is_state )
& ( A @ is_state ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[24,14,28,9,27,26,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW469+1 : TPTP v9.3.1. Released v5.3.0.
% 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
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 15:59:50 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.77/1.12 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.14/1.35 % [INFO] Parsing done (232ms).
% 1.14/1.37 % [INFO] Running in sequential loop mode.
% 1.66/1.75 % [INFO] eprover registered as external prover.
% 1.66/1.76 % [INFO] Scanning for conjecture ...
% 1.84/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.96/1.92 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.96/1.93 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.94 % [INFO] Type checking passed.
% 1.96/1.94 % [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 ...
% 2.99/2.44 % External prover 'e' found a proof!
% 2.99/2.44 % [INFO] Killing All external provers ...
% 2.99/2.44 % Time passed: 1813ms (effective reasoning time: 1067ms)
% 2.99/2.44 % 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)>
% 2.99/2.44 % Axioms used in derivation (6): gsy_c_HOL_Oundefined_000tc__Com__Ostate, fact_0_state__not__singleton__def, fact_3_induct__true__def, fact_1_induct__false__def, conj_0, fact_2_induct__trueI
% 2.99/2.44 % No. of inferences in proof: 16
% 2.99/2.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1813 ms resp. 1067 ms w/o parsing
% 2.99/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------