%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM010-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n012.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 06:57:52 AM UTC 2026
% Result : Unsatisfiable 1.57s 21.23s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 11 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 96 ( 2 ~; 0 |; 0 &; 94 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_UNITY_OInit_decl,type,
c_UNITY_OInit: $i > $i > $i ).
thf(v_F_decl,type,
v_F: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(c_UNITY_OActs_decl,type,
c_UNITY_OActs: $i > $i > $i ).
thf(c_UNITY_OAllowedActs_decl,type,
c_UNITY_OAllowedActs: $i > $i > $i ).
thf(c_UNITY_Omk__program_decl,type,
c_UNITY_Omk__program: $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(1,negated_conjecture,
( ( t_a @ ( v_F @ c_UNITY_OInit ) )
= ( t_a @ ( v_G @ c_UNITY_OInit ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(6,plain,
( ( t_a @ ( v_F @ c_UNITY_OInit ) )
= ( t_a @ ( v_G @ c_UNITY_OInit ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
v_F != v_G,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(9,plain,
v_F != v_G,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
( ( t_a @ ( v_F @ c_UNITY_OActs ) )
= ( t_a @ ( v_G @ c_UNITY_OActs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(7,plain,
( ( t_a @ ( v_F @ c_UNITY_OActs ) )
= ( t_a @ ( v_G @ c_UNITY_OActs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,negated_conjecture,
( ( t_a @ ( v_F @ c_UNITY_OAllowedActs ) )
= ( t_a @ ( v_G @ c_UNITY_OAllowedActs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,plain,
( ( t_a @ ( v_F @ c_UNITY_OAllowedActs ) )
= ( t_a @ ( v_G @ c_UNITY_OAllowedActs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ tc_prod ) @ ( B @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( B @ ( A @ c_UNITY_OActs ) @ c_Pair ) ) ) @ ( B @ ( A @ c_UNITY_OInit ) @ c_Pair ) ) ) @ c_UNITY_Omk__program ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_Osurjective__mk__program_0) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ tc_prod ) @ ( B @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( B @ tc_prod ) @ tc_set @ tc_set @ ( B @ ( A @ c_UNITY_OAllowedActs ) @ ( B @ ( A @ c_UNITY_OActs ) @ c_Pair ) ) ) @ ( B @ ( A @ c_UNITY_OInit ) @ c_Pair ) ) ) @ c_UNITY_Omk__program ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[6,9,7,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % 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
% 0.05/20.35 % Computer : n012.cluster.edu
% 0.05/20.35 % Model : x86_64 x86_64
% 0.05/20.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/20.35 % Memory : 8046.5625MB
% 0.05/20.35 % OS : Linux 6.8.0-71-generic
% 0.05/20.35 % CPULimit : 300
% 0.05/20.35 % WCLimit : 300
% 0.05/20.35 % DateTime : Sat Sep 26 23:20:49 UTC 2026
% 0.05/20.35 % CPUTime :
% 0.05/20.35 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
% 0.09/20.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.09/20.71 % [INFO] Parsing done (84ms).
% 0.09/20.72 % [INFO] Running in sequential loop mode.
% 0.09/20.90 % [INFO] eprover registered as external prover.
% 0.09/20.91 % [INFO] Scanning for conjecture ...
% 0.09/20.95 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 0.09/20.97 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 0.09/20.97 % [INFO] Problem is propositional (TPTP CNF).
% 0.09/20.98 % [INFO] Type checking passed.
% 0.09/20.98 % [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 ...
% 1.57/21.23 % External prover 'e' found a proof!
% 1.57/21.23 % [INFO] Killing All external provers ...
% 1.57/21.23 % Time passed: 809ms (effective reasoning time: 509ms)
% 1.57/21.23 % Axioms used in derivation (1): cls_UNITY_Osurjective__mk__program_0
% 1.57/21.23 % No. of inferences in proof: 11
% 1.57/21.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 809 ms resp. 509 ms w/o parsing
% 1.57/21.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.57/21.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------