%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM010-1 : 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 : n019.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 06:57:51 AM UTC 2026
% Result : Unsatisfiable 6.76s 8.24s
% Output : Refutation 6.93s
% 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 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 204 ( 8 ~; 4 |; 0 &; 192 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% 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_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_UNITY_Omk__program_decl,type,
c_UNITY_Omk__program: $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $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(10,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(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ tc_prod ) @ ( D @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_UNITY_Omk__program ) @ c_UNITY_OInit ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_OInit__eq_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ tc_prod ) @ ( D @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( D @ ( D @ tc_prod ) @ tc_set @ tc_set @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ c_Pair ) ) ) @ c_UNITY_Omk__program ) @ c_UNITY_OInit ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_UNITY_OActs ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_OActs__nonempty_0) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_UNITY_OActs ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
v_F != v_G,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(13,plain,
v_F != v_G,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(12,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(8,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(31,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)],[8]) ).
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(11,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(7,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(26,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(19,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[10,24,33,13,12,31,11,26,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM010-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.14/5.40 % Computer : n019.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Sat Sep 26 23:20:55 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.61/6.51 % [INFO] Parsing done (509ms).
% 2.61/6.53 % [INFO] Running in sequential loop mode.
% 3.44/6.90 % [INFO] eprover registered as external prover.
% 3.44/6.91 % [INFO] Scanning for conjecture ...
% 4.48/7.27 % [INFO] Found a conjecture (or negated_conjecture) and 2736 axioms. Running axiom selection ...
% 5.11/7.43 % [INFO] Axiom selection finished. Selected 5 axioms (removed 2731 axioms).
% 5.11/7.46 % [INFO] Problem is propositional (TPTP CNF).
% 5.11/7.47 % [INFO] Type checking passed.
% 5.11/7.48 % [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 ...
% 6.76/8.23 % External prover 'e' found a proof!
% 6.76/8.23 % [INFO] Killing All external provers ...
% 6.76/8.23 % Time passed: 2679ms (effective reasoning time: 1697ms)
% 6.76/8.23 % Axioms used in derivation (5): cls_UNITY_OActs__nonempty_0, cls_UNITY_OInit__eq_0, cls_Product__Type_OPair__eq_1, cls_UNITY_Osurjective__mk__program_0, cls_Product__Type_OPair__eq_0
% 6.76/8.23 % No. of inferences in proof: 19
% 6.76/8.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2679 ms resp. 1697 ms w/o parsing
% 6.93/8.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.93/8.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------