%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ063-2 : 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 : n014.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 08:21:16 AM UTC 2026
% Result : Unsatisfiable 3.00s 2.20s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 38 ( 2 ~; 0 |; 0 &; 36 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_u_decl,type,
v_u: $i ).
thf(c_Mutil_Otiling_decl,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(4,plain,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( c_emptyset @ c_union ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(5,plain,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( c_emptyset @ c_union ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[4,5,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ063-2 : 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
% 0.15/0.40 % Computer : n014.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 05:11:46 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.82/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.15 % [INFO] Parsing done (162ms).
% 1.18/1.16 % [INFO] Running in sequential loop mode.
% 1.69/1.59 % [INFO] eprover registered as external prover.
% 1.86/1.60 % [INFO] Scanning for conjecture ...
% 1.86/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.00/1.72 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.00/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 2.00/1.73 % [INFO] Type checking passed.
% 2.00/1.74 % [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 ...
% 3.00/2.20 % External prover 'e' found a proof!
% 3.00/2.20 % [INFO] Killing All external provers ...
% 3.00/2.20 % Time passed: 1643ms (effective reasoning time: 1032ms)
% 3.00/2.20 % Axioms used in derivation (1): cls_Set_OUn__empty__left_0
% 3.00/2.20 % No. of inferences in proof: 7
% 3.00/2.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1643 ms resp. 1032 ms w/o parsing
% 3.00/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.00/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------