%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP019^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : 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 : Wed Sep 30 08:06:24 AM UTC 2026
% Result : Theorem 3.68s 2.09s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 2
% Syntax : Number of formulae : 6 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 26 ( 8 ~; 0 |; 0 &; 15 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 5 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Enum_2Enum_type,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Ec_2Enum_2E0_decl,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(1,conjecture,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
!= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( A
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(10,plain,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( A
= ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[4,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP019^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:33:17 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.62/1.05 % [INFO] Parsing done (268ms).
% 1.62/1.06 % [INFO] Running in sequential loop mode.
% 2.39/1.45 % [INFO] eprover registered as external prover.
% 2.39/1.46 % [INFO] Scanning for conjecture ...
% 2.61/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 2.77/1.63 % [INFO] Axiom selection finished. Selected 1 axioms (removed 39 axioms).
% 2.77/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.77/1.64 % [INFO] Type checking passed.
% 2.77/1.64 % [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 ...
% 3.68/2.09 % External prover 'e' found a proof!
% 3.68/2.09 % [INFO] Killing All external provers ...
% 3.68/2.09 % Time passed: 1744ms (effective reasoning time: 1026ms)
% 3.68/2.09 % 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)>
% 3.68/2.09 % Axioms used in derivation (1): thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 3.68/2.09 % No. of inferences in proof: 6
% 3.68/2.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1744 ms resp. 1026 ms w/o parsing
% 3.93/2.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.93/2.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------