%------------------------------------------------------------------------------
% 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/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 : n016.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 07:35:44 AM UTC 2026
% Result : Theorem 3.60s 2.40s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 8 ~; 0 |; 1 &; 30 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 10 ( 10 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Emin_2Ebool_type,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 > 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_2Enum_2E0_2E0_decl,type,
mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1: 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_2E0_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 ).
thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1_decl,type,
mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1: 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_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox2/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_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A
!= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
!= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1) ).
thf(12,plain,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
= ( A @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1) ).
thf(15,plain,
! [A: mono_2Etyop_2Enum_2Enum] :
( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 )
= ( A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
<=> ( A
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(18,plain,
! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
( ( ( A
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) )
& ( ( ( A @ mono_2Ec_2Ecomplex_2Ecomplex__inv_2E1 )
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) )
=> ( A
= ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Ecomplex_2Ecomplex__of__num_2E1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[6,12,15,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % 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
% 0.12/0.38 % Computer : n016.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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 17:33:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.25 % [INFO] Parsing done (278ms).
% 1.48/1.27 % [INFO] Running in sequential loop mode.
% 2.25/1.65 % [INFO] eprover registered as external prover.
% 2.25/1.66 % [INFO] Scanning for conjecture ...
% 2.64/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 2.64/1.87 % [INFO] Axiom selection finished. Selected 3 axioms (removed 43 axioms).
% 2.64/1.88 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.64/1.88 % [INFO] Type checking passed.
% 2.64/1.89 % [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 ...
% 3.60/2.39 % External prover 'e' found a proof!
% 3.60/2.39 % [INFO] Killing All external provers ...
% 3.60/2.39 % Time passed: 1864ms (effective reasoning time: 1121ms)
% 3.60/2.39 % 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)>
% 3.60/2.39 % Axioms used in derivation (3): arityeq1_2Ec_2Ecomplex_2Ecomplex__inv_2E1, arityeq1_2Ec_2Ecomplex_2Ecomplex__of__num_2E1, thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 3.60/2.39 % No. of inferences in proof: 10
% 3.60/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1864 ms resp. 1121 ms w/o parsing
% 3.83/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.83/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------