%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP019^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:54:06 AM UTC 2026
% Result : Theorem 0.30s 1.34s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP019^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:22:02 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ITP019^3 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.27/0.47 % Domain : Interactive Theorem Proving
% 0.27/0.47 % Problem : HOL4 syntactic export of thm_2Ecomplex_2ECOMPLEX__INV__NZ.p, bushy mode
% 0.27/0.47 % Version : [BG+19] axioms.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.27/0.47 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [BG+19]
% 0.27/0.47 % Names : thm_2Ecomplex_2ECOMPLEX__INV__NZ.p [Gau19]
% 0.27/0.47 % : HL409001^3.p [TPAP]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.27/0.47 % Syntax : Number of formulae : 29 ( 6 unt; 17 typ; 0 def)
% 0.27/0.47 % Number of atoms : 24 ( 5 equ; 4 cnn)
% 0.27/0.47 % Maximal formula atoms : 8 ( 2 avg)
% 0.27/0.47 % Number of connectives : 67 ( 4 ~; 1 |; 5 &; 36 @)
% 0.27/0.47 % ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 8 ( 5 avg)
% 0.27/0.47 % Number of types : 4 ( 3 usr)
% 0.27/0.47 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 16 ( 14 usr; 4 con; 0-3 aty)
% 0.27/0.47 % Number of variables : 25 ( 0 ^; 21 !; 1 ?; 25 :)
% 0.27/0.47 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.47 % SPC : TH1_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments :
% 0.27/0.47 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(tyop_2Emin_2Ebool,type,
% 0.27/0.47 tyop_2Emin_2Ebool: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(tyop_2Emin_2Efun,type,
% 0.27/0.47 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 thf(tyop_2Enum_2Enum,type,
% 0.27/0.47 tyop_2Enum_2Enum: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(tyop_2Epair_2Eprod,type,
% 0.27/0.47 tyop_2Epair_2Eprod: $tType > $tType > $tType ).
% 0.27/0.47
% 0.27/0.47 thf(tyop_2Erealax_2Ereal,type,
% 0.27/0.47 tyop_2Erealax_2Ereal: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_21,type,
% 0.27/0.47 c_2Ebool_2E_21:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_2F_5C,type,
% 0.27/0.47 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Enum_2E0,type,
% 0.27/0.47 c_2Enum_2E0: tyop_2Enum_2Enum ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Emin_2E_3D,type,
% 0.27/0.47 c_2Emin_2E_3D:
% 0.27/0.47 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Emin_2E_3D_3D_3E,type,
% 0.27/0.47 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_3F,type,
% 0.27/0.47 c_2Ebool_2E_3F:
% 0.27/0.47 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2EF,type,
% 0.27/0.47 c_2Ebool_2EF: $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2ET,type,
% 0.27/0.47 c_2Ebool_2ET: $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_5C_2F,type,
% 0.27/0.47 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ecomplex_2Ecomplex__inv,type,
% 0.27/0.47 c_2Ecomplex_2Ecomplex__inv: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ecomplex_2Ecomplex__of__num,type,
% 0.27/0.47 c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
% 0.27/0.47
% 0.27/0.47 thf(c_2Ebool_2E_7E,type,
% 0.27/0.47 c_2Ebool_2E_7E: $o > $o ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_2F_5C,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 & V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_5C_2F,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 | V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_7E,axiom,
% 0.27/0.47 ! [V0: $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_7E @ V0 )
% 0.27/0.47 <=> ( (~) @ V0 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_3D_3D_3E,axiom,
% 0.27/0.47 ! [V0: $o,V1: $o] :
% 0.27/0.47 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.27/0.47 <=> ( V0
% 0.27/0.47 => V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(logicdef_2E_3D,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 0.27/0.47 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 0.27/0.47 <=> ( V0 = V1 ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantdef_2E_21,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 0.27/0.47 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantdef_2E_3F,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.27/0.47 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 0.27/0.47 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.27/0.47 c_2Ebool_2ET ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.27/0.47 ! [A_27a: $tType,V0t: $o] :
% 0.27/0.47 ( ! [V1x: A_27a] : V0t
% 0.27/0.47 <=> V0t ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.27/0.47 ! [V0t: $o] :
% 0.27/0.47 ( ( ( c_2Ebool_2ET
% 0.27/0.47 => V0t )
% 0.27/0.47 <=> V0t )
% 0.27/0.47 & ( ( V0t
% 0.27/0.47 => c_2Ebool_2ET )
% 0.27/0.47 <=> c_2Ebool_2ET )
% 0.27/0.47 & ( ( c_2Ebool_2EF
% 0.27/0.47 => V0t )
% 0.27/0.47 <=> c_2Ebool_2ET )
% 0.27/0.47 & ( ( V0t
% 0.27/0.47 => V0t )
% 0.27/0.47 <=> c_2Ebool_2ET )
% 0.27/0.47 & ( ( V0t
% 0.27/0.47 => c_2Ebool_2EF )
% 0.27/0.47 <=> ( (~) @ V0t ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
% 0.27/0.47 ! [V0z: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
% 0.27/0.47 ( ( ( c_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.27/0.47 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
% 0.27/0.47 <=> ( V0z
% 0.27/0.47 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
% 0.27/0.47 ! [V0z: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
% 0.27/0.47 ( ( (~)
% 0.27/0.47 @ ( V0z
% 0.27/0.47 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
% 0.27/0.47 => ( (~)
% 0.27/0.47 @ ( ( c_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.27/0.47 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 0.30/1.30 ---- Embedded in THF ---
% 0.30/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.30 %%% Generated on Tue Feb 24 08:22:03 EST 2026
% 0.30/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.30 %%% Logic specification used:
% 0.30/1.30 %%% thf(spec, logic, $$dhol).
% 0.30/1.30
% 0.30/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3OGFXDuPe7/DTF2DTF7300.p
% 0.30/1.30 thf(tyop_2Emin_2Ebool, type, tyop_2Emin_2Ebool: $tType).
% 0.30/1.30 thf(tyop_2Emin_2Efun, type, tyop_2Emin_2Efun: ($tType > ($tType > $tType))).
% 0.30/1.30 thf(tyop_2Enum_2Enum, type, tyop_2Enum_2Enum: $tType).
% 0.30/1.30 thf(tyop_2Epair_2Eprod, type, tyop_2Epair_2Eprod: ($tType > ($tType > $tType))).
% 0.30/1.30 thf(tyop_2Erealax_2Ereal, type, tyop_2Erealax_2Ereal: $tType).
% 0.30/1.30 thf(c_2Ebool_2E_21, type, c_2Ebool_2E_21: (!> [A_27a:$tType]: (((A_27a > $o) > $o)))).
% 0.30/1.30 thf(c_2Ebool_2E_2F_5C, type, c_2Ebool_2E_2F_5C: ($o > ($o > $o))).
% 0.30/1.30 thf(c_2Enum_2E0, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 0.30/1.30 thf(c_2Emin_2E_3D, type, c_2Emin_2E_3D: (!> [A_27a:$tType]: ((A_27a > (A_27a > $o))))).
% 0.30/1.30 thf(c_2Emin_2E_3D_3D_3E, type, c_2Emin_2E_3D_3D_3E: ($o > ($o > $o))).
% 0.30/1.30 thf(c_2Ebool_2E_3F, type, c_2Ebool_2E_3F: (!> [A_27a:$tType]: (((A_27a > $o) > $o)))).
% 0.30/1.30 thf(c_2Ebool_2EF, type, c_2Ebool_2EF: $o).
% 0.30/1.30 thf(c_2Ebool_2ET, type, c_2Ebool_2ET: $o).
% 0.30/1.30 thf(c_2Ebool_2E_5C_2F, type, c_2Ebool_2E_5C_2F: ($o > ($o > $o))).
% 0.30/1.30 thf(c_2Ecomplex_2Ecomplex__inv, type, c_2Ecomplex_2Ecomplex__inv: (((tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal) @ tyop_2Erealax_2Ereal) > ((tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal) @ tyop_2Erealax_2Ereal))).
% 0.30/1.30 thf(c_2Ecomplex_2Ecomplex__of__num, type, c_2Ecomplex_2Ecomplex__of__num: (tyop_2Enum_2Enum > ((tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal) @ tyop_2Erealax_2Ereal))).
% 0.30/1.30 thf(c_2Ebool_2E_7E, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.30/1.30 thf(logicdef_2E_2F_5C, axiom, (! [V0:$o,V1:$o]: ((((c_2Ebool_2E_2F_5C @ V0) @ V1) <=> (V0 & V1))))).
% 0.30/1.30 thf(logicdef_2E_5C_2F, axiom, (! [V0:$o,V1:$o]: ((((c_2Ebool_2E_5C_2F @ V0) @ V1) <=> (V0 | V1))))).
% 0.30/1.30 thf(logicdef_2E_7E, axiom, (! [V0:$o]: (((c_2Ebool_2E_7E @ V0) <=> ((~) @ V0))))).
% 0.30/1.30 thf(logicdef_2E_3D_3D_3E, axiom, (! [V0:$o,V1:$o]: ((((c_2Emin_2E_3D_3D_3E @ V0) @ V1) <=> (V0 => V1))))).
% 0.30/1.30 thf(logicdef_2E_3D, axiom, (! [A_27a:$tType,V0:A_27a,V1:A_27a]: (((((c_2Emin_2E_3D @ A_27a) @ V0) @ V1) <=> (V0 = V1))))).
% 0.30/1.30 thf(quantdef_2E_21, axiom, (! [A_27a:$tType,V0f:(A_27a > $o)]: ((((c_2Ebool_2E_21 @ A_27a) @ V0f) <=> (! [V1x:A_27a]: ((V0f @ V1x))))))).
% 0.30/1.30 thf(quantdef_2E_3F, axiom, (! [A_27a:$tType,V0f:(A_27a > $o)]: ((((c_2Ebool_2E_3F @ A_27a) @ V0f) <=> (? [V1x:A_27a]: ((V0f @ V1x))))))).
% 0.30/1.30 thf(thm_2Ebool_2ETRUTH, axiom, c_2Ebool_2ET).
% 0.30/1.30 thf(thm_2Ebool_2EFORALL__SIMP, axiom, (! [A_27a:$tType,V0t:$o]: (((! [V1x:A_27a]: (V0t)) <=> V0t)))).
% 0.30/1.30 thf(thm_2Ebool_2EIMP__CLAUSES, axiom, (! [V0t:$o]: ((((c_2Ebool_2ET => V0t) <=> V0t) & (((V0t => c_2Ebool_2ET) <=> c_2Ebool_2ET) & (((c_2Ebool_2EF => V0t) <=> c_2Ebool_2ET) & (((V0t => V0t) <=> c_2Ebool_2ET) & ((V0t => c_2Ebool_2EF) <=> ((~) @ V0t))))))))).
% 0.30/1.30 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, axiom, (! [V0z:((tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal) @ tyop_2Erealax_2Ereal)]: ((((c_2Ecomplex_2Ecomplex__inv @ V0z) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) <=> (V0z = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)))))).
% 0.30/1.30 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ, conjecture, (! [V0z:((tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal) @ tyop_2Erealax_2Ereal)]: ((((~) @ (V0z = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))) => ((~) @ ((c_2Ecomplex_2Ecomplex__inv @ V0z) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))))).
% 0.30/1.30 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3OGFXDuPe7/DTF2DTF7300.p
% 0.30/1.30 ------------------------
% 0.30/1.31 ---- Cleaned THF ---
% 0.30/1.31 thf(tyop_2Emin_2Ebool,type,
% 0.30/1.31 tyop_2Emin_2Ebool: $tType ).
% 0.30/1.31
% 0.30/1.31 thf(tyop_2Emin_2Efun,type,
% 0.30/1.31 tyop_2Emin_2Efun: $tType > $tType > $tType ).
% 0.30/1.31
% 0.30/1.31 thf(tyop_2Enum_2Enum,type,
% 0.30/1.31 tyop_2Enum_2Enum: $tType ).
% 0.30/1.31
% 0.30/1.31 thf(tyop_2Epair_2Eprod,type,
% 0.30/1.31 tyop_2Epair_2Eprod: $tType > $tType > $tType ).
% 0.30/1.31
% 0.30/1.31 thf(tyop_2Erealax_2Ereal,type,
% 0.30/1.31 tyop_2Erealax_2Ereal: $tType ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2E_21,type,
% 0.30/1.31 c_2Ebool_2E_21:
% 0.30/1.31 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2E_2F_5C,type,
% 0.30/1.31 c_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Enum_2E0,type,
% 0.30/1.31 c_2Enum_2E0: tyop_2Enum_2Enum ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Emin_2E_3D,type,
% 0.30/1.31 c_2Emin_2E_3D:
% 0.30/1.31 !>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Emin_2E_3D_3D_3E,type,
% 0.30/1.31 c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2E_3F,type,
% 0.30/1.31 c_2Ebool_2E_3F:
% 0.30/1.31 !>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2EF,type,
% 0.30/1.31 c_2Ebool_2EF: $o ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2ET,type,
% 0.30/1.31 c_2Ebool_2ET: $o ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2E_5C_2F,type,
% 0.30/1.31 c_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ecomplex_2Ecomplex__inv,type,
% 0.30/1.31 c_2Ecomplex_2Ecomplex__inv: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ecomplex_2Ecomplex__of__num,type,
% 0.30/1.31 c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
% 0.30/1.31
% 0.30/1.31 thf(c_2Ebool_2E_7E,type,
% 0.30/1.31 c_2Ebool_2E_7E: $o > $o ).
% 0.30/1.31
% 0.30/1.31 thf(logicdef_2E_2F_5C,axiom,
% 0.30/1.31 ! [V0: $o,V1: $o] :
% 0.30/1.31 ( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.30/1.31 <=> ( V0
% 0.30/1.31 & V1 ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(logicdef_2E_5C_2F,axiom,
% 0.30/1.31 ! [V0: $o,V1: $o] :
% 0.30/1.31 ( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.30/1.31 <=> ( V0
% 0.30/1.31 | V1 ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(logicdef_2E_7E,axiom,
% 0.30/1.31 ! [V0: $o] :
% 0.30/1.31 ( ( c_2Ebool_2E_7E @ V0 )
% 0.30/1.31 <=> ( (~) @ V0 ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(logicdef_2E_3D_3D_3E,axiom,
% 0.30/1.31 ! [V0: $o,V1: $o] :
% 0.30/1.31 ( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.30/1.31 <=> ( V0
% 0.30/1.31 => V1 ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(logicdef_2E_3D,axiom,
% 0.30/1.31 ! [A_27a: $tType,V0: A_27a,V1: A_27a] :
% 0.30/1.31 ( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
% 0.30/1.31 <=> ( V0 = V1 ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(quantdef_2E_21,axiom,
% 0.30/1.31 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.30/1.31 ( ( c_2Ebool_2E_21 @ A_27a @ V0f )
% 0.30/1.31 <=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(quantdef_2E_3F,axiom,
% 0.30/1.31 ! [A_27a: $tType,V0f: A_27a > $o] :
% 0.30/1.31 ( ( c_2Ebool_2E_3F @ A_27a @ V0f )
% 0.30/1.31 <=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.30/1.31 c_2Ebool_2ET ).
% 0.30/1.31
% 0.30/1.31 thf(thm_2Ebool_2EFORALL__SIMP,axiom,
% 0.30/1.31 ! [A_27a: $tType,V0t: $o] :
% 0.30/1.31 ( ! [V1x: A_27a] : V0t
% 0.30/1.31 <=> V0t ) ).
% 0.30/1.31
% 0.30/1.31 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.30/1.31 ! [V0t: $o] :
% 0.30/1.31 ( ( ( c_2Ebool_2ET
% 0.30/1.31 => V0t )
% 0.30/1.31 <=> V0t )
% 0.30/1.31 & ( ( V0t
% 0.30/1.31 => c_2Ebool_2ET )
% 0.30/1.31 <=> c_2Ebool_2ET )
% 0.30/1.31 & ( ( c_2Ebool_2EF
% 0.30/1.31 => V0t )
% 0.30/1.31 <=> c_2Ebool_2ET )
% 0.30/1.31 & ( ( V0t
% 0.30/1.31 => V0t )
% 0.30/1.31 <=> c_2Ebool_2ET )
% 0.30/1.31 & ( ( V0t
% 0.30/1.31 => c_2Ebool_2EF )
% 0.30/1.31 <=> ( (~) @ V0t ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
% 0.30/1.31 ! [V0z: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
% 0.30/1.31 ( ( ( c_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.30/1.31 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
% 0.30/1.31 <=> ( V0z
% 0.30/1.31 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ).
% 0.30/1.31
% 0.30/1.31 thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
% 0.30/1.31 ! [V0z: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
% 0.30/1.31 ( ( (~)
% 0.30/1.31 @ ( V0z
% 0.30/1.31 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) )
% 0.30/1.31 => ( (~)
% 0.30/1.31 @ ( ( c_2Ecomplex_2Ecomplex__inv @ V0z )
% 0.30/1.31 = ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ).
% 0.30/1.31 ------------------------
% 0.30/1.33 % (7573)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/2Mi)
% 0.30/1.33 % (7573)Instruction limit reached!
% 0.30/1.33 % (7573)------------------------------
% 0.30/1.33 % (7573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.33 % (7573)Termination reason: Unknown
% 0.30/1.33 % (7573)Termination phase: Preprocessing 3
% 0.30/1.33
% 0.30/1.33 % (7573)Memory used [KB]: 1023
% 0.30/1.33 % (7573)Time elapsed: 0.002 s
% 0.30/1.33 % (7573)Instructions burned: 3 (million)
% 0.30/1.33 % (7573)------------------------------
% 0.30/1.33 % (7573)------------------------------
% 0.30/1.34 % (7569)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/183Mi)
% 0.30/1.34 % (7570)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/4Mi)
% 0.30/1.34 % (7571)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/27Mi)
% 0.30/1.34 % (7574)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/275Mi)
% 0.30/1.34 % (7575)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/18Mi)
% 0.30/1.34 % (7572)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/2Mi)
% 0.30/1.34 % (7572)Instruction limit reached!
% 0.30/1.34 % (7572)------------------------------
% 0.30/1.34 % (7572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (7572)Termination reason: Unknown
% 0.30/1.34 % (7572)Termination phase: shuffling
% 0.30/1.34
% 0.30/1.34 % (7572)Memory used [KB]: 1023
% 0.30/1.34 % (7572)Time elapsed: 0.003 s
% 0.30/1.34 % (7572)Instructions burned: 2 (million)
% 0.30/1.34 % (7572)------------------------------
% 0.30/1.34 % (7572)------------------------------
% 0.30/1.34 % (7574)First to succeed.
% 0.30/1.34 % (7576)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7300 for (2999ds/3Mi)
% 0.30/1.34 % (7570)Instruction limit reached!
% 0.30/1.34 % (7570)------------------------------
% 0.30/1.34 % (7570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (7570)Termination reason: Unknown
% 0.30/1.34 % (7570)Termination phase: Saturation
% 0.30/1.34
% 0.30/1.34 % (7570)Memory used [KB]: 5500
% 0.30/1.34 % (7570)Time elapsed: 0.005 s
% 0.30/1.34 % (7570)Instructions burned: 5 (million)
% 0.30/1.34 % (7570)------------------------------
% 0.30/1.34 % (7570)------------------------------
% 0.30/1.34 % (7576)Instruction limit reached!
% 0.30/1.34 % (7576)------------------------------
% 0.30/1.34 % (7576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (7576)Termination reason: Unknown
% 0.30/1.34 % (7576)Termination phase: Saturation
% 0.30/1.34
% 0.30/1.34 % (7576)Memory used [KB]: 1023
% 0.30/1.34 % (7576)Time elapsed: 0.002 s
% 0.30/1.34 % (7576)Instructions burned: 3 (million)
% 0.30/1.34 % (7576)------------------------------
% 0.30/1.34 % (7576)------------------------------
% 0.30/1.34 % (7574)Refutation found. Thanks to Tanya!
% 0.30/1.34 % SZS status Theorem for DTF2THF_7300
% 0.30/1.34 % SZS output start Proof for DTF2THF_7300
% 0.30/1.34 thf(type_def_6, type, tyop_2Enum_2Enum: $tType).
% 0.30/1.34 thf(type_def_7, type, tyop_2Erealax_2Ereal: $tType).
% 0.30/1.34 thf(type_def_8, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 0.30/1.34 thf(func_def_0, type, tyop_2Emin_2Ebool: $tType).
% 0.30/1.34 thf(func_def_1, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.30/1.34 thf(func_def_2, type, tyop_2Enum_2Enum: $tType).
% 0.30/1.34 thf(func_def_3, type, tyop_2Epair_2Eprod: ($tType * $tType) > $tType).
% 0.30/1.34 thf(func_def_4, type, tyop_2Erealax_2Ereal: $tType).
% 0.30/1.34 thf(func_def_5, type, c_2Ebool_2E_21: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.30/1.34 thf(func_def_6, type, c_2Ebool_2E_2F_5C: $o > $o > $o).
% 0.30/1.34 thf(func_def_7, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 0.30/1.34 thf(func_def_8, type, c_2Emin_2E_3D: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.30/1.34 thf(func_def_9, type, c_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 0.30/1.34 thf(func_def_10, type, c_2Ebool_2E_3F: !>[X0: $tType]:((X0 > $o) > $o)).
% 0.30/1.34 thf(func_def_13, type, c_2Ebool_2E_5C_2F: $o > $o > $o).
% 0.30/1.34 thf(func_def_14, type, c_2Ecomplex_2Ecomplex__inv: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal > tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal).
% 0.30/1.34 thf(func_def_15, type, c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal).
% 0.30/1.34 thf(func_def_16, type, c_2Ebool_2E_7E: $o > $o).
% 0.30/1.34 thf(func_def_22, type, sK0: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal).
% 0.30/1.34 thf(f55,plain,(
% 0.30/1.34 $false),
% 0.30/1.34 inference(subsumption_resolution,[status(thm)],[f54,f50])).
% 0.30/1.34 thf(f50,plain,(
% 0.30/1.34 ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) != sK0)),
% 0.30/1.34 inference(equality_proxy_clausification,[status(thm)],[f49])).
% 0.30/1.34 thf(f49,plain,(
% 0.30/1.34 (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0) = $false)),
% 0.30/1.34 inference(not_proxy_clausification,[status(thm)],[f47])).
% 0.30/1.34 thf(f47,plain,(
% 0.30/1.34 ($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0)))),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 0.30/1.34 thf(f42,plain,(
% 0.30/1.34 ($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0))) & ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ sK0))) != $true)),
% 0.30/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f41])).
% 0.30/1.34 thf(f41,plain,(
% 0.30/1.34 ? [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0))) & ($true != (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0))))) => (($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0))) & ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ sK0))) != $true))),
% 0.30/1.34 introduced(definition,[],[choice_axiom])).
% 0.30/1.34 thf(f39,plain,(
% 0.30/1.34 ? [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0))) & ($true != (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0)))))),
% 0.30/1.34 inference(ennf_transformation,[status(thm)],[f24])).
% 0.30/1.34 thf(f24,plain,(
% 0.30/1.34 ~! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0))) => ($true = (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0)))))),
% 0.30/1.34 inference(fool_elimination,[status(thm)],[f23])).
% 0.30/1.34 thf(f23,plain,(
% 0.30/1.34 ~! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0)) => (~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0))))),
% 0.30/1.34 inference(rectify,[status(thm)],[f13])).
% 0.30/1.34 thf(f13,negated_conjecture,(
% 0.30/1.34 ~! [X6 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X6)) => (~ ((c_2Ecomplex_2Ecomplex__inv @ X6) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))),
% 0.30/1.34 inference(negated_conjecture,[status(cth)],[f12])).
% 0.30/1.34 thf(f12,conjecture,(
% 0.30/1.34 ! [X6 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X6)) => (~ ((c_2Ecomplex_2Ecomplex__inv @ X6) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0))))),
% 0.30/1.34 file('/export/starexec/sandbox/tmp/tmp.3OGFXDuPe7/DTF2THF_7300.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ)).
% 0.30/1.34 thf(f54,plain,(
% 0.30/1.34 ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0)),
% 0.30/1.34 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 0.30/1.34 thf(f53,plain,(
% 0.30/1.34 ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) != (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) | ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = sK0)),
% 0.30/1.34 inference(superposition,[status(thm)],[f45,f52])).
% 0.30/1.34 thf(f52,plain,(
% 0.30/1.34 ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ sK0))),
% 0.30/1.34 inference(equality_proxy_clausification,[status(thm)],[f51])).
% 0.30/1.34 thf(f51,plain,(
% 0.30/1.34 ($true = ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ sK0)))),
% 0.30/1.34 inference(not_proxy_clausification,[status(thm)],[f46])).
% 0.30/1.34 thf(f46,plain,(
% 0.30/1.34 ((~ ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ sK0))) != $true)),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f42])).
% 0.30/1.34 thf(f45,plain,(
% 0.30/1.34 ( ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) != (c_2Ecomplex_2Ecomplex__inv @ X0)) | ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0)) )),
% 0.30/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 0.30/1.34 thf(f40,plain,(
% 0.30/1.34 ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : ((((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0) | ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) != (c_2Ecomplex_2Ecomplex__inv @ X0))) & (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0)) | ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) != X0)))),
% 0.30/1.34 inference(nnf_transformation,[status(thm)],[f38])).
% 0.30/1.34 thf(f38,plain,(
% 0.30/1.34 ! [X0 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X0) <=> ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = (c_2Ecomplex_2Ecomplex__inv @ X0)))),
% 0.30/1.34 inference(rectify,[status(thm)],[f11])).
% 0.30/1.34 thf(f11,axiom,(
% 0.30/1.34 ! [X6 : tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] : (((c_2Ecomplex_2Ecomplex__inv @ X6) = (c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0)) <=> ((c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0) = X6))),
% 0.30/1.34 file('/export/starexec/sandbox/tmp/tmp.3OGFXDuPe7/DTF2THF_7300.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0)).
% 0.30/1.34 % SZS output end Proof for DTF2THF_7300
% 0.30/1.34 % (7574)------------------------------
% 0.30/1.34 % (7574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.34 % (7574)Termination reason: Refutation
% 0.30/1.34
% 0.30/1.34 % (7574)Memory used [KB]: 5500
% 0.30/1.34 % (7574)Time elapsed: 0.005 s
% 0.30/1.34 % (7574)Instructions burned: 2 (million)
% 0.30/1.34 % (7574)------------------------------
% 0.30/1.34 % (7574)------------------------------
% 0.30/1.34 % (7568)Success in time 0.019 s
%------------------------------------------------------------------------------