%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : CSR144^1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 08:43:10 AM UTC 2026
% Result : Theorem 0.20s 1.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 367 ( 71 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 379 ( 45 ~; 43 |; 0 &; 275 @)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 8 con; 0-2 aty)
% ( 0 !!; 3 ??; 0 @@+; 0 @@-)
% Number of variables : 98 ( 4 ^; 83 !; 11 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
num: $tType ).
thf(func_def_1,type,
believes_THFTYPE_IiooI: $i > $o > $o ).
thf(func_def_2,type,
considers_THFTYPE_IiooI: $i > $o > $o ).
thf(func_def_3,type,
holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
thf(func_def_4,type,
husband_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_6,type,
wife_THFTYPE_IiioI: $i > $i > $o ).
thf(func_def_7,type,
inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK0: $i > $o > $i ).
thf(func_def_18,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f91,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f45,f63,f66,f77,f90]) ).
thf(f90,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f89]) ).
thf(f89,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[status(thm)],[f83,f41]) ).
thf(f41,plain,
( ! [X1: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl1_1
<=> ! [X1: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f83,plain,
( ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ lMax_THFTYPE_i @ $false ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) ) )
| ~ spl1_3 ),
inference(backward_demodulation,[status(thm)],[f35,f59]) ).
thf(f59,plain,
( ! [X0: $i] :
( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl1_3
<=> ! [X0: $i] :
( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f35,plain,
! [X0: $i] :
( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i] :
( ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f28]) ).
thf(f28,plain,
! [X0: $i] :
( ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $i] :
( $true
!= ( ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i] :
( $true
!= ( ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ? [X0: $i] :
( $true
= ( ~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ? [X0: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ? [X8: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X8 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
? [X8: $i] :
~ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',con) ).
thf(f25,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( believes_THFTYPE_IiooI @ X1 @ X0 ) )
| ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ X1 @ X0 ) @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $o,X1: $i] :
( ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ X1 @ X0 ) @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) ) )
| ( $true
!= ( believes_THFTYPE_IiooI @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f21]) ).
thf(f21,plain,
! [X0: $o,X1: $i] :
( ? [X2: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) )
= $true )
=> ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ X1 @ X0 ) @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
! [X0: $o,X1: $i] :
( ? [X2: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) )
= $true )
| ( $true
!= ( believes_THFTYPE_IiooI @ X1 @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $o,X1: $i] :
( ( $true
= ( believes_THFTYPE_IiooI @ X1 @ X0 ) )
=> ? [X2: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $o,X1: $i] :
( ( believes_THFTYPE_IiooI @ X1 @ X0 )
=> ? [X2: $i] : ( holdsDuring_THFTYPE_IiooI @ X2 @ ( considers_THFTYPE_IiooI @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X4: $o,X5: $i] :
( ( believes_THFTYPE_IiooI @ X5 @ X4 )
=> ? [X6: $i] : ( holdsDuring_THFTYPE_IiooI @ X6 @ ( considers_THFTYPE_IiooI @ X5 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_002) ).
thf(f77,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f76,f61,f58]) ).
thf(f61,definition,
( spl1_4
<=> ! [X1: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f76,plain,
( ! [X0: $i] :
( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) )
| ~ spl1_4 ),
inference(forward_demodulation,[status(thm)],[f72,f62]) ).
thf(f62,plain,
( ! [X1: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f72,plain,
! [X0: $i] :
( ( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ( $true
= ( holdsDuring_THFTYPE_IiooI @ ( sK0 @ lMax_THFTYPE_i @ $true ) @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) ) ) ),
inference(superposition,[status(thm)],[f35,f55]) ).
thf(f55,plain,
! [X0: $i,X1: $i] :
( ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $true )
| ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f54]) ).
thf(f54,plain,
! [X0: $i,X1: $i] :
( ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $true )
| ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f37,f47]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( wife_THFTYPE_IiioI @ X1 @ X0 ) )
| ( ( husband_THFTYPE_IiioI @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( wife_THFTYPE_IiioI @ X1 @ X0 ) )
| ( ( husband_THFTYPE_IiioI @ X0 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f33,f26]) ).
thf(f26,plain,
( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
= $true ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI,
file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax) ).
thf(f33,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
!= $true )
| ( $false
= ( X0 @ X2 @ X3 ) )
| ( $true
= ( X1 @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( X0 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
| ( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
| ( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
= $true )
=> ! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
<=> ( X0 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i > $i > $o,X0: $i > $i > $o] :
( ( inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0 )
=> ! [X2: $i,X3: $i] :
( ( X0 @ X3 @ X2 )
<=> ( X1 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_001) ).
thf(f37,plain,
! [X0: $i,X1: $i] :
( ( ( wife_THFTYPE_IiioI @ X0 @ X1 )
= $false )
| ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i,X1: $i] :
( ( ( husband_THFTYPE_IiioI @ X1 @ X0 )
= $true )
| ( ( wife_THFTYPE_IiioI @ X0 @ X1 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f32,f26]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1 )
!= $true )
| ( $false
= ( X1 @ X3 @ X2 ) )
| ( $true
= ( X0 @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f66,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_3 ),
inference(backward_demodulation,[status(thm)],[f44,f59]) ).
thf(f44,plain,
( ! [X0: $i] :
( $true
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl1_2
<=> ! [X0: $i] :
( $true
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f63,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f53,f61,f58]) ).
thf(f53,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true ) )
= $false ) ),
inference(superposition,[status(thm)],[f31,f47]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i,X1: $i] :
( $false
= ( ^ [Y0: $i] : ( holdsDuring_THFTYPE_IiooI @ Y0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] : ( holdsDuring_THFTYPE_IiooI @ Y0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: $i] :
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( holdsDuring_THFTYPE_IiooI @ Y0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( $true
= ( ~ ( ?? @ $i
@ ^ [Y0: $i] : ( holdsDuring_THFTYPE_IiooI @ Y0 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i] :
~ ? [X1: $i] : ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X7: $i] :
~ ? [X8: $i] : ( holdsDuring_THFTYPE_IiooI @ X8 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X7 @ lMax_THFTYPE_i ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_003) ).
thf(f45,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f43,f40]) ).
thf(f38,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0 ) )
| ( ( holdsDuring_THFTYPE_IiooI @ X1 @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false ) )
= $false ) ),
inference(superposition,[status(thm)],[f31,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : CSR144^1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.29 % Computer : n018.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Feb 24 05:50:31 EST 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.38 ---- Original DTF file ---
% 0.15/0.38 thf(spec,logic,$$dhol).
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 % File : CSR144^1 : TPTP v9.2.1. Released v4.1.0.
% 0.15/0.38 % Domain : Commonsense Reasoning
% 0.15/0.38 % Problem : Does Max think he's single?
% 0.15/0.38 % Version : Especial.
% 0.15/0.38 % English : There is no time during which Max considers to have a wife. Is it
% 0.15/0.38 % true that Max does not believe that he is a husband of somebody?.
% 0.15/0.38
% 0.15/0.38 % Refs : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% 0.15/0.38 % Source : [Ben10]
% 0.15/0.38 % Names : ex_3.tq_SUMO_handselected [Ben10]
% 0.15/0.38
% 0.15/0.38 % Status : Theorem
% 0.15/0.38 % Rating : 0.17 v9.1.0, 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.67 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.00 v5.3.0, 0.50 v5.0.0, 0.25 v4.1.0
% 0.15/0.38 % Syntax : Number of formulae : 13 ( 1 unt; 8 typ; 0 def)
% 0.15/0.38 % Number of atoms : 14 ( 0 equ; 2 cnn)
% 0.15/0.38 % Maximal formula atoms : 4 ( 2 avg)
% 0.15/0.38 % Number of connectives : 31 ( 2 ~; 0 |; 0 &; 26 @)
% 0.15/0.38 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.38 % Maximal formula depth : 9 ( 7 avg)
% 0.15/0.38 % Number of types : 3 ( 1 usr)
% 0.15/0.38 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.15/0.38 % Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% 0.15/0.38 % Number of variables : 10 ( 0 ^; 7 !; 3 ?; 10 :)
% 0.15/0.38 % SPC : TH0_THM_NEQ_NAR
% 0.15/0.38
% 0.15/0.38 % Comments : This is a simple test problem for reasoning in/about SUMO.
% 0.15/0.38 % Initally the problem has been hand generated in KIF syntax in
% 0.15/0.38 % SigmaKEE and then automatically translated by Benzmueller's
% 0.15/0.38 % KIF2TH0 translator into THF syntax.
% 0.15/0.38 % : The translation has been applied in three modes: handselected,
% 0.15/0.38 % SInE, and local. The local mode only translates the local
% 0.15/0.38 % assumptions and the query. The SInE mode additionally translates
% 0.15/0.38 % the SInE extract of the loaded knowledge base (usually SUMO). The
% 0.15/0.38 % handselected mode contains a hand-selected relevant axioms.
% 0.15/0.38 % : The examples are selected to illustrate the benefits of
% 0.15/0.38 % higher-order reasoning in ontology reasoning.
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 %----The extracted signature
% 0.15/0.38 thf(numbers,type,
% 0.15/0.38 num: $tType ).
% 0.15/0.38
% 0.15/0.38 thf(believes_THFTYPE_IiooI,type,
% 0.15/0.38 believes_THFTYPE_IiooI: $i > $o > $o ).
% 0.15/0.38
% 0.15/0.38 thf(considers_THFTYPE_IiooI,type,
% 0.15/0.38 considers_THFTYPE_IiooI: $i > $o > $o ).
% 0.15/0.38
% 0.15/0.38 thf(holdsDuring_THFTYPE_IiooI,type,
% 0.15/0.38 holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
% 0.15/0.38
% 0.15/0.38 thf(husband_THFTYPE_IiioI,type,
% 0.15/0.38 husband_THFTYPE_IiioI: $i > $i > $o ).
% 0.15/0.38
% 0.15/0.38 thf(lMax_THFTYPE_i,type,
% 0.15/0.38 lMax_THFTYPE_i: $i ).
% 0.15/0.38
% 0.15/0.38 thf(wife_THFTYPE_IiioI,type,
% 0.15/0.38 wife_THFTYPE_IiioI: $i > $i > $o ).
% 0.15/0.38
% 0.15/0.38 %----The handselected axioms from the knowledge base
% 0.15/0.38 thf(inverse_THFTYPE_IIiioIIiioIoI,type,
% 0.15/0.38 inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.15/0.38
% 0.15/0.38 thf(ax,axiom,
% 0.15/0.38 inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ).
% 0.15/0.38
% 0.15/0.38 thf(ax_001,axiom,
% 0.15/0.38 ! [REL2: $i > $i > $o,REL1: $i > $i > $o] :
% 0.15/0.38 ( ( inverse_THFTYPE_IIiioIIiioIoI @ REL1 @ REL2 )
% 0.15/0.38 => ! [INST1: $i,INST2: $i] :
% 0.15/0.38 ( ( REL1 @ INST1 @ INST2 )
% 0.15/0.38 <=> ( REL2 @ INST2 @ INST1 ) ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(ax_002,axiom,
% 0.15/0.38 ! [FORMULA: $o,AGENT: $i] :
% 0.15/0.38 ( ( believes_THFTYPE_IiooI @ AGENT @ FORMULA )
% 0.15/0.38 => ? [TIME: $i] : ( holdsDuring_THFTYPE_IiooI @ TIME @ ( considers_THFTYPE_IiooI @ AGENT @ FORMULA ) ) ) ).
% 0.15/0.38
% 0.15/0.38 %----The translated axioms
% 0.15/0.38 thf(ax_003,axiom,
% 0.15/0.38 ! [X: $i] :
% 0.15/0.38 ( (~)
% 0.15/0.38 @ ? [Z: $i] : ( holdsDuring_THFTYPE_IiooI @ Z @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X @ lMax_THFTYPE_i ) ) ) ) ).
% 0.15/0.38
% 0.15/0.38 %----The translated conjectures
% 0.15/0.38 thf(con,conjecture,
% 0.15/0.38 ? [Z: $i] : ( (~) @ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ Z ) ) ) ).
% 0.15/0.38
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 ------------------------
% 0.20/1.30 ---- Embedded in THF ---
% 0.20/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.20/1.30 %%% Generated on Tue Feb 24 05:50:32 EST 2026
% 0.20/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.20/1.30 %%% Logic specification used:
% 0.20/1.30 %%% thf(spec, logic, $$dhol).
% 0.20/1.30
% 0.20/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2DTF14121.p
% See solution above
% 0.20/1.30 ------------------------
% 0.20/1.31 ---- Cleaned THF ---
% 0.20/1.31 thf(numbers,type,
% 0.20/1.31 num: $tType ).
% 0.20/1.31
% 0.20/1.31 thf(believes_THFTYPE_IiooI,type,
% 0.20/1.31 believes_THFTYPE_IiooI: $i > $o > $o ).
% 0.20/1.31
% 0.20/1.31 thf(considers_THFTYPE_IiooI,type,
% 0.20/1.31 considers_THFTYPE_IiooI: $i > $o > $o ).
% 0.20/1.31
% 0.20/1.31 thf(holdsDuring_THFTYPE_IiooI,type,
% 0.20/1.31 holdsDuring_THFTYPE_IiooI: $i > $o > $o ).
% 0.20/1.31
% 0.20/1.31 thf(husband_THFTYPE_IiioI,type,
% 0.20/1.31 husband_THFTYPE_IiioI: $i > $i > $o ).
% 0.20/1.31
% 0.20/1.31 thf(lMax_THFTYPE_i,type,
% 0.20/1.31 lMax_THFTYPE_i: $i ).
% 0.20/1.31
% 0.20/1.31 thf(wife_THFTYPE_IiioI,type,
% 0.20/1.31 wife_THFTYPE_IiioI: $i > $i > $o ).
% 0.20/1.31
% 0.20/1.31 thf(inverse_THFTYPE_IIiioIIiioIoI,type,
% 0.20/1.31 inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.20/1.31
% 0.20/1.31 thf(ax,axiom,
% 0.20/1.31 inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ).
% 0.20/1.31
% 0.20/1.31 thf(ax_001,axiom,
% 0.20/1.31 ! [REL2: $i > $i > $o,REL1: $i > $i > $o] :
% 0.20/1.31 ( ( inverse_THFTYPE_IIiioIIiioIoI @ REL1 @ REL2 )
% 0.20/1.31 => ! [INST1: $i,INST2: $i] :
% 0.20/1.31 ( ( REL1 @ INST1 @ INST2 )
% 0.20/1.31 <=> ( REL2 @ INST2 @ INST1 ) ) ) ).
% 0.20/1.31
% 0.20/1.31 thf(ax_002,axiom,
% 0.20/1.31 ! [FORMULA: $o,AGENT: $i] :
% 0.20/1.31 ( ( believes_THFTYPE_IiooI @ AGENT @ FORMULA )
% 0.20/1.31 => ? [TIME: $i] : ( holdsDuring_THFTYPE_IiooI @ TIME @ ( considers_THFTYPE_IiooI @ AGENT @ FORMULA ) ) ) ).
% 0.20/1.31
% 0.20/1.31 thf(ax_003,axiom,
% 0.20/1.31 ! [X: $i] :
% 0.20/1.31 ( (~)
% 0.20/1.31 @ ? [Z: $i] : ( holdsDuring_THFTYPE_IiooI @ Z @ ( considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( wife_THFTYPE_IiioI @ X @ lMax_THFTYPE_i ) ) ) ) ).
% 0.20/1.31
% 0.20/1.31 thf(con,conjecture,
% 0.20/1.31 ? [Z: $i] : ( (~) @ ( believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ ( husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ Z ) ) ) ).
% 0.20/1.31 ------------------------
% 0.20/1.33 % (14223)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14121 for (2999ds/2Mi)
% 0.20/1.33 % (14224)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_14121 for (2999ds/2Mi)
% 0.20/1.33 % (14221)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_14121 for (2999ds/4Mi)
% 0.20/1.33 % (14226)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14121 for (2999ds/18Mi)
% 0.20/1.33 % (14220)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14121 for (2999ds/183Mi)
% 0.20/1.33 % (14225)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_14121 for (2999ds/275Mi)
% 0.20/1.33 % (14222)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_14121 for (2999ds/27Mi)
% 0.20/1.33 % (14223)Instruction limit reached!
% 0.20/1.33 % (14223)------------------------------
% 0.20/1.33 % (14223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/1.33 % (14223)Termination reason: Unknown
% 0.20/1.33 % (14223)Termination phase: Saturation
% 0.20/1.33
% 0.20/1.33 % (14223)Memory used [KB]: 5500
% 0.20/1.33 % (14223)Time elapsed: 0.003 s
% 0.20/1.33 % (14223)Instructions burned: 2 (million)
% 0.20/1.33 % (14223)------------------------------
% 0.20/1.33 % (14223)------------------------------
% 0.20/1.33 % (14225)Refutation not found, incomplete strategy
% 0.20/1.33 % (14225)------------------------------
% 0.20/1.33 % (14225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/1.33 % (14225)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.33
% 0.20/1.33
% 0.20/1.33 % (14225)Memory used [KB]: 5500
% 0.20/1.33 % (14225)Time elapsed: 0.003 s
% 0.20/1.33 % (14225)Instructions burned: 2 (million)
% 0.20/1.33 % (14225)------------------------------
% 0.20/1.33 % (14225)------------------------------
% 0.20/1.33 % (14221)Instruction limit reached!
% 0.20/1.33 % (14221)------------------------------
% 0.20/1.33 % (14221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/1.33 % (14221)Termination reason: Unknown
% 0.20/1.33 % (14221)Termination phase: Saturation
% 0.20/1.33
% 0.20/1.33 % (14221)Memory used [KB]: 5500
% 0.20/1.33 % (14221)Time elapsed: 0.004 s
% 0.20/1.33 % (14221)Instructions burned: 4 (million)
% 0.20/1.33 % (14221)------------------------------
% 0.20/1.33 % (14221)------------------------------
% 0.20/1.33 % (14224)Instruction limit reached!
% 0.20/1.33 % (14224)------------------------------
% 0.20/1.33 % (14224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/1.33 % (14224)Termination reason: Unknown
% 0.20/1.33 % (14224)Termination phase: Saturation
% 0.20/1.33
% 0.20/1.33 % (14224)Memory used [KB]: 5500
% 0.20/1.33 % (14224)Time elapsed: 0.004 s
% 0.20/1.33 % (14224)Instructions burned: 3 (million)
% 0.20/1.33 % (14224)------------------------------
% 0.20/1.33 % (14224)------------------------------
% 0.20/1.34 % (14222)First to succeed.
% 0.20/1.34 % (14222)Refutation found. Thanks to Tanya!
% 0.20/1.34 % SZS status Theorem for DTF2THF_14121
% 0.20/1.34 % SZS output start Proof for DTF2THF_14121
% 0.20/1.34 thf(func_def_0, type, num: $tType).
% 0.20/1.34 thf(func_def_1, type, believes_THFTYPE_IiooI: $i > $o > $o).
% 0.20/1.34 thf(func_def_2, type, considers_THFTYPE_IiooI: $i > $o > $o).
% 0.20/1.34 thf(func_def_3, type, holdsDuring_THFTYPE_IiooI: $i > $o > $o).
% 0.20/1.34 thf(func_def_4, type, husband_THFTYPE_IiioI: $i > $i > $o).
% 0.20/1.34 thf(func_def_6, type, wife_THFTYPE_IiioI: $i > $i > $o).
% 0.20/1.34 thf(func_def_7, type, inverse_THFTYPE_IIiioIIiioIoI: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.20/1.34 thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.20/1.34 thf(func_def_16, type, sK0: $i > $o > $i).
% 0.20/1.34 thf(func_def_18, type, ph2: !>[X0: $tType]:(X0)).
% 0.20/1.34 thf(f91,plain,(
% 0.20/1.34 $false),
% 0.20/1.34 inference(avatar_sat_refutation,[status(thm)],[f45,f63,f66,f77,f90])).
% 0.20/1.34 thf(f90,plain,(
% 0.20/1.34 ~spl1_1 | ~spl1_3),
% 0.20/1.34 inference(avatar_contradiction_clause,[status(thm)],[f89])).
% 0.20/1.34 thf(f89,plain,(
% 0.20/1.34 $false | (~spl1_1 | ~spl1_3)),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 0.20/1.34 thf(f88,plain,(
% 0.20/1.34 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.20/1.34 inference(forward_demodulation,[status(thm)],[f83,f41])).
% 0.20/1.34 thf(f41,plain,(
% 0.20/1.34 ( ! [X1 : $i] : (((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $false)) ) | ~spl1_1),
% 0.20/1.34 inference(avatar_component_clause,[status(thm)],[f40])).
% 0.20/1.34 thf(f40,definition,(
% 0.20/1.34 spl1_1 <=> ! [X1 : $i] : ((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $false)),
% 0.20/1.34 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 0.20/1.34 thf(f83,plain,(
% 0.20/1.34 ($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ lMax_THFTYPE_i @ $false) @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false))) | ~spl1_3),
% 0.20/1.34 inference(backward_demodulation,[status(thm)],[f35,f59])).
% 0.20/1.34 thf(f59,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))) ) | ~spl1_3),
% 0.20/1.34 inference(avatar_component_clause,[status(thm)],[f58])).
% 0.20/1.34 thf(f58,definition,(
% 0.20/1.34 spl1_3 <=> ! [X0 : $i] : ($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))),
% 0.20/1.34 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 0.20/1.34 thf(f35,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))))) )),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 0.20/1.34 thf(f34,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))) | ($true != $true)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f25,f28])).
% 0.20/1.34 thf(f28,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (((believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) = $true)) )),
% 0.20/1.34 inference(not_proxy_clausification,[status(thm)],[f27])).
% 0.20/1.34 thf(f27,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true != (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))))) )),
% 0.20/1.34 inference(cnf_transformation,[status(thm)],[f19])).
% 0.20/1.34 thf(f19,plain,(
% 0.20/1.34 ! [X0 : $i] : ($true != (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))))),
% 0.20/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 0.20/1.34 thf(f11,plain,(
% 0.20/1.34 ~? [X0 : $i] : ($true = (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))))),
% 0.20/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 0.20/1.34 thf(f10,plain,(
% 0.20/1.34 ~? [X0 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)))),
% 0.20/1.34 inference(rectify,[status(thm)],[f6])).
% 0.20/1.34 thf(f6,negated_conjecture,(
% 0.20/1.34 ~? [X8 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X8)))),
% 0.20/1.34 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/1.34 thf(f5,conjecture,(
% 0.20/1.34 ? [X8 : $i] : (~ (believes_THFTYPE_IiooI @ lMax_THFTYPE_i @ (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X8)))),
% 0.20/1.34 file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',con)).
% 0.20/1.34 thf(f25,plain,(
% 0.20/1.34 ( ! [X0 : $o,X1 : $i] : (($true != (believes_THFTYPE_IiooI @ X1 @ X0)) | ($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X1 @ X0)))) )),
% 0.20/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 0.20/1.34 thf(f22,plain,(
% 0.20/1.34 ! [X0 : $o,X1 : $i] : (($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X1 @ X0))) | ($true != (believes_THFTYPE_IiooI @ X1 @ X0)))),
% 0.20/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f21])).
% 0.20/1.34 thf(f21,plain,(
% 0.20/1.34 ! [X0 : $o,X1 : $i] : (? [X2 : $i] : ((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)) = $true) => ($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ X1 @ X0) @ (considers_THFTYPE_IiooI @ X1 @ X0))))),
% 0.20/1.34 introduced(definition,[],[choice_axiom])).
% 0.20/1.34 thf(f18,plain,(
% 0.20/1.34 ! [X0 : $o,X1 : $i] : (? [X2 : $i] : ((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)) = $true) | ($true != (believes_THFTYPE_IiooI @ X1 @ X0)))),
% 0.20/1.34 inference(ennf_transformation,[status(thm)],[f13])).
% 0.20/1.34 thf(f13,plain,(
% 0.20/1.34 ! [X0 : $o,X1 : $i] : (($true = (believes_THFTYPE_IiooI @ X1 @ X0)) => ? [X2 : $i] : ((holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)) = $true))),
% 0.20/1.34 inference(fool_elimination,[status(thm)],[f12])).
% 0.20/1.34 thf(f12,plain,(
% 0.20/1.34 ! [X0 : $o,X1 : $i] : ((believes_THFTYPE_IiooI @ X1 @ X0) => ? [X2 : $i] : (holdsDuring_THFTYPE_IiooI @ X2 @ (considers_THFTYPE_IiooI @ X1 @ X0)))),
% 0.20/1.34 inference(rectify,[status(thm)],[f3])).
% 0.20/1.34 thf(f3,axiom,(
% 0.20/1.34 ! [X4 : $o,X5 : $i] : ((believes_THFTYPE_IiooI @ X5 @ X4) => ? [X6 : $i] : (holdsDuring_THFTYPE_IiooI @ X6 @ (considers_THFTYPE_IiooI @ X5 @ X4)))),
% 0.20/1.34 file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_002)).
% 0.20/1.34 thf(f77,plain,(
% 0.20/1.34 spl1_3 | ~spl1_4),
% 0.20/1.34 inference(avatar_split_clause,[status(thm)],[f76,f61,f58])).
% 0.20/1.34 thf(f61,definition,(
% 0.20/1.34 spl1_4 <=> ! [X1 : $i] : ((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $false)),
% 0.20/1.34 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 0.20/1.34 thf(f76,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))) ) | ~spl1_4),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 0.20/1.34 thf(f75,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true = $false) | ($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))) ) | ~spl1_4),
% 0.20/1.34 inference(forward_demodulation,[status(thm)],[f72,f62])).
% 0.20/1.34 thf(f62,plain,(
% 0.20/1.34 ( ! [X1 : $i] : (((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $false)) ) | ~spl1_4),
% 0.20/1.34 inference(avatar_component_clause,[status(thm)],[f61])).
% 0.20/1.34 thf(f72,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) | ($true = (holdsDuring_THFTYPE_IiooI @ (sK0 @ lMax_THFTYPE_i @ $true) @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)))) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f35,f55])).
% 0.20/1.34 thf(f55,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (((husband_THFTYPE_IiioI @ X1 @ X0) = $true) | ((husband_THFTYPE_IiioI @ X1 @ X0) = $false)) )),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f54])).
% 0.20/1.34 thf(f54,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (((husband_THFTYPE_IiioI @ X1 @ X0) = $true) | ((husband_THFTYPE_IiioI @ X1 @ X0) = $false) | ($true = $false)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f37,f47])).
% 0.20/1.34 thf(f47,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (($true = (wife_THFTYPE_IiioI @ X1 @ X0)) | ((husband_THFTYPE_IiioI @ X0 @ X1) = $false)) )),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 0.20/1.34 thf(f46,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (wife_THFTYPE_IiioI @ X1 @ X0)) | ((husband_THFTYPE_IiioI @ X0 @ X1) = $false)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f33,f26])).
% 0.20/1.34 thf(f26,plain,(
% 0.20/1.34 ((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI) = $true)),
% 0.20/1.34 inference(cnf_transformation,[status(thm)],[f17])).
% 0.20/1.34 thf(f17,plain,(
% 0.20/1.34 ((inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI) = $true)),
% 0.20/1.34 inference(fool_elimination,[status(thm)],[f16])).
% 0.20/1.34 thf(f16,plain,(
% 0.20/1.34 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.20/1.34 inference(rectify,[status(thm)],[f1])).
% 0.20/1.34 thf(f1,axiom,(
% 0.20/1.34 (inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI)),
% 0.20/1.34 file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax)).
% 0.20/1.34 thf(f33,plain,(
% 0.20/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) != $true) | ($false = (X0 @ X2 @ X3)) | ($true = (X1 @ X3 @ X2))) )),
% 0.20/1.34 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 0.20/1.34 thf(f23,plain,(
% 0.20/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((X0 @ X2 @ X3) = (X1 @ X3 @ X2)) | ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) != $true)) )),
% 0.20/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 0.20/1.34 thf(f20,plain,(
% 0.20/1.34 ! [X0 : $i > $i > $o,X1 : $i > $i > $o] : (! [X2 : $i,X3 : $i] : ((X0 @ X2 @ X3) = (X1 @ X3 @ X2)) | ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) != $true))),
% 0.20/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 0.20/1.34 thf(f9,plain,(
% 0.20/1.34 ! [X0 : $i > $i > $o,X1 : $i > $i > $o] : (((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) = $true) => ! [X2 : $i,X3 : $i] : ((X0 @ X2 @ X3) = (X1 @ X3 @ X2)))),
% 0.20/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 0.20/1.34 thf(f8,plain,(
% 0.20/1.34 ! [X0 : $i > $i > $o,X1 : $i > $i > $o] : ((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) => ! [X2 : $i,X3 : $i] : ((X1 @ X3 @ X2) <=> (X0 @ X2 @ X3)))),
% 0.20/1.34 inference(rectify,[status(thm)],[f2])).
% 0.20/1.34 thf(f2,axiom,(
% 0.20/1.34 ! [X1 : $i > $i > $o,X0 : $i > $i > $o] : ((inverse_THFTYPE_IIiioIIiioIoI @ X1 @ X0) => ! [X2 : $i,X3 : $i] : ((X0 @ X3 @ X2) <=> (X1 @ X2 @ X3)))),
% 0.20/1.34 file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_001)).
% 0.20/1.34 thf(f37,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (((wife_THFTYPE_IiioI @ X0 @ X1) = $false) | ((husband_THFTYPE_IiioI @ X1 @ X0) = $true)) )),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 0.20/1.34 thf(f36,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (((husband_THFTYPE_IiioI @ X1 @ X0) = $true) | ((wife_THFTYPE_IiioI @ X0 @ X1) = $false) | ($true != $true)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f32,f26])).
% 0.20/1.34 thf(f32,plain,(
% 0.20/1.34 ( ! [X2 : $i,X3 : $i,X0 : $i > $i > $o,X1 : $i > $i > $o] : (((inverse_THFTYPE_IIiioIIiioIoI @ X0 @ X1) != $true) | ($false = (X1 @ X3 @ X2)) | ($true = (X0 @ X2 @ X3))) )),
% 0.20/1.34 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 0.20/1.34 thf(f66,plain,(
% 0.20/1.34 ~spl1_2 | ~spl1_3),
% 0.20/1.34 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 0.20/1.34 thf(f65,plain,(
% 0.20/1.34 $false | (~spl1_2 | ~spl1_3)),
% 0.20/1.34 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 0.20/1.34 thf(f64,plain,(
% 0.20/1.34 ($true = $false) | (~spl1_2 | ~spl1_3)),
% 0.20/1.34 inference(backward_demodulation,[status(thm)],[f44,f59])).
% 0.20/1.34 thf(f44,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))) ) | ~spl1_2),
% 0.20/1.34 inference(avatar_component_clause,[status(thm)],[f43])).
% 0.20/1.34 thf(f43,definition,(
% 0.20/1.34 spl1_2 <=> ! [X0 : $i] : ($true = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0))),
% 0.20/1.34 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 0.20/1.34 thf(f63,plain,(
% 0.20/1.34 spl1_3 | spl1_4),
% 0.20/1.34 inference(avatar_split_clause,[status(thm)],[f53,f61,f58])).
% 0.20/1.34 thf(f53,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (($false = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) | ((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $true)) = $false)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f31,f47])).
% 0.20/1.34 thf(f31,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))) = $false)) )),
% 0.20/1.34 inference(beta_eta_normalization,[status(thm)],[f30])).
% 0.20/1.34 thf(f30,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))) @ X1))) )),
% 0.20/1.34 inference(pi_clausification,[status(thm)],[f29])).
% 0.20/1.34 thf(f29,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (((?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))) = $false)) )),
% 0.20/1.34 inference(not_proxy_clausification,[status(thm)],[f24])).
% 0.20/1.34 thf(f24,plain,(
% 0.20/1.34 ( ! [X0 : $i] : (($true = (~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))))))) )),
% 0.20/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 0.20/1.34 thf(f15,plain,(
% 0.20/1.34 ! [X0 : $i] : ($true = (~ (?? @ $i @ (^[Y0 : $i]: (holdsDuring_THFTYPE_IiooI @ Y0 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i)))))))),
% 0.20/1.34 inference(fool_elimination,[status(thm)],[f14])).
% 0.20/1.34 thf(f14,plain,(
% 0.20/1.34 ! [X0 : $i] : (~ ? [X1 : $i] : (holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X0 @ lMax_THFTYPE_i))))),
% 0.20/1.34 inference(rectify,[status(thm)],[f4])).
% 0.20/1.34 thf(f4,axiom,(
% 0.20/1.34 ! [X7 : $i] : (~ ? [X8 : $i] : (holdsDuring_THFTYPE_IiooI @ X8 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ (wife_THFTYPE_IiioI @ X7 @ lMax_THFTYPE_i))))),
% 0.20/1.34 file('/export/starexec/sandbox2/tmp/tmp.GvYwaf0iyu/DTF2THF_14121.p',ax_003)).
% 0.20/1.34 thf(f45,plain,(
% 0.20/1.34 spl1_1 | spl1_2),
% 0.20/1.34 inference(avatar_split_clause,[status(thm)],[f38,f43,f40])).
% 0.20/1.34 thf(f38,plain,(
% 0.20/1.34 ( ! [X0 : $i,X1 : $i] : (($true = (husband_THFTYPE_IiioI @ lMax_THFTYPE_i @ X0)) | ((holdsDuring_THFTYPE_IiooI @ X1 @ (considers_THFTYPE_IiooI @ lMax_THFTYPE_i @ $false)) = $false)) )),
% 0.20/1.34 inference(superposition,[status(thm)],[f31,f37])).
% 0.20/1.34 % SZS output end Proof for DTF2THF_14121
% 0.20/1.34 % (14222)------------------------------
% 0.20/1.34 % (14222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.20/1.34 % (14222)Termination reason: Refutation
% 0.20/1.34
% 0.20/1.34 % (14222)Memory used [KB]: 5628
% 0.20/1.34 % (14222)Time elapsed: 0.012 s
% 0.20/1.34 % (14222)Instructions burned: 13 (million)
% 0.20/1.34 % (14222)------------------------------
% 0.20/1.34 % (14222)------------------------------
% 0.20/1.34 % (14219)Success in time 0.026 s
%------------------------------------------------------------------------------