%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU855^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 09:37:35 AM UTC 2026
% Result : Theorem 1.49s 1.28s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 4 unt; 0 typ; 4 def)
% Number of atoms : 460 ( 147 equ; 0 cnn)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 572 ( 119 ~; 102 |; 95 &; 223 @)
% ( 9 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 141 ( 54 ^; 63 !; 24 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_9,type,
sK0: a > $o ).
thf(func_def_10,type,
sK1: a > $o ).
thf(func_def_11,type,
sK2: a > $o ).
thf(func_def_12,type,
sK3: a ).
thf(func_def_14,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK6: a ).
thf(f72,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f27,f32,f37,f53,f71]) ).
thf(f71,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f70]) ).
thf(f70,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true = $false )
| ~ spl4_1
| spl4_2 ),
inference(forward_demodulation,[status(thm)],[f67,f63]) ).
thf(f63,plain,
( ( $false
= ( sK1 @ sK6 ) )
| spl4_2 ),
inference(not_proxy_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
= ( ~ ( sK1 @ sK6 ) ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 ) )
= $true )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false
!= ( ~ ( sK1 @ sK6 )
& ( sK2 @ sK6 )
& ( sK0 @ sK6 ) ) )
| spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: a] : $false
@ sK6 )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ sK6 ) )
| spl4_2 ),
inference(negative_extensionality,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f24,definition,
( spl4_2
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f67,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl4_1
| spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK6 ) )
| ~ spl4_1
| spl4_2 ),
inference(superposition,[status(thm)],[f22,f61]) ).
thf(f61,plain,
( ( $true
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f22,plain,
( ! [X4: a] :
( ( $true
!= ( sK2 @ X4 ) )
| ( $true
= ( sK1 @ X4 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl4_1
<=> ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f53,plain,
( ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f52]) ).
thf(f52,plain,
( $false
| ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( $true = $false )
| ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(backward_demodulation,[status(thm)],[f39,f50]) ).
thf(f50,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f49]) ).
thf(f49,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2
| spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[status(thm)],[f48,f36]) ).
thf(f36,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl4_4
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f48,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_2
| spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true != $true )
| ~ spl4_2
| spl4_3 ),
inference(superposition,[status(thm)],[f31,f44]) ).
thf(f44,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl4_2 ),
inference(not_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( ~ ( sK1 @ X1 ) ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ! [X1: a] :
( ( $false
= ( ~ ( sK1 @ X1 )
& ( sK2 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X1: a] :
( ( ~ ( sK1 @ X1 )
& ( sK2 @ X1 )
& ( sK0 @ X1 ) )
= $false )
| ~ spl4_2 ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
@ X1 ) )
| ~ spl4_2 ),
inference(argument_congruence,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f24]) ).
thf(f31,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl4_3
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f39,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true != $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f16,f36]) ).
thf(f16,plain,
! [X5: a] :
( ( $true
!= ( sK2 @ X5 ) )
| ( $true
= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ( ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK2 @ sK3 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
!= ( sK2 @ X5 ) ) )
& ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( $true
= ( sK0 @ X6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12]) ).
thf(f12,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ? [X3: a] :
( ( ( X1 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X0 @ X6 ) ) ) )
=> ( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ? [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
& ( $true
= ( sK2 @ X3 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
| ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( sK0 @ X5 ) )
| ( $true
!= ( sK2 @ X5 ) ) )
& ! [X6: a] :
( ( $true
!= ( sK1 @ X6 ) )
| ( $true
= ( sK0 @ X6 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X3: a] :
( ( $true
!= ( sK1 @ X3 ) )
& ( $true
= ( sK2 @ X3 ) ) )
=> ( ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK2 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ? [X3: a] :
( ( ( X1 @ X3 )
!= $true )
& ( ( X2 @ X3 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ! [X4: a] :
( ( $true
= ( X1 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) ) )
& ! [X5: a] :
( ( $true
= ( X0 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) )
& ! [X6: a] :
( ( $true
!= ( X1 @ X6 ) )
| ( $true
= ( X0 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
& ( ( X2 @ X5 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ? [X5: a] :
( ( $true
!= ( X1 @ X5 ) )
& ( ( X2 @ X5 )
= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
| ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) )
<~> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( ( X2 @ X5 )
!= $true ) )
<~> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) ) )
& ! [X3: a] :
( ( ( X1 @ X3 )
!= $true )
| ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
<=> ! [X5: a] :
( ( ( X2 @ X5 )
= $true )
=> ( $true
= ( X1 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
=> ( $true
= ( X0 @ X4 ) ) ) )
=> ( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( X1 @ Y0 )
& ( X2 @ Y0 )
& ( X0 @ Y0 ) ) ) )
<=> ! [X7: a] :
( ( $true
= ( X2 @ X7 ) )
=> ( $true
= ( X1 @ X7 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X0 @ X3 ) )
& ! [X4: a] :
( ( X2 @ X4 )
=> ( X0 @ X4 ) ) )
=> ( ( ( ^ [X5: a] : $false )
= ( ^ [X6: a] :
( ( X0 @ X6 )
& ( X2 @ X6 )
& ~ ( X1 @ X6 ) ) ) )
<=> ! [X7: a] :
( ( X2 @ X7 )
=> ( X1 @ X7 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X1: a > $o,X0: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) )
=> ( ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ( X0 @ X3 )
& ~ ( X1 @ X3 ) ) ) )
<=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xPvGWdElb0/DTF2THF_5909.p',cGAZING_THM33_pme) ).
thf(f37,plain,
( ~ spl4_2
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f34,f24]) ).
thf(f18,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f32,plain,
( ~ spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f19,f24,f29]) ).
thf(f19,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f27,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f24,f21]) ).
thf(f17,plain,
! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( $true
!= ( sK2 @ X4 ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ~ ( sK1 @ Y0 )
& ( sK2 @ Y0 )
& ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU855^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:34:11 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU855^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : TPS problem GAZING-THM33
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.29/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0420 [Bro09]
% 0.29/0.46 % : 33 [Bar92]
% 0.29/0.46 % : GAZING-THM33 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.29/0.46 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 2 avg)
% 0.29/0.46 % Number of connectives : 18 ( 1 ~; 0 |; 3 &; 9 @)
% 0.29/0.46 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cGAZING_THM33_pme,conjecture,
% 0.29/0.46 ! [S: a > $o,T: a > $o,U: a > $o] :
% 0.29/0.46 ( ( ! [Xx: a] :
% 0.29/0.46 ( ( S @ Xx )
% 0.29/0.46 => ( U @ Xx ) )
% 0.29/0.46 & ! [Xx: a] :
% 0.29/0.46 ( ( T @ Xx )
% 0.29/0.46 => ( U @ Xx ) ) )
% 0.29/0.46 => ( ! [Xx: a] :
% 0.29/0.46 ( ( S @ Xx )
% 0.29/0.46 => ( T @ Xx ) )
% 0.29/0.46 <=> ( ( ^ [Xx: a] :
% 0.29/0.46 ( ( S @ Xx )
% 0.29/0.46 & ( U @ Xx )
% 0.29/0.46 & ~ ( T @ Xx ) ) )
% 0.29/0.46 = ( ^ [Xx: a] : $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.25 ---- Embedded in THF ---
% 1.49/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.25 %%% Generated on Tue Feb 24 12:34:11 EST 2026
% 1.49/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.25 %%% Logic specification used:
% 1.49/1.25 %%% thf(spec, logic, $$dhol).
% 1.49/1.25
% 1.49/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xPvGWdElb0/DTF2DTF5909.p
% See solution above
% 1.49/1.25 ------------------------
% 1.49/1.26 ---- Cleaned THF ---
% 1.49/1.26 thf(a_type,type,
% 1.49/1.26 a: $tType ).
% 1.49/1.26
% 1.49/1.26 thf(cGAZING_THM33_pme,conjecture,
% 1.49/1.26 ! [S: a > $o,T: a > $o,U: a > $o] :
% 1.49/1.26 ( ( ! [Xx: a] :
% 1.49/1.26 ( ( S @ Xx )
% 1.49/1.26 => ( U @ Xx ) )
% 1.49/1.26 & ! [Xx: a] :
% 1.49/1.26 ( ( T @ Xx )
% 1.49/1.26 => ( U @ Xx ) ) )
% 1.49/1.26 => ( ! [Xx: a] :
% 1.49/1.26 ( ( S @ Xx )
% 1.49/1.26 => ( T @ Xx ) )
% 1.49/1.26 <=> ( ( ^ [Xx: a] :
% 1.49/1.26 ( ( S @ Xx )
% 1.49/1.26 & ( U @ Xx )
% 1.49/1.26 & ~ ( T @ Xx ) ) )
% 1.49/1.26 = ( ^ [Xx: a] : $false ) ) ) ) ).
% 1.49/1.26 ------------------------
% 1.49/1.28 % (6190)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_5909 for (2999ds/2Mi)
% 1.49/1.28 % (6190)Instruction limit reached!
% 1.49/1.28 % (6190)------------------------------
% 1.49/1.28 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (6190)Termination reason: Unknown
% 1.49/1.28 % (6190)Termination phase: Saturation
% 1.49/1.28
% 1.49/1.28 % (6190)Memory used [KB]: 895
% 1.49/1.28 % (6190)Time elapsed: 0.002 s
% 1.49/1.28 % (6190)Instructions burned: 2 (million)
% 1.49/1.28 % (6190)------------------------------
% 1.49/1.28 % (6190)------------------------------
% 1.49/1.28 % (6188)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_5909 for (2999ds/27Mi)
% 1.49/1.28 % (6188)First to succeed.
% 1.49/1.28 % (6188)Refutation found. Thanks to Tanya!
% 1.49/1.28 % SZS status Theorem for DTF2THF_5909
% 1.49/1.28 % SZS output start Proof for DTF2THF_5909
% 1.49/1.28 thf(type_def_5, type, a: $tType).
% 1.49/1.28 thf(func_def_0, type, a: $tType).
% 1.49/1.28 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.28 thf(func_def_9, type, sK0: a > $o).
% 1.49/1.28 thf(func_def_10, type, sK1: a > $o).
% 1.49/1.28 thf(func_def_11, type, sK2: a > $o).
% 1.49/1.28 thf(func_def_12, type, sK3: a).
% 1.49/1.28 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.49/1.28 thf(func_def_15, type, sK6: a).
% 1.49/1.28 thf(f72,plain,(
% 1.49/1.28 $false),
% 1.49/1.28 inference(avatar_sat_refutation,[status(thm)],[f27,f32,f37,f53,f71])).
% 1.49/1.28 thf(f71,plain,(
% 1.49/1.28 ~spl4_1 | spl4_2),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f70])).
% 1.49/1.28 thf(f70,plain,(
% 1.49/1.28 $false | (~spl4_1 | spl4_2)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.49/1.28 thf(f69,plain,(
% 1.49/1.28 ($true = $false) | (~spl4_1 | spl4_2)),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f67,f63])).
% 1.49/1.28 thf(f63,plain,(
% 1.49/1.28 ($false = (sK1 @ sK6)) | spl4_2),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f62])).
% 1.49/1.28 thf(f62,plain,(
% 1.49/1.28 ($true = (~ (sK1 @ sK6))) | spl4_2),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.49/1.28 thf(f60,plain,(
% 1.49/1.28 (((~ (sK1 @ sK6)) & (sK2 @ sK6)) = $true) | spl4_2),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f58])).
% 1.49/1.28 thf(f58,plain,(
% 1.49/1.28 ($false != (((~ (sK1 @ sK6)) & (sK2 @ sK6)) & (sK0 @ sK6))) | spl4_2),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.49/1.28 thf(f57,plain,(
% 1.49/1.28 (((^[Y0 : a]: ($false)) @ sK6) != ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))) @ sK6)) | spl4_2),
% 1.49/1.28 inference(negative_extensionality,[status(thm)],[f25])).
% 1.49/1.28 thf(f25,plain,(
% 1.49/1.28 ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | spl4_2),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.49/1.28 thf(f24,definition,(
% 1.49/1.28 spl4_2 <=> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.49/1.28 thf(f67,plain,(
% 1.49/1.28 ($true = (sK1 @ sK6)) | (~spl4_1 | spl4_2)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.49/1.28 thf(f64,plain,(
% 1.49/1.28 ($true != $true) | ($true = (sK1 @ sK6)) | (~spl4_1 | spl4_2)),
% 1.49/1.28 inference(superposition,[status(thm)],[f22,f61])).
% 1.49/1.28 thf(f61,plain,(
% 1.49/1.28 ($true = (sK2 @ sK6)) | spl4_2),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.49/1.28 thf(f22,plain,(
% 1.49/1.28 ( ! [X4 : a] : (($true != (sK2 @ X4)) | ($true = (sK1 @ X4))) ) | ~spl4_1),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.49/1.28 thf(f21,definition,(
% 1.49/1.28 spl4_1 <=> ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4)))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.49/1.28 thf(f53,plain,(
% 1.49/1.28 ~spl4_2 | spl4_3 | ~spl4_4),
% 1.49/1.28 inference(avatar_contradiction_clause,[status(thm)],[f52])).
% 1.49/1.28 thf(f52,plain,(
% 1.49/1.28 $false | (~spl4_2 | spl4_3 | ~spl4_4)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.49/1.28 thf(f51,plain,(
% 1.49/1.28 ($true = $false) | (~spl4_2 | spl4_3 | ~spl4_4)),
% 1.49/1.28 inference(backward_demodulation,[status(thm)],[f39,f50])).
% 1.49/1.28 thf(f50,plain,(
% 1.49/1.28 ($false = (sK0 @ sK3)) | (~spl4_2 | spl4_3 | ~spl4_4)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.49/1.28 thf(f49,plain,(
% 1.49/1.28 ($true = $false) | ($false = (sK0 @ sK3)) | (~spl4_2 | spl4_3 | ~spl4_4)),
% 1.49/1.28 inference(forward_demodulation,[status(thm)],[f48,f36])).
% 1.49/1.28 thf(f36,plain,(
% 1.49/1.28 ($true = (sK2 @ sK3)) | ~spl4_4),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.49/1.28 thf(f34,definition,(
% 1.49/1.28 spl4_4 <=> ($true = (sK2 @ sK3))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.49/1.28 thf(f48,plain,(
% 1.49/1.28 ($false = (sK2 @ sK3)) | ($false = (sK0 @ sK3)) | (~spl4_2 | spl4_3)),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.49/1.28 thf(f45,plain,(
% 1.49/1.28 ($false = (sK2 @ sK3)) | ($false = (sK0 @ sK3)) | ($true != $true) | (~spl4_2 | spl4_3)),
% 1.49/1.28 inference(superposition,[status(thm)],[f31,f44])).
% 1.49/1.28 thf(f44,plain,(
% 1.49/1.28 ( ! [X1 : a] : (($true = (sK1 @ X1)) | ($false = (sK2 @ X1)) | ($false = (sK0 @ X1))) ) | ~spl4_2),
% 1.49/1.28 inference(not_proxy_clausification,[status(thm)],[f43])).
% 1.49/1.28 thf(f43,plain,(
% 1.49/1.28 ( ! [X1 : a] : (($false = (sK2 @ X1)) | ($false = (sK0 @ X1)) | ($false = (~ (sK1 @ X1)))) ) | ~spl4_2),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.49/1.28 thf(f42,plain,(
% 1.49/1.28 ( ! [X1 : a] : (($false = ((~ (sK1 @ X1)) & (sK2 @ X1))) | ($false = (sK0 @ X1))) ) | ~spl4_2),
% 1.49/1.28 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.49/1.28 thf(f41,plain,(
% 1.49/1.28 ( ! [X1 : a] : (((((~ (sK1 @ X1)) & (sK2 @ X1)) & (sK0 @ X1)) = $false)) ) | ~spl4_2),
% 1.49/1.28 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.49/1.28 thf(f40,plain,(
% 1.49/1.28 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))) @ X1))) ) | ~spl4_2),
% 1.49/1.28 inference(argument_congruence,[status(thm)],[f26])).
% 1.49/1.28 thf(f26,plain,(
% 1.49/1.28 ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | ~spl4_2),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f24])).
% 1.49/1.28 thf(f31,plain,(
% 1.49/1.28 ($true != (sK1 @ sK3)) | spl4_3),
% 1.49/1.28 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.49/1.28 thf(f29,definition,(
% 1.49/1.28 spl4_3 <=> ($true = (sK1 @ sK3))),
% 1.49/1.28 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.49/1.28 thf(f39,plain,(
% 1.49/1.28 ($true = (sK0 @ sK3)) | ~spl4_4),
% 1.49/1.28 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.49/1.28 thf(f38,plain,(
% 1.49/1.28 ($true = (sK0 @ sK3)) | ($true != $true) | ~spl4_4),
% 1.49/1.28 inference(superposition,[status(thm)],[f16,f36])).
% 1.49/1.28 thf(f16,plain,(
% 1.49/1.28 ( ! [X5 : a] : (($true != (sK2 @ X5)) | ($true = (sK0 @ X5))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.28 thf(f14,plain,(
% 1.49/1.28 (((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | (($true != (sK1 @ sK3)) & ($true = (sK2 @ sK3)))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4)))) & ! [X5 : a] : (($true = (sK0 @ X5)) | ($true != (sK2 @ X5))) & ! [X6 : a] : (($true != (sK1 @ X6)) | ($true = (sK0 @ X6)))),
% 1.49/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f11,f13,f12])).
% 1.49/1.28 thf(f12,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ? [X3 : a] : (((X1 @ X3) != $true) & ((X2 @ X3) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X2 @ X4)))) & ! [X5 : a] : (($true = (X0 @ X5)) | ((X2 @ X5) != $true)) & ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X0 @ X6)))) => ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | ? [X3 : a] : (($true != (sK1 @ X3)) & ($true = (sK2 @ X3)))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0)))) | ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4)))) & ! [X5 : a] : (($true = (sK0 @ X5)) | ($true != (sK2 @ X5))) & ! [X6 : a] : (($true != (sK1 @ X6)) | ($true = (sK0 @ X6))))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f13,plain,(
% 1.49/1.28 ? [X3 : a] : (($true != (sK1 @ X3)) & ($true = (sK2 @ X3))) => (($true != (sK1 @ sK3)) & ($true = (sK2 @ sK3)))),
% 1.49/1.28 introduced(definition,[],[choice_axiom])).
% 1.49/1.28 thf(f11,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ? [X3 : a] : (((X1 @ X3) != $true) & ((X2 @ X3) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ! [X4 : a] : (($true = (X1 @ X4)) | ($true != (X2 @ X4)))) & ! [X5 : a] : (($true = (X0 @ X5)) | ((X2 @ X5) != $true)) & ! [X6 : a] : (($true != (X1 @ X6)) | ($true = (X0 @ X6))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f10])).
% 1.49/1.28 thf(f10,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ? [X5 : a] : (($true != (X1 @ X5)) & ((X2 @ X5) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ! [X5 : a] : (($true = (X1 @ X5)) | ((X2 @ X5) != $true))) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.49/1.28 inference(flattening,[status(thm)],[f9])).
% 1.49/1.28 thf(f9,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ? [X5 : a] : (($true != (X1 @ X5)) & ((X2 @ X5) = $true))) & (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) | ! [X5 : a] : (($true = (X1 @ X5)) | ((X2 @ X5) != $true)))) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.49/1.28 inference(nnf_transformation,[status(thm)],[f8])).
% 1.49/1.28 thf(f8,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X5 : a] : (($true = (X1 @ X5)) | ((X2 @ X5) != $true)) <~> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0))))) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4))) & ! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true)))),
% 1.49/1.28 inference(flattening,[status(thm)],[f7])).
% 1.49/1.28 thf(f7,plain,(
% 1.49/1.28 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X5 : a] : (($true = (X1 @ X5)) | ((X2 @ X5) != $true)) <~> ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0))))) & (! [X3 : a] : (((X1 @ X3) != $true) | ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X0 @ X4)) | ($true != (X2 @ X4)))))),
% 1.49/1.28 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.28 thf(f6,plain,(
% 1.49/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X2 @ X4)) => ($true = (X0 @ X4)))) => (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) <=> ! [X5 : a] : (((X2 @ X5) = $true) => ($true = (X1 @ X5)))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f5])).
% 1.49/1.28 thf(f5,plain,(
% 1.49/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X1 @ X3) = $true) => ((X0 @ X3) = $true)) & ! [X4 : a] : (($true = (X2 @ X4)) => ($true = (X0 @ X4)))) => (((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (X1 @ Y0)) & (X2 @ Y0)) & (X0 @ Y0)))) <=> ! [X7 : a] : (($true = (X2 @ X7)) => ($true = (X1 @ X7)))))),
% 1.49/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.28 thf(f4,plain,(
% 1.49/1.28 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X0 @ X3)) & ! [X4 : a] : ((X2 @ X4) => (X0 @ X4))) => (((^[X5 : a] : ($false)) = (^[X6 : a] : ((X0 @ X6) & (X2 @ X6) & ~(X1 @ X6)))) <=> ! [X7 : a] : ((X2 @ X7) => (X1 @ X7))))),
% 1.49/1.28 inference(rectify,[status(thm)],[f2])).
% 1.49/1.28 thf(f2,negated_conjecture,(
% 1.49/1.28 ~! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X0 @ X3) & ~(X1 @ X3)))) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 1.49/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.28 thf(f1,conjecture,(
% 1.49/1.28 ! [X2 : a > $o,X1 : a > $o,X0 : a > $o] : ((! [X3 : a] : ((X1 @ X3) => (X2 @ X3)) & ! [X3 : a] : ((X0 @ X3) => (X2 @ X3))) => (((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & (X0 @ X3) & ~(X1 @ X3)))) <=> ! [X3 : a] : ((X0 @ X3) => (X1 @ X3))))),
% 1.49/1.28 file('/export/starexec/sandbox/tmp/tmp.xPvGWdElb0/DTF2THF_5909.p',cGAZING_THM33_pme)).
% 1.49/1.28 thf(f37,plain,(
% 1.49/1.28 ~spl4_2 | spl4_4),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f18,f34,f24])).
% 1.49/1.28 thf(f18,plain,(
% 1.49/1.28 ($true = (sK2 @ sK3)) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.28 thf(f32,plain,(
% 1.49/1.28 ~spl4_3 | ~spl4_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f19,f24,f29])).
% 1.49/1.28 thf(f19,plain,(
% 1.49/1.28 ($true != (sK1 @ sK3)) | ((^[Y0 : a]: ($false)) != (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))))),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.28 thf(f27,plain,(
% 1.49/1.28 spl4_1 | spl4_2),
% 1.49/1.28 inference(avatar_split_clause,[status(thm)],[f17,f24,f21])).
% 1.49/1.28 thf(f17,plain,(
% 1.49/1.28 ( ! [X4 : a] : (($true = (sK1 @ X4)) | ($true != (sK2 @ X4)) | ((^[Y0 : a]: ($false)) = (^[Y0 : a]: (((~ (sK1 @ Y0)) & (sK2 @ Y0)) & (sK0 @ Y0))))) )),
% 1.49/1.28 inference(cnf_transformation,[status(thm)],[f14])).
% 1.49/1.28 % SZS output end Proof for DTF2THF_5909
% 1.49/1.28 % (6188)------------------------------
% 1.49/1.28 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.28 % (6188)Termination reason: Refutation
% 1.49/1.28
% 1.49/1.28 % (6188)Memory used [KB]: 5500
% 1.49/1.28 % (6188)Time elapsed: 0.005 s
% 1.49/1.28 % (6188)Instructions burned: 6 (million)
% 1.49/1.28 % (6188)------------------------------
% 1.49/1.28 % (6188)------------------------------
% 1.49/1.28 % (6185)Success in time 0.015 s
%------------------------------------------------------------------------------