%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV085^5 : 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 : n016.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 09:40:14 AM UTC 2026
% Result : Theorem 1.65s 1.40s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 389 ( 183 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 437 ( 55 ~; 48 |; 32 &; 295 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 297 ( 297 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 249 ( 108 ^; 100 !; 41 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_4,type,
sK1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_5,type,
sK2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_6,type,
sK3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f155,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
$false = $true,
inference(beta_eta_normalization,[status(thm)],[f133]) ).
thf(f133,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : $false
@ X1 ) ),
inference(primitive_instantiation,[status(thm)],[f131]) ).
thf(f131,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( X0 @ X1 ) ),
inference(condensation,[status(thm)],[f130]) ).
thf(f130,plain,
! [X3: $i,X1: $i > $o,X6: $i > $o] :
( ( ( X1 @ X3 )
= $true )
| ( ( X6 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X3: $i,X1: $i > $o,X6: $i > $o] :
( ( ( X1 @ X3 )
= $true )
| ( $false
= ( ~ ( X6 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f103]) ).
thf(f103,plain,
! [X3: $i,X1: $i > $o,X6: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
~ ( X6 @ Y0 )
@ X3 ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( X2 @ X3 ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ),
inference(argument_congruence,[status(thm)],[f91]) ).
thf(f91,plain,
! [X2: $i > $o,X1: $i > $o] : ( X1 = X2 ),
inference(subsumption_resolution,[status(thm)],[f84,f63]) ).
thf(f63,plain,
( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ),
inference(forward_demodulation,[status(thm)],[f60,f41]) ).
thf(f41,plain,
( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) @ ( sK2 @ X0 ) )
= $true ) ),
inference(condensation,[status(thm)],[f16]) ).
thf(f16,plain,
! [X2: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o] :
( ( ( X0 @ ( sK0 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
| ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true ) ),
inference(condensation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o,X8: $i > $o,X6: $i > $o,X7: $i > $o,X5: $i > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK0 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
| ( $true
= ( X0 @ X8 @ X7 ) )
| ( ( X0 @ X5 @ X6 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( ( X0 @ ( sK0 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) )
| ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ! [X5: $i > $o,X6: $i > $o] :
( ( X0 @ X5 @ X6 )
!= $true )
| ! [X7: $i > $o,X8: $i > $o] :
( $true
= ( X0 @ X8 @ X7 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X2 )
= $true ) )
=> ( ( ( X0 @ ( sK0 @ X0 ) @ ( sK2 @ X0 ) )
= $true )
& ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
& ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X4: $i > $o] :
( $true
!= ( X0 @ X4 @ X4 ) )
=> ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( X0 @ X1 @ X3 )
= $true )
& ( ( X0 @ X1 @ X2 )
!= $true )
& ( ( X0 @ X3 @ X2 )
= $true ) )
| ? [X4: $i > $o] :
( $true
!= ( X0 @ X4 @ X4 ) )
| ! [X5: $i > $o,X6: $i > $o] :
( ( X0 @ X5 @ X6 )
!= $true )
| ! [X7: $i > $o,X8: $i > $o] :
( $true
= ( X0 @ X8 @ X7 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X5: $i > $o,X4: $i > $o,X6: $i > $o] :
( ( ( X0 @ X5 @ X6 )
= $true )
& ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X4 ) ) )
| ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ! [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X2 @ X1 )
!= $true )
| ! [X8: $i > $o,X7: $i > $o] :
( ( X0 @ X7 @ X8 )
= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
!= $true )
| ! [X8: $i > $o,X7: $i > $o] :
( ( X0 @ X7 @ X8 )
= $true )
| ! [X2: $i > $o,X1: $i > $o] :
( ( X0 @ X2 @ X1 )
!= $true )
| ? [X6: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X4 )
!= $true )
& ( $true
= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X6 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ! [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
= $true )
& ? [X8: $i > $o,X7: $i > $o] :
( ( X0 @ X7 @ X8 )
!= $true )
& ? [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X2 @ X1 )
= $true )
& ! [X6: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X6 )
= $true ) )
=> ( ( X0 @ X5 @ X4 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] :
( ( X0 @ X2 @ X1 )
= $true )
& ! [X3: $i > $o] :
( ( X0 @ X3 @ X3 )
= $true )
& ! [X6: $i > $o,X4: $i > $o,X5: $i > $o] :
( ( ( $true
= ( X0 @ X6 @ X4 ) )
& ( ( X0 @ X5 @ X6 )
= $true ) )
=> ( ( X0 @ X5 @ X4 )
= $true ) )
& ? [X7: $i > $o,X8: $i > $o] :
( ( X0 @ X7 @ X8 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X1: $i > $o,X2: $i > $o] : ( X0 @ X2 @ X1 )
& ! [X3: $i > $o] : ( X0 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X4 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X5 @ X4 ) )
& ? [X7: $i > $o,X8: $i > $o] :
~ ( X0 @ X7 @ X8 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X5: $i > $o] : ( X0 @ X5 @ X5 )
& ! [X7: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X7 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X5 @ X7 ) )
& ? [X3: $i > $o,X4: $i > $o] :
~ ( X0 @ X3 @ X4 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ? [X2: $i > $o,X1: $i > $o] : ( X0 @ X1 @ X2 )
& ! [X5: $i > $o] : ( X0 @ X5 @ X5 )
& ! [X7: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X0 @ X6 @ X7 )
& ( X0 @ X5 @ X6 ) )
=> ( X0 @ X5 @ X7 ) )
& ? [X3: $i > $o,X4: $i > $o] :
~ ( X0 @ X3 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.BVIVH7SlYS/DTF2THF_22672.p',cTHM120_2_pme) ).
thf(f60,plain,
( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true != $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ) ),
inference(boolean_simplification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true )
| ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK2
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ),
inference(condensation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o] :
( ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ),
inference(condensation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o,X8: $i > $o,X6: $i > $o,X7: $i > $o,X5: $i > $o] :
( ( ( X0 @ X5 @ X6 )
!= $true )
| ( $true
= ( X0 @ X8 @ X7 ) )
| ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK2 @ X0 ) @ ( sK1 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f84,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( X1 = X2 )
| ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
!= ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
| ( ( X2 = X1 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( X2 = X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( X2 = X1 )
= $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( X2 = X1 )
= $true )
| ( ( ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
= ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ X1
@ X2 )
= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK0
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK1
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true )
| ( ( ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) )
@ ( sK3
@ ^ [Y0: $i > $o,Y1: $i > $o] : ( Y1 = Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X2: $i > $o,X0: ( $i > $o ) > ( $i > $o ) > $o,X1: $i > $o] :
( ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true )
| ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
!= $true ) ),
inference(condensation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $o,X8: $i > $o,X6: $i > $o,X7: $i > $o,X5: $i > $o] :
( ( ( X0 @ ( sK0 @ X0 ) @ ( sK1 @ X0 ) )
!= $true )
| ( $true
= ( X0 @ X8 @ X7 ) )
| ( ( X0 @ X5 @ X6 )
!= $true )
| ( ( X0 @ ( sK3 @ X0 ) @ ( sK3 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV085^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:40:21 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.44 ---- Original DTF file ---
% 0.21/0.44 thf(spec,logic,$$dhol).
% 0.21/0.44 %------------------------------------------------------------------------------
% 0.21/0.44 % File : SEV085^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.44 % Domain : Set Theory (Relations)
% 0.21/0.44 % Problem : TPS problem from RELN-THMS
% 0.21/0.44 % Version : Especial.
% 0.21/0.44 % English :
% 0.21/0.44
% 0.21/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.44 % Source : [Bro09]
% 0.21/0.44 % Names : tps_0902 [Bro09]
% 0.21/0.44
% 0.21/0.44 % Status : Theorem
% 0.21/0.44 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.33 v8.2.0, 0.45 v8.1.0, 0.58 v7.5.0, 0.50 v7.4.0, 0.56 v7.3.0, 0.60 v7.2.0, 0.62 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.67 v6.1.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.50 v4.1.0, 0.33 v4.0.0
% 0.21/0.44 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.21/0.44 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.44 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.44 % Number of connectives : 18 ( 1 ~; 0 |; 4 &; 12 @)
% 0.21/0.44 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.44 % Maximal formula depth : 12 ( 12 avg)
% 0.21/0.44 % Number of types : 2 ( 0 usr)
% 0.21/0.44 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.21/0.44 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.44 % Number of variables : 9 ( 0 ^; 4 !; 5 ?; 9 :)
% 0.21/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.44
% 0.21/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.44 %------------------------------------------------------------------------------
% 0.21/0.44 thf(cTHM120_2_pme,conjecture,
% 0.21/0.44 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 0.21/0.44 ( ? [X: $i > $o,Y: $i > $o] : ( R @ X @ Y )
% 0.21/0.44 & ? [U: $i > $o,V: $i > $o] :
% 0.21/0.44 ~ ( R @ U @ V )
% 0.21/0.44 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 0.21/0.44 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 0.21/0.44 ( ( ( R @ Xx @ Xy )
% 0.21/0.44 & ( R @ Xy @ Xz ) )
% 0.21/0.44 => ( R @ Xx @ Xz ) ) ) ).
% 0.21/0.44
% 0.21/0.44 %------------------------------------------------------------------------------
% 0.21/0.44 ------------------------
% 1.50/1.36 ---- Embedded in THF ---
% 1.50/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.36 %%% Generated on Tue Feb 24 12:40:22 EST 2026
% 1.50/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.36 %%% Logic specification used:
% 1.50/1.36 %%% thf(spec, logic, $$dhol).
% 1.50/1.36
% 1.50/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BVIVH7SlYS/DTF2DTF22672.p
% See solution above
% 1.50/1.36 ------------------------
% 1.50/1.37 ---- Cleaned THF ---
% 1.50/1.37 thf(cTHM120_2_pme,conjecture,
% 1.50/1.37 ? [R: ( $i > $o ) > ( $i > $o ) > $o] :
% 1.50/1.37 ( ? [X: $i > $o,Y: $i > $o] : ( R @ X @ Y )
% 1.50/1.37 & ? [U: $i > $o,V: $i > $o] :
% 1.50/1.37 ~ ( R @ U @ V )
% 1.50/1.37 & ! [Xx: $i > $o] : ( R @ Xx @ Xx )
% 1.50/1.37 & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
% 1.50/1.37 ( ( ( R @ Xx @ Xy )
% 1.50/1.37 & ( R @ Xy @ Xz ) )
% 1.50/1.37 => ( R @ Xx @ Xz ) ) ) ).
% 1.50/1.37 ------------------------
% 1.50/1.39 % (22772)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22672 for (2999ds/2Mi)
% 1.50/1.39 % (22774)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_22672 for (2999ds/275Mi)
% 1.50/1.39 % (22775)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22672 for (2999ds/18Mi)
% 1.50/1.39 % (22771)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_22672 for (2999ds/27Mi)
% 1.50/1.39 % (22769)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22672 for (2999ds/183Mi)
% 1.50/1.39 % (22770)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_22672 for (2999ds/4Mi)
% 1.50/1.39 % (22773)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_22672 for (2999ds/2Mi)
% 1.50/1.39 % (22772)Instruction limit reached!
% 1.50/1.39 % (22772)------------------------------
% 1.50/1.39 % (22772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (22772)Termination reason: Unknown
% 1.50/1.39 % (22772)Termination phase: Saturation
% 1.50/1.39
% 1.50/1.39 % (22772)Memory used [KB]: 5373
% 1.50/1.39 % (22772)Time elapsed: 0.003 s
% 1.50/1.39 % (22772)Instructions burned: 2 (million)
% 1.50/1.39 % (22772)------------------------------
% 1.50/1.39 % (22772)------------------------------
% 1.50/1.39 % (22773)Instruction limit reached!
% 1.50/1.39 % (22773)------------------------------
% 1.50/1.39 % (22773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (22773)Termination reason: Unknown
% 1.50/1.39 % (22773)Termination phase: Saturation
% 1.50/1.39
% 1.50/1.39 % (22773)Memory used [KB]: 5500
% 1.50/1.39 % (22773)Time elapsed: 0.003 s
% 1.50/1.39 % (22773)Instructions burned: 2 (million)
% 1.50/1.39 % (22773)------------------------------
% 1.50/1.39 % (22773)------------------------------
% 1.50/1.39 % (22771)Refutation not found, incomplete strategy
% 1.50/1.39 % (22771)------------------------------
% 1.50/1.39 % (22771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (22771)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.39
% 1.50/1.39
% 1.50/1.39 % (22771)Memory used [KB]: 5500
% 1.50/1.39 % (22771)Time elapsed: 0.003 s
% 1.50/1.39 % (22771)Instructions burned: 2 (million)
% 1.50/1.39 % (22771)------------------------------
% 1.50/1.39 % (22771)------------------------------
% 1.50/1.39 % (22770)Instruction limit reached!
% 1.50/1.39 % (22770)------------------------------
% 1.50/1.39 % (22770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.39 % (22770)Termination reason: Unknown
% 1.50/1.39 % (22770)Termination phase: Saturation
% 1.50/1.39
% 1.50/1.39 % (22770)Memory used [KB]: 5500
% 1.50/1.39 % (22770)Time elapsed: 0.005 s
% 1.50/1.39 % (22770)Instructions burned: 5 (million)
% 1.50/1.39 % (22770)------------------------------
% 1.50/1.39 % (22770)------------------------------
% 1.65/1.40 % (22775)First to succeed.
% 1.65/1.40 % (22775)Refutation found. Thanks to Tanya!
% 1.65/1.40 % SZS status Theorem for DTF2THF_22672
% 1.65/1.40 % SZS output start Proof for DTF2THF_22672
% 1.65/1.40 thf(func_def_3, type, sK0: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.65/1.40 thf(func_def_4, type, sK1: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.65/1.40 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.65/1.40 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o).
% 1.65/1.40 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.65/1.40 thf(f155,plain,(
% 1.65/1.40 $false),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.65/1.40 thf(f154,plain,(
% 1.65/1.40 ($false = $true)),
% 1.65/1.40 inference(beta_eta_normalization,[status(thm)],[f133])).
% 1.65/1.40 thf(f133,plain,(
% 1.65/1.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ($false)) @ X1))) )),
% 1.65/1.40 inference(primitive_instantiation,[status(thm)],[f131])).
% 1.65/1.40 thf(f131,plain,(
% 1.65/1.40 ( ! [X0 : $i > $o,X1 : $i] : (($true = (X0 @ X1))) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f130])).
% 1.65/1.40 thf(f130,plain,(
% 1.65/1.40 ( ! [X3 : $i,X1 : $i > $o,X6 : $i > $o] : (((X1 @ X3) = $true) | ((X6 @ X3) = $true)) )),
% 1.65/1.40 inference(not_proxy_clausification,[status(thm)],[f129])).
% 1.65/1.40 thf(f129,plain,(
% 1.65/1.40 ( ! [X3 : $i,X1 : $i > $o,X6 : $i > $o] : (((X1 @ X3) = $true) | ($false = (~ (X6 @ X3)))) )),
% 1.65/1.40 inference(beta_eta_normalization,[status(thm)],[f103])).
% 1.65/1.40 thf(f103,plain,(
% 1.65/1.40 ( ! [X3 : $i,X1 : $i > $o,X6 : $i > $o] : (($false = ((^[Y0 : $i]: (~ (X6 @ Y0))) @ X3)) | ((X1 @ X3) = $true)) )),
% 1.65/1.40 inference(primitive_instantiation,[status(thm)],[f99])).
% 1.65/1.40 thf(f99,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $o] : (($false = (X2 @ X3)) | ((X1 @ X3) = $true)) )),
% 1.65/1.40 inference(binary_proxy_clausification,[status(thm)],[f92])).
% 1.65/1.40 thf(f92,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i > $o] : (((X1 @ X3) = (X2 @ X3))) )),
% 1.65/1.40 inference(argument_congruence,[status(thm)],[f91])).
% 1.65/1.40 thf(f91,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : ((X1 = X2)) )),
% 1.65/1.40 inference(subsumption_resolution,[status(thm)],[f84,f63])).
% 1.65/1.40 thf(f63,plain,(
% 1.65/1.40 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.65/1.40 inference(forward_demodulation,[status(thm)],[f60,f41])).
% 1.65/1.40 thf(f41,plain,(
% 1.65/1.40 ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.65/1.40 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.65/1.40 thf(f40,plain,(
% 1.65/1.40 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.65/1.40 thf(f39,plain,(
% 1.65/1.40 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true)),
% 1.65/1.40 inference(boolean_simplification,[status(thm)],[f38])).
% 1.65/1.40 thf(f38,plain,(
% 1.65/1.40 (((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 1.65/1.40 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.65/1.40 thf(f21,plain,(
% 1.65/1.40 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 1.65/1.40 inference(primitive_instantiation,[status(thm)],[f17])).
% 1.65/1.40 thf(f17,plain,(
% 1.65/1.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK0 @ X0) @ (sK2 @ X0)) = $true)) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f16])).
% 1.65/1.40 thf(f16,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X0 : ($i > $o) > ($i > $o) > $o,X1 : $i > $o] : (((X0 @ (sK0 @ X0) @ (sK2 @ X0)) = $true) | ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ X1 @ X2) = $true)) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f15])).
% 1.65/1.40 thf(f15,plain,(
% 1.65/1.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o,X8 : $i > $o,X6 : $i > $o,X7 : $i > $o,X5 : $i > $o] : (((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK0 @ X0) @ (sK2 @ X0)) = $true) | ($true = (X0 @ X8 @ X7)) | ((X0 @ X5 @ X6) != $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.40 thf(f12,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK0 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK0 @ X0) @ (sK1 @ X0)) != $true) & ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) = $true)) | ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ! [X5 : $i > $o,X6 : $i > $o] : ((X0 @ X5 @ X6) != $true) | ! [X7 : $i > $o,X8 : $i > $o] : ($true = (X0 @ X8 @ X7)))),
% 1.65/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
% 1.65/1.40 thf(f10,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X3) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X3 @ X2) = $true)) => (((X0 @ (sK0 @ X0) @ (sK2 @ X0)) = $true) & ((X0 @ (sK0 @ X0) @ (sK1 @ X0)) != $true) & ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) = $true)))),
% 1.65/1.40 introduced(definition,[],[choice_axiom])).
% 1.65/1.40 thf(f11,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) => ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true))),
% 1.65/1.40 introduced(definition,[],[choice_axiom])).
% 1.65/1.40 thf(f9,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X3) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X3 @ X2) = $true)) | ? [X4 : $i > $o] : ($true != (X0 @ X4 @ X4)) | ! [X5 : $i > $o,X6 : $i > $o] : ((X0 @ X5 @ X6) != $true) | ! [X7 : $i > $o,X8 : $i > $o] : ($true = (X0 @ X8 @ X7)))),
% 1.65/1.40 inference(rectify,[status(thm)],[f8])).
% 1.65/1.40 thf(f8,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X5 : $i > $o,X4 : $i > $o,X6 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ((X0 @ X5 @ X4) != $true) & ($true = (X0 @ X6 @ X4))) | ? [X3 : $i > $o] : ((X0 @ X3 @ X3) != $true) | ! [X2 : $i > $o,X1 : $i > $o] : ((X0 @ X2 @ X1) != $true) | ! [X8 : $i > $o,X7 : $i > $o] : ((X0 @ X7 @ X8) = $true))),
% 1.65/1.40 inference(flattening,[status(thm)],[f7])).
% 1.65/1.40 thf(f7,plain,(
% 1.65/1.40 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3 : $i > $o] : ((X0 @ X3 @ X3) != $true) | ! [X8 : $i > $o,X7 : $i > $o] : ((X0 @ X7 @ X8) = $true) | ! [X2 : $i > $o,X1 : $i > $o] : ((X0 @ X2 @ X1) != $true) | ? [X6 : $i > $o,X4 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X4) != $true) & (($true = (X0 @ X6 @ X4)) & ((X0 @ X5 @ X6) = $true))))),
% 1.65/1.40 inference(ennf_transformation,[status(thm)],[f6])).
% 1.65/1.40 thf(f6,plain,(
% 1.65/1.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X3 : $i > $o] : ((X0 @ X3 @ X3) = $true) & ? [X8 : $i > $o,X7 : $i > $o] : ((X0 @ X7 @ X8) != $true) & ? [X1 : $i > $o,X2 : $i > $o] : ((X0 @ X2 @ X1) = $true) & ! [X6 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((($true = (X0 @ X6 @ X4)) & ((X0 @ X5 @ X6) = $true)) => ((X0 @ X5 @ X4) = $true)))),
% 1.65/1.40 inference(flattening,[status(thm)],[f5])).
% 1.65/1.40 thf(f5,plain,(
% 1.65/1.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : ((X0 @ X2 @ X1) = $true) & ! [X3 : $i > $o] : ((X0 @ X3 @ X3) = $true) & ! [X6 : $i > $o,X4 : $i > $o,X5 : $i > $o] : ((($true = (X0 @ X6 @ X4)) & ((X0 @ X5 @ X6) = $true)) => ((X0 @ X5 @ X4) = $true)) & ? [X7 : $i > $o,X8 : $i > $o] : ~((X0 @ X7 @ X8) = $true))),
% 1.65/1.40 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.40 thf(f4,plain,(
% 1.65/1.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (X0 @ X2 @ X1) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X4 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X4) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X4)) & ? [X7 : $i > $o,X8 : $i > $o] : ~(X0 @ X7 @ X8))),
% 1.65/1.40 inference(rectify,[status(thm)],[f2])).
% 1.65/1.40 thf(f2,negated_conjecture,(
% 1.65/1.40 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (X0 @ X1 @ X2) & ! [X5 : $i > $o] : (X0 @ X5 @ X5) & ! [X7 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X7) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X7)) & ? [X3 : $i > $o,X4 : $i > $o] : ~(X0 @ X3 @ X4))),
% 1.65/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.40 thf(f1,conjecture,(
% 1.65/1.40 ? [X0 : ($i > $o) > ($i > $o) > $o] : (? [X2 : $i > $o,X1 : $i > $o] : (X0 @ X1 @ X2) & ! [X5 : $i > $o] : (X0 @ X5 @ X5) & ! [X7 : $i > $o,X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X7) & (X0 @ X5 @ X6)) => (X0 @ X5 @ X7)) & ? [X3 : $i > $o,X4 : $i > $o] : ~(X0 @ X3 @ X4))),
% 1.65/1.40 file('/export/starexec/sandbox/tmp/tmp.BVIVH7SlYS/DTF2THF_22672.p',cTHM120_2_pme)).
% 1.65/1.40 thf(f60,plain,(
% 1.65/1.40 ((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))),
% 1.65/1.40 inference(equality_proxy_clausification,[status(thm)],[f59])).
% 1.65/1.40 thf(f59,plain,(
% 1.65/1.40 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.40 thf(f58,plain,(
% 1.65/1.40 ($true != $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.65/1.40 inference(boolean_simplification,[status(thm)],[f57])).
% 1.65/1.40 thf(f57,plain,(
% 1.65/1.40 (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)),
% 1.65/1.40 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.65/1.40 thf(f42,plain,(
% 1.65/1.40 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)),
% 1.65/1.40 inference(primitive_instantiation,[status(thm)],[f20])).
% 1.65/1.40 thf(f20,plain,(
% 1.65/1.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) = $true)) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f19])).
% 1.65/1.40 thf(f19,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X0 : ($i > $o) > ($i > $o) > $o,X1 : $i > $o] : (((X0 @ X1 @ X2) = $true) | ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) = $true)) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f13])).
% 1.65/1.40 thf(f13,plain,(
% 1.65/1.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o,X8 : $i > $o,X6 : $i > $o,X7 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) != $true) | ($true = (X0 @ X8 @ X7)) | ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ (sK2 @ X0) @ (sK1 @ X0)) = $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.40 thf(f84,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : ((X1 = X2) | ((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) )),
% 1.65/1.40 inference(equality_proxy_clausification,[status(thm)],[f83])).
% 1.65/1.40 thf(f83,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((X2 = X1) = $true)) )),
% 1.65/1.40 inference(equality_proxy_clausification,[status(thm)],[f82])).
% 1.65/1.40 thf(f82,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((X2 = X1) = $true)) )),
% 1.65/1.40 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.65/1.40 thf(f81,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : (((X2 = X1) = $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true != $true)) )),
% 1.65/1.40 inference(boolean_simplification,[status(thm)],[f80])).
% 1.65/1.40 thf(f80,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((X2 = X1) = $true) | (((sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)) )),
% 1.65/1.40 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.65/1.40 thf(f64,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ X1 @ X2) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true)) )),
% 1.65/1.40 inference(primitive_instantiation,[status(thm)],[f18])).
% 1.65/1.40 thf(f18,plain,(
% 1.65/1.40 ( ! [X2 : $i > $o,X0 : ($i > $o) > ($i > $o) > $o,X1 : $i > $o] : (((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true) | ((X0 @ X1 @ X2) = $true) | ((X0 @ (sK0 @ X0) @ (sK1 @ X0)) != $true)) )),
% 1.65/1.40 inference(condensation,[status(thm)],[f14])).
% 1.65/1.40 thf(f14,plain,(
% 1.65/1.40 ( ! [X0 : ($i > $o) > ($i > $o) > $o,X8 : $i > $o,X6 : $i > $o,X7 : $i > $o,X5 : $i > $o] : (((X0 @ (sK0 @ X0) @ (sK1 @ X0)) != $true) | ($true = (X0 @ X8 @ X7)) | ((X0 @ X5 @ X6) != $true) | ((X0 @ (sK3 @ X0) @ (sK3 @ X0)) != $true)) )),
% 1.65/1.40 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.40 % SZS output end Proof for DTF2THF_22672
% 1.65/1.40 % (22775)------------------------------
% 1.65/1.40 % (22775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (22775)Termination reason: Refutation
% 1.65/1.40
% 1.65/1.40 % (22775)Memory used [KB]: 5500
% 1.65/1.40 % (22775)Time elapsed: 0.011 s
% 1.65/1.40 % (22775)Instructions burned: 14 (million)
% 1.65/1.40 % (22775)------------------------------
% 1.65/1.40 % (22775)------------------------------
% 1.65/1.40 % (22768)Success in time 0.025 s
%------------------------------------------------------------------------------