%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO170^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:53:34 AM UTC 2026
% Result : Theorem 1.62s 1.47s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 573 ( 83 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 988 ( 4 ~; 0 |; 56 &; 773 @)
% ( 3 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 7 con; 0-3 aty)
% ( 106 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 215 ( 115 ^; 100 !; 0 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
cP: $i > $i > $i > $o ).
thf(func_def_21,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f1264,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1262]) ).
thf(f1262,plain,
$true = $false,
inference(superposition,[status(thm)],[f1215,f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( cP @ X1 @ e @ X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) ) ),
inference(boolean_simplification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f27,f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f23,f24]) ).
thf(f24,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f11,f20]) ).
thf(f20,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 ) ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 ) ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ e @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 ) ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] : ( cP @ e @ X0 @ X0 )
& ! [X1: $i] : ( cP @ X1 @ X1 @ e )
& ! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( cP @ X5 @ X3 @ X4 )
& ( cP @ X3 @ X6 @ X2 ) )
=> ( ( cP @ X4 @ X6 @ X7 )
<=> ( cP @ X5 @ X2 @ X7 ) ) )
& ! [X8: $i] : ( cP @ X8 @ e @ X8 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] : ( cP @ e @ X0 @ X0 )
& ! [X2: $i] : ( cP @ X2 @ X2 @ e )
& ! [X4: $i,X1: $i,X3: $i,X0: $i,X2: $i,X5: $i] :
( ( ( cP @ X0 @ X1 @ X3 )
& ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
<=> ( cP @ X0 @ X4 @ X5 ) ) )
& ! [X1: $i] : ( cP @ X1 @ e @ X1 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] : ( cP @ e @ X0 @ X0 )
& ! [X2: $i] : ( cP @ X2 @ X2 @ e )
& ! [X4: $i,X1: $i,X3: $i,X0: $i,X2: $i,X5: $i] :
( ( ( cP @ X0 @ X1 @ X3 )
& ( cP @ X1 @ X2 @ X4 ) )
=> ( ( cP @ X3 @ X2 @ X5 )
<=> ( cP @ X0 @ X4 @ X5 ) ) )
& ! [X1: $i] : ( cP @ X1 @ e @ X1 ) )
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jUI57ZfkmQ/DTF2THF_21841.p',cTHM105) ).
thf(f1215,plain,
( ( cP @ ab @ e @ ab )
= $false ),
inference(superposition,[status(thm)],[f14,f1092]) ).
thf(f1092,plain,
! [X0: $i] :
( ( cP @ ab @ e @ X0 )
= ( cP @ b @ a @ X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1091]) ).
thf(f1091,plain,
! [X0: $i] :
( $true
= ( ( cP @ b @ a @ X0 )
= ( cP @ ab @ e @ X0 ) ) ),
inference(boolean_simplification,[status(thm)],[f1065]) ).
thf(f1065,plain,
! [X0: $i] :
( ( $true
=> ( ( cP @ b @ a @ X0 )
= ( cP @ ab @ e @ X0 ) ) )
= $true ),
inference(superposition,[status(thm)],[f72,f949]) ).
thf(f949,plain,
( $true
= ( cP @ ab @ a @ b ) ),
inference(superposition,[status(thm)],[f29,f829]) ).
thf(f829,plain,
! [X0: $i] :
( ( cP @ e @ b @ X0 )
= ( cP @ ab @ a @ X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f828]) ).
thf(f828,plain,
! [X0: $i] :
( $true
= ( ( cP @ e @ b @ X0 )
= ( cP @ ab @ a @ X0 ) ) ),
inference(boolean_simplification,[status(thm)],[f809]) ).
thf(f809,plain,
! [X0: $i] :
( $true
= ( $true
=> ( ( cP @ e @ b @ X0 )
= ( cP @ ab @ a @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f86,f284]) ).
thf(f284,plain,
( ( cP @ ab @ b @ a )
= $true ),
inference(superposition,[status(thm)],[f122,f35]) ).
thf(f122,plain,
! [X0: $i] :
( ( cP @ a @ e @ X0 )
= ( cP @ ab @ b @ X0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X0: $i] :
( $true
= ( ( cP @ ab @ b @ X0 )
= ( cP @ a @ e @ X0 ) ) ),
inference(boolean_simplification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X0: $i] :
( $true
= ( $true
=> ( ( cP @ ab @ b @ X0 )
= ( cP @ a @ e @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f72,f15]) ).
thf(f15,plain,
( ( cP @ a @ b @ ab )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( $true
=> ( ( cP @ a @ b @ ab )
=> ( cP @ b @ a @ ab ) ) ) ),
inference(backward_demodulation,[status(thm)],[f7,f11]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( $true
= ( ( cP @ X0 @ X1 @ X2 )
=> ( ( cP @ e @ X1 @ X3 )
= ( cP @ X0 @ X2 @ X3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( $true
= ( ( ( cP @ X0 @ X1 @ X2 )
& $true )
=> ( ( cP @ e @ X1 @ X3 )
= ( cP @ X0 @ X2 @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f49,f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( cP @ X1 @ X1 @ e ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( cP @ Y0 @ Y0 @ e )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( $true
= ( ( ( cP @ X5 @ X2 @ X6 )
& ( cP @ X3 @ X5 @ X4 ) )
=> ( ( cP @ X4 @ X2 @ X1 )
= ( cP @ X3 @ X6 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( cP @ X5 @ X2 @ Y0 )
& ( cP @ X3 @ X5 @ X4 ) )
=> ( ( cP @ X4 @ X2 @ X1 )
= ( cP @ X3 @ Y0 @ X1 ) ) )
@ X6 ) ),
inference(pi_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( cP @ X5 @ X2 @ Y0 )
& ( cP @ X3 @ X5 @ X4 ) )
=> ( ( cP @ X4 @ X2 @ X1 )
= ( cP @ X3 @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cP @ Y0 @ X2 @ Y1 )
& ( cP @ X3 @ Y0 @ X4 ) )
=> ( ( cP @ X4 @ X2 @ X1 )
= ( cP @ X3 @ Y1 @ X1 ) ) ) )
@ X5 ) ),
inference(pi_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( cP @ Y0 @ X2 @ Y1 )
& ( cP @ X3 @ Y0 @ X4 ) )
=> ( ( cP @ X4 @ X2 @ X1 )
= ( cP @ X3 @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( cP @ Y1 @ X2 @ Y2 )
& ( cP @ X3 @ Y1 @ Y0 ) )
=> ( ( cP @ Y0 @ X2 @ X1 )
= ( cP @ X3 @ Y2 @ X1 ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( cP @ Y1 @ X2 @ Y2 )
& ( cP @ X3 @ Y1 @ Y0 ) )
=> ( ( cP @ Y0 @ X2 @ X1 )
= ( cP @ X3 @ Y2 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( cP @ Y2 @ X2 @ Y3 )
& ( cP @ Y0 @ Y2 @ Y1 ) )
=> ( ( cP @ Y1 @ X2 @ X1 )
= ( cP @ Y0 @ Y3 @ X1 ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( cP @ Y2 @ X2 @ Y3 )
& ( cP @ Y0 @ Y2 @ Y1 ) )
=> ( ( cP @ Y1 @ X2 @ X1 )
= ( cP @ Y0 @ Y3 @ X1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( cP @ Y3 @ Y0 @ Y4 )
& ( cP @ Y1 @ Y3 @ Y2 ) )
=> ( ( cP @ Y2 @ Y0 @ X1 )
= ( cP @ Y1 @ Y4 @ X1 ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( cP @ Y3 @ Y0 @ Y4 )
& ( cP @ Y1 @ Y3 @ Y2 ) )
=> ( ( cP @ Y2 @ Y0 @ X1 )
= ( cP @ Y1 @ Y4 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( ( cP @ Y4 @ Y1 @ Y5 )
& ( cP @ Y2 @ Y4 @ Y3 ) )
=> ( ( cP @ Y3 @ Y1 @ Y0 )
= ( cP @ Y2 @ Y5 @ Y0 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( cP @ e @ X1 @ X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( cP @ e @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f20]) ).
thf(f72,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( cP @ X1 @ X0 @ X2 )
=> ( ( cP @ X2 @ X0 @ X3 )
= ( cP @ X1 @ e @ X3 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( $true
= ( ( $true
& ( cP @ X1 @ X0 @ X2 ) )
=> ( ( cP @ X2 @ X0 @ X3 )
= ( cP @ X1 @ e @ X3 ) ) ) ),
inference(superposition,[status(thm)],[f49,f37]) ).
thf(f14,plain,
( ( cP @ b @ a @ ab )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO170^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:25:14 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO170^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : TPS problem from BASIC-FO-THMS
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0996 [Bro09]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.28/0.46 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 9 ( 9 avg)
% 0.28/0.46 % Number of connectives : 35 ( 0 ~; 0 |; 4 &; 27 @)
% 0.28/0.46 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 16 ( 16 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 5 ( 5 usr; 4 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.28/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(ab,type,
% 0.28/0.46 ab: $i ).
% 0.28/0.46
% 0.28/0.46 thf(a,type,
% 0.28/0.46 a: $i ).
% 0.28/0.46
% 0.28/0.46 thf(b,type,
% 0.28/0.46 b: $i ).
% 0.28/0.46
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $i > $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(e,type,
% 0.28/0.46 e: $i ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM105,conjecture,
% 0.28/0.46 ( ( ! [Xx: $i] : ( cP @ e @ Xx @ Xx )
% 0.28/0.46 & ! [Xy: $i] : ( cP @ Xy @ e @ Xy )
% 0.28/0.46 & ! [Xz: $i] : ( cP @ Xz @ Xz @ e )
% 0.28/0.46 & ! [Xx: $i,Xy: $i,Xz: $i,Xxy: $i,Xyz: $i,Xxyz: $i] :
% 0.28/0.46 ( ( ( cP @ Xx @ Xy @ Xxy )
% 0.28/0.46 & ( cP @ Xy @ Xz @ Xyz ) )
% 0.28/0.46 => ( ( cP @ Xxy @ Xz @ Xxyz )
% 0.28/0.46 <=> ( cP @ Xx @ Xyz @ Xxyz ) ) ) )
% 0.28/0.46 => ( ( cP @ a @ b @ ab )
% 0.28/0.46 => ( cP @ b @ a @ ab ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 14:25:15 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.jUI57ZfkmQ/DTF2DTF21841.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf(ab,type,
% 1.45/1.28 ab: $i ).
% 1.45/1.28
% 1.45/1.28 thf(a,type,
% 1.45/1.28 a: $i ).
% 1.45/1.28
% 1.45/1.28 thf(b,type,
% 1.45/1.28 b: $i ).
% 1.45/1.28
% 1.45/1.28 thf(cP,type,
% 1.45/1.28 cP: $i > $i > $i > $o ).
% 1.45/1.28
% 1.45/1.28 thf(e,type,
% 1.45/1.28 e: $i ).
% 1.45/1.28
% 1.45/1.28 thf(cTHM105,conjecture,
% 1.45/1.28 ( ( ! [Xx: $i] : ( cP @ e @ Xx @ Xx )
% 1.45/1.28 & ! [Xy: $i] : ( cP @ Xy @ e @ Xy )
% 1.45/1.28 & ! [Xz: $i] : ( cP @ Xz @ Xz @ e )
% 1.45/1.28 & ! [Xx: $i,Xy: $i,Xz: $i,Xxy: $i,Xyz: $i,Xxyz: $i] :
% 1.45/1.28 ( ( ( cP @ Xx @ Xy @ Xxy )
% 1.45/1.28 & ( cP @ Xy @ Xz @ Xyz ) )
% 1.45/1.28 => ( ( cP @ Xxy @ Xz @ Xxyz )
% 1.45/1.28 <=> ( cP @ Xx @ Xyz @ Xxyz ) ) ) )
% 1.45/1.28 => ( ( cP @ a @ b @ ab )
% 1.45/1.28 => ( cP @ b @ a @ ab ) ) ) ).
% 1.45/1.28 ------------------------
% 1.45/1.29 % (22060)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_21841 for (2999ds/2Mi)
% 1.45/1.29 % (22058)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_21841 for (2999ds/27Mi)
% 1.45/1.29 % (22060)Instruction limit reached!
% 1.45/1.29 % (22060)------------------------------
% 1.45/1.29 % (22060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (22060)Termination reason: Unknown
% 1.45/1.29 % (22060)Termination phase: Saturation
% 1.45/1.29
% 1.45/1.29 % (22060)Memory used [KB]: 5500
% 1.45/1.29 % (22060)Time elapsed: 0.003 s
% 1.45/1.29 % (22060)Instructions burned: 3 (million)
% 1.45/1.29 % (22060)------------------------------
% 1.45/1.29 % (22060)------------------------------
% 1.62/1.30 % (22056)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/183Mi)
% 1.62/1.30 % (22057)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_21841 for (2999ds/4Mi)
% 1.62/1.30 % (22061)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_21841 for (2999ds/275Mi)
% 1.62/1.30 % (22062)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/18Mi)
% 1.62/1.30 % (22059)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/2Mi)
% 1.62/1.30 % (22059)Instruction limit reached!
% 1.62/1.30 % (22059)------------------------------
% 1.62/1.30 % (22059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (22059)Termination reason: Unknown
% 1.62/1.30 % (22059)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (22059)Memory used [KB]: 5500
% 1.62/1.30 % (22059)Time elapsed: 0.003 s
% 1.62/1.30 % (22059)Instructions burned: 2 (million)
% 1.62/1.30 % (22059)------------------------------
% 1.62/1.30 % (22059)------------------------------
% 1.62/1.30 % (22057)Instruction limit reached!
% 1.62/1.30 % (22057)------------------------------
% 1.62/1.30 % (22057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (22057)Termination reason: Unknown
% 1.62/1.30 % (22057)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (22057)Memory used [KB]: 5500
% 1.62/1.30 % (22057)Time elapsed: 0.005 s
% 1.62/1.30 % (22057)Instructions burned: 4 (million)
% 1.62/1.30 % (22057)------------------------------
% 1.62/1.30 % (22057)------------------------------
% 1.62/1.30 % (22058)Instruction limit reached!
% 1.62/1.30 % (22058)------------------------------
% 1.62/1.30 % (22058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (22058)Termination reason: Unknown
% 1.62/1.30 % (22058)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (22058)Memory used [KB]: 5628
% 1.62/1.30 % (22058)Time elapsed: 0.011 s
% 1.62/1.30 % (22058)Instructions burned: 28 (million)
% 1.62/1.30 % (22058)------------------------------
% 1.62/1.30 % (22058)------------------------------
% 1.62/1.30 % (22063)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/3Mi)
% 1.62/1.30 % (22063)Instruction limit reached!
% 1.62/1.30 % (22063)------------------------------
% 1.62/1.30 % (22063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (22063)Termination reason: Unknown
% 1.62/1.30 % (22063)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (22063)Memory used [KB]: 5500
% 1.62/1.30 % (22063)Time elapsed: 0.002 s
% 1.62/1.30 % (22063)Instructions burned: 3 (million)
% 1.62/1.30 % (22063)------------------------------
% 1.62/1.30 % (22063)------------------------------
% 1.62/1.31 % (22062)Instruction limit reached!
% 1.62/1.31 % (22062)------------------------------
% 1.62/1.31 % (22062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (22062)Termination reason: Unknown
% 1.62/1.31 % (22062)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (22062)Memory used [KB]: 5628
% 1.62/1.31 % (22062)Time elapsed: 0.014 s
% 1.62/1.31 % (22062)Instructions burned: 19 (million)
% 1.62/1.31 % (22062)------------------------------
% 1.62/1.31 % (22062)------------------------------
% 1.62/1.31 % (22066)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/3Mi)
% 1.62/1.31 % (22067)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/1041Mi)
% 1.62/1.31 % (22066)Instruction limit reached!
% 1.62/1.31 % (22066)------------------------------
% 1.62/1.31 % (22066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (22066)Termination reason: Unknown
% 1.62/1.31 % (22066)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (22066)Memory used [KB]: 5500
% 1.62/1.31 % (22066)Time elapsed: 0.003 s
% 1.62/1.31 % (22066)Instructions burned: 3 (million)
% 1.62/1.31 % (22066)------------------------------
% 1.62/1.31 % (22066)------------------------------
% 1.62/1.32 % (22064)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/37Mi)
% 1.62/1.32 % (22065)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/15Mi)
% 1.62/1.32 % (22069)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/16Mi)
% 1.62/1.33 % (22065)Instruction limit reached!
% 1.62/1.33 % (22065)------------------------------
% 1.62/1.33 % (22065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (22065)Termination reason: Unknown
% 1.62/1.33 % (22065)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (22065)Memory used [KB]: 5500
% 1.62/1.33 % (22065)Time elapsed: 0.011 s
% 1.62/1.33 % (22065)Instructions burned: 15 (million)
% 1.62/1.33 % (22065)------------------------------
% 1.62/1.33 % (22065)------------------------------
% 1.62/1.33 % (22068)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/7Mi)
% 1.62/1.33 % (22069)Instruction limit reached!
% 1.62/1.33 % (22069)------------------------------
% 1.62/1.33 % (22069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (22069)Termination reason: Unknown
% 1.62/1.33 % (22069)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (22069)Memory used [KB]: 5628
% 1.62/1.33 % (22069)Time elapsed: 0.008 s
% 1.62/1.33 % (22069)Instructions burned: 17 (million)
% 1.62/1.33 % (22069)------------------------------
% 1.62/1.33 % (22069)------------------------------
% 1.62/1.33 % (22068)Instruction limit reached!
% 1.62/1.33 % (22068)------------------------------
% 1.62/1.33 % (22068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (22068)Termination reason: Unknown
% 1.62/1.33 % (22068)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (22068)Memory used [KB]: 1023
% 1.62/1.33 % (22068)Time elapsed: 0.006 s
% 1.62/1.33 % (22068)Instructions burned: 7 (million)
% 1.62/1.33 % (22068)------------------------------
% 1.62/1.33 % (22068)------------------------------
% 1.62/1.34 % (22064)Instruction limit reached!
% 1.62/1.34 % (22064)------------------------------
% 1.62/1.34 % (22064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (22064)Termination reason: Unknown
% 1.62/1.34 % (22064)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (22064)Memory used [KB]: 5628
% 1.62/1.34 % (22064)Time elapsed: 0.023 s
% 1.62/1.34 % (22064)Instructions burned: 37 (million)
% 1.62/1.34 % (22064)------------------------------
% 1.62/1.34 % (22064)------------------------------
% 1.62/1.34 % (22071)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/3Mi)
% 1.62/1.34 % (22071)Instruction limit reached!
% 1.62/1.34 % (22071)------------------------------
% 1.62/1.34 % (22071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (22071)Termination reason: Unknown
% 1.62/1.34 % (22071)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (22071)Memory used [KB]: 5500
% 1.62/1.34 % (22071)Time elapsed: 0.003 s
% 1.62/1.34 % (22071)Instructions burned: 4 (million)
% 1.62/1.34 % (22071)------------------------------
% 1.62/1.34 % (22071)------------------------------
% 1.62/1.35 % (22072)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/7Mi)
% 1.62/1.35 % (22070)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/3Mi)
% 1.62/1.35 % (22072)Refutation not found, incomplete strategy
% 1.62/1.35 % (22072)------------------------------
% 1.62/1.35 % (22072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (22072)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.35
% 1.62/1.35
% 1.62/1.35 % (22072)Memory used [KB]: 5500
% 1.62/1.35 % (22072)Time elapsed: 0.002 s
% 1.62/1.35 % (22072)Instructions burned: 2 (million)
% 1.62/1.35 % (22072)------------------------------
% 1.62/1.35 % (22072)------------------------------
% 1.62/1.35 % (22070)Instruction limit reached!
% 1.62/1.35 % (22070)------------------------------
% 1.62/1.35 % (22070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (22070)Termination reason: Unknown
% 1.62/1.35 % (22070)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (22070)Memory used [KB]: 5500
% 1.62/1.35 % (22070)Time elapsed: 0.004 s
% 1.62/1.35 % (22070)Instructions burned: 3 (million)
% 1.62/1.35 % (22070)------------------------------
% 1.62/1.35 % (22070)------------------------------
% 1.62/1.35 % (22074)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/4Mi)
% 1.62/1.35 % (22074)Instruction limit reached!
% 1.62/1.35 % (22074)------------------------------
% 1.62/1.35 % (22074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (22074)Termination reason: Unknown
% 1.62/1.35 % (22074)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (22074)Memory used [KB]: 5500
% 1.62/1.35 % (22074)Time elapsed: 0.004 s
% 1.62/1.35 % (22074)Instructions burned: 6 (million)
% 1.62/1.35 % (22074)------------------------------
% 1.62/1.35 % (22074)------------------------------
% 1.62/1.36 % (22073)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/3Mi)
% 1.62/1.36 % (22075)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/18Mi)
% 1.62/1.36 % (22073)Instruction limit reached!
% 1.62/1.36 % (22073)------------------------------
% 1.62/1.36 % (22073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (22073)Termination reason: Unknown
% 1.62/1.36 % (22073)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (22073)Memory used [KB]: 5500
% 1.62/1.36 % (22073)Time elapsed: 0.004 s
% 1.62/1.36 % (22073)Instructions burned: 4 (million)
% 1.62/1.36 % (22073)------------------------------
% 1.62/1.36 % (22073)------------------------------
% 1.62/1.36 % (22077)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/6Mi)
% 1.62/1.36 % (22075)Instruction limit reached!
% 1.62/1.36 % (22075)------------------------------
% 1.62/1.36 % (22075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (22075)Termination reason: Unknown
% 1.62/1.36 % (22075)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (22075)Memory used [KB]: 5500
% 1.62/1.36 % (22075)Time elapsed: 0.008 s
% 1.62/1.36 % (22075)Instructions burned: 20 (million)
% 1.62/1.36 % (22075)------------------------------
% 1.62/1.36 % (22075)------------------------------
% 1.62/1.37 % (22076)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/710Mi)
% 1.62/1.37 % (22077)Instruction limit reached!
% 1.62/1.37 % (22077)------------------------------
% 1.62/1.37 % (22077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (22077)Termination reason: Unknown
% 1.62/1.37 % (22077)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (22077)Memory used [KB]: 5500
% 1.62/1.37 % (22077)Time elapsed: 0.004 s
% 1.62/1.37 % (22077)Instructions burned: 6 (million)
% 1.62/1.37 % (22077)------------------------------
% 1.62/1.37 % (22077)------------------------------
% 1.62/1.37 % (22079)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/21Mi)
% 1.62/1.37 % (22056)Instruction limit reached!
% 1.62/1.37 % (22056)------------------------------
% 1.62/1.37 % (22056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (22056)Termination reason: Unknown
% 1.62/1.37 % (22056)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (22056)Memory used [KB]: 6140
% 1.62/1.37 % (22056)Time elapsed: 0.078 s
% 1.62/1.37 % (22056)Instructions burned: 184 (million)
% 1.62/1.37 % (22056)------------------------------
% 1.62/1.37 % (22056)------------------------------
% 1.62/1.38 % (22080)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/5Mi)
% 1.62/1.38 % (22078)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/902Mi)
% 1.62/1.38 % (22080)Instruction limit reached!
% 1.62/1.38 % (22080)------------------------------
% 1.62/1.38 % (22080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (22080)Termination reason: Unknown
% 1.62/1.38 % (22080)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (22080)Memory used [KB]: 5500
% 1.62/1.38 % (22080)Time elapsed: 0.004 s
% 1.62/1.38 % (22080)Instructions burned: 7 (million)
% 1.62/1.38 % (22080)------------------------------
% 1.62/1.38 % (22080)------------------------------
% 1.62/1.38 % (22079)Instruction limit reached!
% 1.62/1.38 % (22079)------------------------------
% 1.62/1.38 % (22079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (22079)Termination reason: Unknown
% 1.62/1.38 % (22079)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (22079)Memory used [KB]: 5628
% 1.62/1.38 % (22079)Time elapsed: 0.009 s
% 1.62/1.38 % (22079)Instructions burned: 21 (million)
% 1.62/1.38 % (22079)------------------------------
% 1.62/1.38 % (22079)------------------------------
% 1.62/1.39 % (22081)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/6Mi)
% 1.62/1.39 % (22081)Instruction limit reached!
% 1.62/1.39 % (22081)------------------------------
% 1.62/1.39 % (22081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (22081)Termination reason: Unknown
% 1.62/1.39 % (22081)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (22081)Memory used [KB]: 5500
% 1.62/1.39 % (22081)Time elapsed: 0.004 s
% 1.62/1.39 % (22081)Instructions burned: 8 (million)
% 1.62/1.39 % (22081)------------------------------
% 1.62/1.39 % (22081)------------------------------
% 1.62/1.39 % (22082)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21841 for (2999ds/377Mi)
% 1.62/1.39 % (22083)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/779Mi)
% 1.62/1.40 % (22084)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/19Mi)
% 1.62/1.40 % (22084)Instruction limit reached!
% 1.62/1.40 % (22084)------------------------------
% 1.62/1.40 % (22084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.40 % (22084)Termination reason: Unknown
% 1.62/1.40 % (22084)Termination phase: Saturation
% 1.62/1.40
% 1.62/1.40 % (22084)Memory used [KB]: 5500
% 1.62/1.40 % (22084)Time elapsed: 0.008 s
% 1.62/1.40 % (22084)Instructions burned: 19 (million)
% 1.62/1.40 % (22084)------------------------------
% 1.62/1.40 % (22084)------------------------------
% 1.62/1.41 % (22085)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/879Mi)
% 1.62/1.41 % (22061)Instruction limit reached!
% 1.62/1.41 % (22061)------------------------------
% 1.62/1.41 % (22061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.41 % (22061)Termination reason: Unknown
% 1.62/1.41 % (22061)Termination phase: Saturation
% 1.62/1.41
% 1.62/1.41 % (22061)Memory used [KB]: 5756
% 1.62/1.41 % (22061)Time elapsed: 0.117 s
% 1.62/1.41 % (22061)Instructions burned: 278 (million)
% 1.62/1.41 % (22061)------------------------------
% 1.62/1.41 % (22061)------------------------------
% 1.62/1.42 % (22086)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/17Mi)
% 1.62/1.43 % (22086)Instruction limit reached!
% 1.62/1.43 % (22086)------------------------------
% 1.62/1.43 % (22086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.43 % (22086)Termination reason: Unknown
% 1.62/1.43 % (22086)Termination phase: Saturation
% 1.62/1.43
% 1.62/1.43 % (22086)Memory used [KB]: 5500
% 1.62/1.43 % (22086)Time elapsed: 0.008 s
% 1.62/1.43 % (22086)Instructions burned: 18 (million)
% 1.62/1.43 % (22086)------------------------------
% 1.62/1.43 % (22086)------------------------------
% 1.62/1.44 % (22087)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/3Mi)
% 1.62/1.44 % (22087)Instruction limit reached!
% 1.62/1.44 % (22087)------------------------------
% 1.62/1.44 % (22087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.44 % (22087)Termination reason: Unknown
% 1.62/1.44 % (22087)Termination phase: Saturation
% 1.62/1.44
% 1.62/1.44 % (22087)Memory used [KB]: 5500
% 1.62/1.44 % (22087)Time elapsed: 0.003 s
% 1.62/1.44 % (22087)Instructions burned: 4 (million)
% 1.62/1.44 % (22087)------------------------------
% 1.62/1.44 % (22087)------------------------------
% 1.62/1.45 % (22088)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21841 for (2998ds/30Mi)
% 1.62/1.46 % (22088)Instruction limit reached!
% 1.62/1.46 % (22088)------------------------------
% 1.62/1.46 % (22088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.46 % (22088)Termination reason: Unknown
% 1.62/1.46 % (22088)Termination phase: Saturation
% 1.62/1.46
% 1.62/1.46 % (22088)Memory used [KB]: 5500
% 1.62/1.46 % (22088)Time elapsed: 0.012 s
% 1.62/1.46 % (22088)Instructions burned: 30 (million)
% 1.62/1.46 % (22088)------------------------------
% 1.62/1.46 % (22088)------------------------------
% 1.62/1.46 % (22067)First to succeed.
% 1.62/1.47 % (22067)Refutation found. Thanks to Tanya!
% 1.62/1.47 % SZS status Theorem for DTF2THF_21841
% 1.62/1.47 % SZS output start Proof for DTF2THF_21841
% 1.62/1.47 thf(func_def_3, type, cP: $i > $i > $i > $o).
% 1.62/1.47 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.47 thf(f1264,plain,(
% 1.62/1.47 $false),
% 1.62/1.47 inference(trivial_inequality_removal,[status(thm)],[f1262])).
% 1.62/1.47 thf(f1262,plain,(
% 1.62/1.47 ($true = $false)),
% 1.62/1.47 inference(superposition,[status(thm)],[f1215,f35])).
% 1.62/1.47 thf(f35,plain,(
% 1.62/1.47 ( ! [X1 : $i] : (((cP @ X1 @ e @ X1) = $true)) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.62/1.47 thf(f34,plain,(
% 1.62/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (cP @ Y0 @ e @ Y0)) @ X1) = $true)) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f33])).
% 1.62/1.47 thf(f33,plain,(
% 1.62/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))))),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f32])).
% 1.62/1.47 thf(f32,plain,(
% 1.62/1.47 (((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & $true) = $true)),
% 1.62/1.47 inference(backward_demodulation,[status(thm)],[f27,f30])).
% 1.62/1.47 thf(f30,plain,(
% 1.62/1.47 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0))))))))))))))) = $true)),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.62/1.47 thf(f27,plain,(
% 1.62/1.47 (((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) = $true)),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f26])).
% 1.62/1.47 thf(f26,plain,(
% 1.62/1.47 ($true = (((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & $true))),
% 1.62/1.47 inference(backward_demodulation,[status(thm)],[f23,f24])).
% 1.62/1.47 thf(f24,plain,(
% 1.62/1.47 ((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e))) = $true)),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.62/1.47 thf(f23,plain,(
% 1.62/1.47 ((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) = $true)),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f22])).
% 1.62/1.47 thf(f22,plain,(
% 1.62/1.47 ($true = ((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) & $true))),
% 1.62/1.47 inference(backward_demodulation,[status(thm)],[f11,f20])).
% 1.62/1.47 thf(f20,plain,(
% 1.62/1.47 ($true = (!! @ $i @ (^[Y0 : $i]: (cP @ e @ Y0 @ Y0))))),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.62/1.47 thf(f11,plain,(
% 1.62/1.47 (((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) & (!! @ $i @ (^[Y0 : $i]: (cP @ e @ Y0 @ Y0)))) = $true)),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.62/1.47 thf(f7,plain,(
% 1.62/1.47 ((((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) & (!! @ $i @ (^[Y0 : $i]: (cP @ e @ Y0 @ Y0)))) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab))) = $false)),
% 1.62/1.47 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.62/1.47 thf(f6,plain,(
% 1.62/1.47 ((~ (((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) & (!! @ $i @ (^[Y0 : $i]: (cP @ e @ Y0 @ Y0)))) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))) = $true)),
% 1.62/1.47 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.47 thf(f5,plain,(
% 1.62/1.47 ((~ (((((!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ e @ Y0))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))))) & (!! @ $i @ (^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)))) & (!! @ $i @ (^[Y0 : $i]: (cP @ e @ Y0 @ Y0)))) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))) = $true)),
% 1.62/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.47 thf(f4,plain,(
% 1.62/1.47 ~((! [X0 : $i] : (cP @ e @ X0 @ X0) & ! [X1 : $i] : (cP @ X1 @ X1 @ e) & ! [X2 : $i,X3 : $i,X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((cP @ X5 @ X3 @ X4) & (cP @ X3 @ X6 @ X2)) => ((cP @ X4 @ X6 @ X7) <=> (cP @ X5 @ X2 @ X7))) & ! [X8 : $i] : (cP @ X8 @ e @ X8)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 1.62/1.47 inference(rectify,[status(thm)],[f2])).
% 1.62/1.47 thf(f2,negated_conjecture,(
% 1.62/1.47 ~((! [X0 : $i] : (cP @ e @ X0 @ X0) & ! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X4 : $i,X1 : $i,X3 : $i,X0 : $i,X2 : $i,X5 : $i] : (((cP @ X0 @ X1 @ X3) & (cP @ X1 @ X2 @ X4)) => ((cP @ X3 @ X2 @ X5) <=> (cP @ X0 @ X4 @ X5))) & ! [X1 : $i] : (cP @ X1 @ e @ X1)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab)))),
% 1.62/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.47 thf(f1,conjecture,(
% 1.62/1.47 (! [X0 : $i] : (cP @ e @ X0 @ X0) & ! [X2 : $i] : (cP @ X2 @ X2 @ e) & ! [X4 : $i,X1 : $i,X3 : $i,X0 : $i,X2 : $i,X5 : $i] : (((cP @ X0 @ X1 @ X3) & (cP @ X1 @ X2 @ X4)) => ((cP @ X3 @ X2 @ X5) <=> (cP @ X0 @ X4 @ X5))) & ! [X1 : $i] : (cP @ X1 @ e @ X1)) => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab))),
% 1.62/1.47 file('/export/starexec/sandbox2/tmp/tmp.jUI57ZfkmQ/DTF2THF_21841.p',cTHM105)).
% 1.62/1.47 thf(f1215,plain,(
% 1.62/1.47 ((cP @ ab @ e @ ab) = $false)),
% 1.62/1.47 inference(superposition,[status(thm)],[f14,f1092])).
% 1.62/1.47 thf(f1092,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (((cP @ ab @ e @ X0) = (cP @ b @ a @ X0))) )),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f1091])).
% 1.62/1.47 thf(f1091,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (($true = ((cP @ b @ a @ X0) = (cP @ ab @ e @ X0)))) )),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f1065])).
% 1.62/1.47 thf(f1065,plain,(
% 1.62/1.47 ( ! [X0 : $i] : ((($true => ((cP @ b @ a @ X0) = (cP @ ab @ e @ X0))) = $true)) )),
% 1.62/1.47 inference(superposition,[status(thm)],[f72,f949])).
% 1.62/1.47 thf(f949,plain,(
% 1.62/1.47 ($true = (cP @ ab @ a @ b))),
% 1.62/1.47 inference(superposition,[status(thm)],[f29,f829])).
% 1.62/1.47 thf(f829,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (((cP @ e @ b @ X0) = (cP @ ab @ a @ X0))) )),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f828])).
% 1.62/1.47 thf(f828,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (($true = ((cP @ e @ b @ X0) = (cP @ ab @ a @ X0)))) )),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f809])).
% 1.62/1.47 thf(f809,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (($true = ($true => ((cP @ e @ b @ X0) = (cP @ ab @ a @ X0))))) )),
% 1.62/1.47 inference(superposition,[status(thm)],[f86,f284])).
% 1.62/1.47 thf(f284,plain,(
% 1.62/1.47 ((cP @ ab @ b @ a) = $true)),
% 1.62/1.47 inference(superposition,[status(thm)],[f122,f35])).
% 1.62/1.47 thf(f122,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (((cP @ a @ e @ X0) = (cP @ ab @ b @ X0))) )),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.62/1.47 thf(f121,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (($true = ((cP @ ab @ b @ X0) = (cP @ a @ e @ X0)))) )),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f104])).
% 1.62/1.47 thf(f104,plain,(
% 1.62/1.47 ( ! [X0 : $i] : (($true = ($true => ((cP @ ab @ b @ X0) = (cP @ a @ e @ X0))))) )),
% 1.62/1.47 inference(superposition,[status(thm)],[f72,f15])).
% 1.62/1.47 thf(f15,plain,(
% 1.62/1.47 ((cP @ a @ b @ ab) = $true)),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.62/1.47 thf(f13,plain,(
% 1.62/1.47 (((cP @ a @ b @ ab) => (cP @ b @ a @ ab)) = $false)),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f12])).
% 1.62/1.47 thf(f12,plain,(
% 1.62/1.47 ($false = ($true => ((cP @ a @ b @ ab) => (cP @ b @ a @ ab))))),
% 1.62/1.47 inference(backward_demodulation,[status(thm)],[f7,f11])).
% 1.62/1.47 thf(f86,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((cP @ X0 @ X1 @ X2) => ((cP @ e @ X1 @ X3) = (cP @ X0 @ X2 @ X3))))) )),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f65])).
% 1.62/1.47 thf(f65,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (((cP @ X0 @ X1 @ X2) & $true) => ((cP @ e @ X1 @ X3) = (cP @ X0 @ X2 @ X3))))) )),
% 1.62/1.47 inference(superposition,[status(thm)],[f49,f37])).
% 1.62/1.47 thf(f37,plain,(
% 1.62/1.47 ( ! [X1 : $i] : (($true = (cP @ X1 @ X1 @ e))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.62/1.47 thf(f36,plain,(
% 1.62/1.47 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (cP @ Y0 @ Y0 @ e)) @ X1))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f24])).
% 1.62/1.47 thf(f49,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((cP @ X5 @ X2 @ X6) & (cP @ X3 @ X5 @ X4)) => ((cP @ X4 @ X2 @ X1) = (cP @ X3 @ X6 @ X1))))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.62/1.47 thf(f48,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((^[Y0 : $i]: (((cP @ X5 @ X2 @ Y0) & (cP @ X3 @ X5 @ X4)) => ((cP @ X4 @ X2 @ X1) = (cP @ X3 @ Y0 @ X1)))) @ X6))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f47])).
% 1.62/1.47 thf(f47,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((cP @ X5 @ X2 @ Y0) & (cP @ X3 @ X5 @ X4)) => ((cP @ X4 @ X2 @ X1) = (cP @ X3 @ Y0 @ X1))))))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.62/1.47 thf(f46,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cP @ Y0 @ X2 @ Y1) & (cP @ X3 @ Y0 @ X4)) => ((cP @ X4 @ X2 @ X1) = (cP @ X3 @ Y1 @ X1)))))) @ X5))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f45])).
% 1.62/1.47 thf(f45,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((cP @ Y0 @ X2 @ Y1) & (cP @ X3 @ Y0 @ X4)) => ((cP @ X4 @ X2 @ X1) = (cP @ X3 @ Y1 @ X1))))))))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.62/1.47 thf(f44,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((cP @ Y1 @ X2 @ Y2) & (cP @ X3 @ Y1 @ Y0)) => ((cP @ Y0 @ X2 @ X1) = (cP @ X3 @ Y2 @ X1)))))))) @ X4))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f43])).
% 1.62/1.47 thf(f43,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((cP @ Y1 @ X2 @ Y2) & (cP @ X3 @ Y1 @ Y0)) => ((cP @ Y0 @ X2 @ X1) = (cP @ X3 @ Y2 @ X1))))))))))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.62/1.47 thf(f42,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((cP @ Y2 @ X2 @ Y3) & (cP @ Y0 @ Y2 @ Y1)) => ((cP @ Y1 @ X2 @ X1) = (cP @ Y0 @ Y3 @ X1)))))))))) @ X3))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f41])).
% 1.62/1.47 thf(f41,plain,(
% 1.62/1.47 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((cP @ Y2 @ X2 @ Y3) & (cP @ Y0 @ Y2 @ Y1)) => ((cP @ Y1 @ X2 @ X1) = (cP @ Y0 @ Y3 @ X1))))))))))))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.62/1.47 thf(f40,plain,(
% 1.62/1.47 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((cP @ Y3 @ Y0 @ Y4) & (cP @ Y1 @ Y3 @ Y2)) => ((cP @ Y2 @ Y0 @ X1) = (cP @ Y1 @ Y4 @ X1)))))))))))) @ X2))) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f39])).
% 1.62/1.47 thf(f39,plain,(
% 1.62/1.47 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((cP @ Y3 @ Y0 @ Y4) & (cP @ Y1 @ Y3 @ Y2)) => ((cP @ Y2 @ Y0 @ X1) = (cP @ Y1 @ Y4 @ X1))))))))))))) = $true)) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.62/1.47 thf(f38,plain,(
% 1.62/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((cP @ Y4 @ Y1 @ Y5) & (cP @ Y2 @ Y4 @ Y3)) => ((cP @ Y3 @ Y1 @ Y0) = (cP @ Y2 @ Y5 @ Y0)))))))))))))) @ X1) = $true)) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f30])).
% 1.62/1.47 thf(f29,plain,(
% 1.62/1.47 ( ! [X1 : $i] : (($true = (cP @ e @ X1 @ X1))) )),
% 1.62/1.47 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.62/1.47 thf(f28,plain,(
% 1.62/1.47 ( ! [X1 : $i] : ((((^[Y0 : $i]: (cP @ e @ Y0 @ Y0)) @ X1) = $true)) )),
% 1.62/1.47 inference(pi_clausification,[status(thm)],[f20])).
% 1.62/1.47 thf(f72,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((cP @ X1 @ X0 @ X2) => ((cP @ X2 @ X0 @ X3) = (cP @ X1 @ e @ X3))) = $true)) )),
% 1.62/1.47 inference(boolean_simplification,[status(thm)],[f70])).
% 1.62/1.47 thf(f70,plain,(
% 1.62/1.47 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (($true & (cP @ X1 @ X0 @ X2)) => ((cP @ X2 @ X0 @ X3) = (cP @ X1 @ e @ X3))))) )),
% 1.62/1.47 inference(superposition,[status(thm)],[f49,f37])).
% 1.62/1.47 thf(f14,plain,(
% 1.62/1.47 ((cP @ b @ a @ ab) = $false)),
% 1.62/1.47 inference(binary_proxy_clausification,[status(thm)],[f13])).
% 1.62/1.47 % SZS output end Proof for DTF2THF_21841
% 1.62/1.47 % (22067)------------------------------
% 1.62/1.47 % (22067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.47 % (22067)Termination reason: Refutation
% 1.62/1.47
% 1.62/1.47 % (22067)Memory used [KB]: 7547
% 1.62/1.47 % (22067)Time elapsed: 0.152 s
% 1.62/1.47 % (22067)Instructions burned: 473 (million)
% 1.62/1.47 % (22067)------------------------------
% 1.62/1.47 % (22067)------------------------------
% 1.62/1.47 % (22055)Success in time 0.19 s
%------------------------------------------------------------------------------