%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG284^5 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:37:50 AM UTC 2026
% Result : Theorem 1.68s 1.62s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 220 ( 93 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 515 ( 4 ~; 0 |; 18 &; 438 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 6 con; 0-2 aty)
% ( 48 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 115 ( 55 ^; 60 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cJ: $i > $i ).
thf(func_def_1,type,
cP: $i > $i > $i ).
thf(func_def_16,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f641,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f640]) ).
thf(f640,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f639]) ).
thf(f639,plain,
( ( ( cJ @ ( cP @ sK3 @ sK2 ) )
= ( cJ @ ( cP @ sK3 @ sK2 ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f17,f597]) ).
thf(f597,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X1 ) @ ( cJ @ X0 ) )
= ( cJ @ ( cP @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f167,f71]) ).
thf(f71,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[status(thm)],[f66,f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( $true
= ( ( cP @ cE @ X1 )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) )
& $true ) ),
inference(backward_demodulation,[status(thm)],[f11,f19]) ).
thf(f19,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ cE @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X3: $i] :
( cE
= ( cP @ ( cJ @ X3 ) @ X3 ) )
& ! [X4: $i] :
( ( cP @ cE @ X4 )
= X4 ) )
=> ! [X5: $i,X6: $i] :
( ( cP @ ( cJ @ X6 ) @ ( cJ @ X5 ) )
= ( cJ @ ( cP @ X5 @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 ) )
=> ! [X3: $i,X4: $i] :
( ( cJ @ ( cP @ X3 @ X4 ) )
= ( cP @ ( cJ @ X4 ) @ ( cJ @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 ) )
=> ! [X3: $i,X4: $i] :
( ( cJ @ ( cP @ X3 @ X4 ) )
= ( cP @ ( cJ @ X4 ) @ ( cJ @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oLyTMbwlcc/DTF2THF_32051.p',cTHM18_pme) ).
thf(f66,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= ( cP @ cE @ X1 ) ),
inference(superposition,[status(thm)],[f43,f29]) ).
thf(f29,plain,
! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
= ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( cE
= ( cP @ ( cJ @ Y0 ) @ Y0 ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f22,f24]) ).
thf(f43,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( cP @ ( cP @ X3 @ X2 ) @ X1 )
= ( cP @ X3 @ ( cP @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( cP @ ( cP @ X3 @ X2 ) @ X1 )
= ( cP @ X3 @ ( cP @ X2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cP @ ( cP @ Y0 @ X2 ) @ X1 )
= ( cP @ Y0 @ ( cP @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ ( cP @ Y0 @ X2 ) @ X1 )
= ( cP @ Y0 @ ( cP @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cP @ Y1 @ Y0 ) @ X1 )
= ( cP @ Y1 @ ( cP @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cP @ Y1 @ Y0 ) @ X1 )
= ( cP @ Y1 @ ( cP @ Y0 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y2 @ Y1 ) @ Y0 )
= ( cP @ Y2 @ ( cP @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f167,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ ( cP @ X1 @ X0 ) ) @ X1 )
= ( cJ @ X0 ) ),
inference(forward_demodulation,[status(thm)],[f161,f88]) ).
thf(f88,plain,
! [X0: $i] :
( ( cP @ X0 @ cE )
= X0 ),
inference(superposition,[status(thm)],[f77,f74]) ).
thf(f74,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(superposition,[status(thm)],[f71,f29]) ).
thf(f77,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ X1 )
= ( cP @ ( cJ @ ( cJ @ X0 ) ) @ X1 ) ),
inference(superposition,[status(thm)],[f71,f71]) ).
thf(f161,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ ( cP @ X1 @ X0 ) ) @ ( cP @ X1 @ cE ) )
= ( cJ @ X0 ) ),
inference(superposition,[status(thm)],[f76,f87]) ).
thf(f87,plain,
! [X0: $i] :
( cE
= ( cP @ X0 @ ( cJ @ X0 ) ) ),
inference(superposition,[status(thm)],[f77,f29]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cP @ ( cJ @ ( cP @ X0 @ X1 ) ) @ ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
= X2 ),
inference(superposition,[status(thm)],[f71,f43]) ).
thf(f17,plain,
( $false
= ( ( cP @ ( cJ @ sK2 ) @ ( cJ @ sK3 ) )
= ( cJ @ ( cP @ sK3 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ^ [Y0: $i] :
( ( cP @ ( cJ @ sK2 ) @ ( cJ @ Y0 ) )
= ( cJ @ ( cP @ Y0 @ sK2 ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ ( cJ @ sK2 ) @ ( cJ @ Y0 ) )
= ( cJ @ ( cP @ Y0 @ sK2 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cJ @ Y0 ) @ ( cJ @ Y1 ) )
= ( cJ @ ( cP @ Y1 @ Y0 ) ) ) ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f7,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : ALG284^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.16 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.37 % Computer : n006.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Tue Feb 24 03:42:45 EST 2026
% 0.17/0.37 % CPUTime :
% 0.17/0.37 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.52 ---- Original DTF file ---
% 0.28/0.52 thf(spec,logic,$$dhol).
% 0.28/0.52 %------------------------------------------------------------------------------
% 0.28/0.52 % File : ALG284^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.52 % Domain : General Algebra
% 0.28/0.52 % Problem : TPS problem from GRP-THMS
% 0.28/0.52 % Version : Especial.
% 0.28/0.52 % English :
% 0.28/0.52
% 0.28/0.52 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.52 % Source : [Bro09]
% 0.28/0.52 % Names : tps_0930 [Bro09]
% 0.28/0.52
% 0.28/0.52 % Status : Theorem
% 0.28/0.52 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.0
% 0.28/0.52 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.28/0.52 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.28/0.52 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.52 % Number of connectives : 23 ( 0 ~; 0 |; 2 &; 20 @)
% 0.28/0.52 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.52 % Maximal formula depth : 6 ( 6 avg)
% 0.28/0.52 % Number of types : 1 ( 0 usr)
% 0.28/0.52 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.52 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.28/0.52 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.28/0.52 % SPC : TH0_THM_EQU_NAR
% 0.28/0.52
% 0.28/0.52 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.52 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.52 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.52 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.52 %------------------------------------------------------------------------------
% 0.28/0.52 thf(cJ,type,
% 0.28/0.52 cJ: $i > $i ).
% 0.28/0.52
% 0.28/0.52 thf(cP,type,
% 0.28/0.52 cP: $i > $i > $i ).
% 0.28/0.52
% 0.28/0.52 thf(cE,type,
% 0.28/0.52 cE: $i ).
% 0.28/0.52
% 0.28/0.52 thf(cTHM18_pme,conjecture,
% 0.28/0.52 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.52 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.28/0.52 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 0.28/0.52 & ! [Xx: $i] :
% 0.28/0.52 ( ( cP @ cE @ Xx )
% 0.28/0.52 = Xx )
% 0.28/0.52 & ! [Xy: $i] :
% 0.28/0.52 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 0.28/0.52 = cE ) )
% 0.28/0.52 => ! [X: $i,Y: $i] :
% 0.28/0.52 ( ( cJ @ ( cP @ X @ Y ) )
% 0.28/0.52 = ( cP @ ( cJ @ Y ) @ ( cJ @ X ) ) ) ) ).
% 0.28/0.52
% 0.28/0.52 %------------------------------------------------------------------------------
% 0.28/0.52 ------------------------
% 1.54/1.46 ---- Embedded in THF ---
% 1.54/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.46 %%% Generated on Tue Feb 24 03:42:46 EST 2026
% 1.54/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.46 %%% Logic specification used:
% 1.54/1.46 %%% thf(spec, logic, $$dhol).
% 1.54/1.46
% 1.54/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oLyTMbwlcc/DTF2DTF32051.p
% See solution above
% 1.54/1.46 ------------------------
% 1.54/1.47 ---- Cleaned THF ---
% 1.54/1.47 thf(cJ,type,
% 1.54/1.47 cJ: $i > $i ).
% 1.54/1.47
% 1.54/1.47 thf(cP,type,
% 1.54/1.47 cP: $i > $i > $i ).
% 1.54/1.47
% 1.54/1.47 thf(cE,type,
% 1.54/1.47 cE: $i ).
% 1.54/1.47
% 1.54/1.47 thf(cTHM18_pme,conjecture,
% 1.54/1.47 ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.54/1.47 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.54/1.47 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
% 1.54/1.47 & ! [Xx: $i] :
% 1.54/1.47 ( ( cP @ cE @ Xx )
% 1.54/1.47 = Xx )
% 1.54/1.47 & ! [Xy: $i] :
% 1.54/1.47 ( ( cP @ ( cJ @ Xy ) @ Xy )
% 1.54/1.47 = cE ) )
% 1.54/1.47 => ! [X: $i,Y: $i] :
% 1.54/1.47 ( ( cJ @ ( cP @ X @ Y ) )
% 1.54/1.47 = ( cP @ ( cJ @ Y ) @ ( cJ @ X ) ) ) ) ).
% 1.54/1.47 ------------------------
% 1.54/1.49 % (32163)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/183Mi)
% 1.54/1.49 % (32164)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_32051 for (2999ds/4Mi)
% 1.54/1.49 % (32167)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_32051 for (2999ds/2Mi)
% 1.54/1.49 % (32165)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_32051 for (2999ds/27Mi)
% 1.54/1.49 % (32166)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/2Mi)
% 1.54/1.49 % (32169)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/18Mi)
% 1.54/1.49 % (32168)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_32051 for (2999ds/275Mi)
% 1.54/1.49 % (32166)Instruction limit reached!
% 1.54/1.49 % (32166)------------------------------
% 1.54/1.49 % (32166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.49 % (32166)Termination reason: Unknown
% 1.54/1.49 % (32167)Instruction limit reached!
% 1.54/1.49 % (32167)------------------------------
% 1.54/1.49 % (32167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.49 % (32166)Termination phase: Saturation
% 1.54/1.49
% 1.54/1.49 % (32166)Memory used [KB]: 5500
% 1.54/1.49 % (32166)Time elapsed: 0.003 s
% 1.54/1.49 % (32166)Instructions burned: 2 (million)
% 1.54/1.49 % (32166)------------------------------
% 1.54/1.49 % (32166)------------------------------
% 1.54/1.49 % (32167)Termination reason: Unknown
% 1.54/1.49 % (32167)Termination phase: Saturation
% 1.54/1.49
% 1.54/1.49 % (32167)Memory used [KB]: 5500
% 1.54/1.49 % (32167)Time elapsed: 0.003 s
% 1.54/1.49 % (32167)Instructions burned: 2 (million)
% 1.54/1.49 % (32167)------------------------------
% 1.54/1.49 % (32167)------------------------------
% 1.54/1.49 % (32164)Instruction limit reached!
% 1.54/1.49 % (32164)------------------------------
% 1.54/1.49 % (32164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.49 % (32164)Termination reason: Unknown
% 1.54/1.49 % (32164)Termination phase: Saturation
% 1.54/1.49
% 1.54/1.49 % (32164)Memory used [KB]: 5500
% 1.54/1.49 % (32164)Time elapsed: 0.005 s
% 1.54/1.49 % (32164)Instructions burned: 5 (million)
% 1.54/1.49 % (32164)------------------------------
% 1.54/1.49 % (32164)------------------------------
% 1.68/1.50 % (32169)Instruction limit reached!
% 1.68/1.50 % (32169)------------------------------
% 1.68/1.50 % (32169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.50 % (32169)Termination reason: Unknown
% 1.68/1.50 % (32169)Termination phase: Saturation
% 1.68/1.50
% 1.68/1.50 % (32169)Memory used [KB]: 5500
% 1.68/1.50 % (32169)Time elapsed: 0.012 s
% 1.68/1.50 % (32169)Instructions burned: 19 (million)
% 1.68/1.50 % (32169)------------------------------
% 1.68/1.50 % (32169)------------------------------
% 1.68/1.50 % (32165)Instruction limit reached!
% 1.68/1.50 % (32165)------------------------------
% 1.68/1.50 % (32165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.50 % (32165)Termination reason: Unknown
% 1.68/1.50 % (32165)Termination phase: Saturation
% 1.68/1.50
% 1.68/1.50 % (32165)Memory used [KB]: 5628
% 1.68/1.50 % (32165)Time elapsed: 0.016 s
% 1.68/1.50 % (32165)Instructions burned: 28 (million)
% 1.68/1.50 % (32165)------------------------------
% 1.68/1.50 % (32165)------------------------------
% 1.68/1.51 % (32170)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/3Mi)
% 1.68/1.51 % (32171)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_32051 for (2999ds/37Mi)
% 1.68/1.51 % (32170)Instruction limit reached!
% 1.68/1.51 % (32170)------------------------------
% 1.68/1.51 % (32170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.51 % (32170)Termination reason: Unknown
% 1.68/1.51 % (32170)Termination phase: Saturation
% 1.68/1.51
% 1.68/1.51 % (32170)Memory used [KB]: 5500
% 1.68/1.51 % (32170)Time elapsed: 0.003 s
% 1.68/1.51 % (32170)Instructions burned: 3 (million)
% 1.68/1.51 % (32170)------------------------------
% 1.68/1.51 % (32170)------------------------------
% 1.68/1.51 % (32172)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_32051 for (2999ds/15Mi)
% 1.68/1.51 % (32173)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_32051 for (2999ds/3Mi)
% 1.68/1.51 % (32172)Instruction limit reached!
% 1.68/1.51 % (32172)------------------------------
% 1.68/1.51 % (32172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.51 % (32172)Termination reason: Unknown
% 1.68/1.51 % (32172)Termination phase: Saturation
% 1.68/1.51
% 1.68/1.51 % (32172)Memory used [KB]: 5500
% 1.68/1.51 % (32172)Time elapsed: 0.009 s
% 1.68/1.51 % (32172)Instructions burned: 15 (million)
% 1.68/1.51 % (32172)------------------------------
% 1.68/1.51 % (32172)------------------------------
% 1.68/1.52 % (32173)Instruction limit reached!
% 1.68/1.52 % (32173)------------------------------
% 1.68/1.52 % (32173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.52 % (32173)Termination reason: Unknown
% 1.68/1.52 % (32173)Termination phase: Saturation
% 1.68/1.52
% 1.68/1.52 % (32173)Memory used [KB]: 5500
% 1.68/1.52 % (32173)Time elapsed: 0.003 s
% 1.68/1.52 % (32173)Instructions burned: 3 (million)
% 1.68/1.52 % (32173)------------------------------
% 1.68/1.52 % (32173)------------------------------
% 1.68/1.52 % (32174)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_32051 for (2999ds/1041Mi)
% 1.68/1.52 % (32175)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/7Mi)
% 1.68/1.52 % (32171)Instruction limit reached!
% 1.68/1.52 % (32171)------------------------------
% 1.68/1.52 % (32171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.52 % (32171)Termination reason: Unknown
% 1.68/1.52 % (32171)Termination phase: Saturation
% 1.68/1.52
% 1.68/1.52 % (32171)Memory used [KB]: 5756
% 1.68/1.52 % (32171)Time elapsed: 0.020 s
% 1.68/1.52 % (32171)Instructions burned: 38 (million)
% 1.68/1.52 % (32171)------------------------------
% 1.68/1.52 % (32171)------------------------------
% 1.68/1.53 % (32175)Instruction limit reached!
% 1.68/1.53 % (32175)------------------------------
% 1.68/1.53 % (32175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.53 % (32175)Termination reason: Unknown
% 1.68/1.53 % (32175)Termination phase: Saturation
% 1.68/1.53
% 1.68/1.53 % (32175)Memory used [KB]: 1023
% 1.68/1.53 % (32175)Time elapsed: 0.005 s
% 1.68/1.53 % (32175)Instructions burned: 7 (million)
% 1.68/1.53 % (32175)------------------------------
% 1.68/1.53 % (32175)------------------------------
% 1.68/1.53 % (32176)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/16Mi)
% 1.68/1.53 % (32177)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_32051 for (2999ds/3Mi)
% 1.68/1.53 % (32177)Instruction limit reached!
% 1.68/1.53 % (32177)------------------------------
% 1.68/1.53 % (32177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.53 % (32177)Termination reason: Unknown
% 1.68/1.53 % (32177)Termination phase: Saturation
% 1.68/1.53
% 1.68/1.53 % (32177)Memory used [KB]: 5500
% 1.68/1.53 % (32177)Time elapsed: 0.003 s
% 1.68/1.53 % (32177)Instructions burned: 3 (million)
% 1.68/1.53 % (32177)------------------------------
% 1.68/1.53 % (32177)------------------------------
% 1.68/1.54 % (32176)Instruction limit reached!
% 1.68/1.54 % (32176)------------------------------
% 1.68/1.54 % (32176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.54 % (32178)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_32051 for (2999ds/3Mi)
% 1.68/1.54 % (32176)Termination reason: Unknown
% 1.68/1.54 % (32176)Termination phase: Saturation
% 1.68/1.54
% 1.68/1.54 % (32176)Memory used [KB]: 5628
% 1.68/1.54 % (32176)Time elapsed: 0.011 s
% 1.68/1.54 % (32176)Instructions burned: 17 (million)
% 1.68/1.54 % (32176)------------------------------
% 1.68/1.54 % (32176)------------------------------
% 1.68/1.54 % (32178)Instruction limit reached!
% 1.68/1.54 % (32178)------------------------------
% 1.68/1.54 % (32178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.54 % (32178)Termination reason: Unknown
% 1.68/1.54 % (32178)Termination phase: Saturation
% 1.68/1.54
% 1.68/1.54 % (32178)Memory used [KB]: 1023
% 1.68/1.54 % (32178)Time elapsed: 0.003 s
% 1.68/1.54 % (32178)Instructions burned: 3 (million)
% 1.68/1.54 % (32178)------------------------------
% 1.68/1.54 % (32178)------------------------------
% 1.68/1.54 % (32179)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/7Mi)
% 1.68/1.54 % (32179)Refutation not found, incomplete strategy
% 1.68/1.54 % (32179)------------------------------
% 1.68/1.54 % (32179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.54 % (32179)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.54
% 1.68/1.54
% 1.68/1.54 % (32179)Memory used [KB]: 5500
% 1.68/1.54 % (32179)Time elapsed: 0.002 s
% 1.68/1.54 % (32179)Instructions burned: 2 (million)
% 1.68/1.54 % (32179)------------------------------
% 1.68/1.54 % (32179)------------------------------
% 1.68/1.55 % (32180)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/3Mi)
% 1.68/1.55 % (32180)Instruction limit reached!
% 1.68/1.55 % (32180)------------------------------
% 1.68/1.55 % (32180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.55 % (32180)Termination reason: Unknown
% 1.68/1.55 % (32180)Termination phase: Saturation
% 1.68/1.55
% 1.68/1.55 % (32180)Memory used [KB]: 5500
% 1.68/1.55 % (32180)Time elapsed: 0.003 s
% 1.68/1.55 % (32180)Instructions burned: 3 (million)
% 1.68/1.55 % (32180)------------------------------
% 1.68/1.55 % (32180)------------------------------
% 1.68/1.56 % (32181)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/4Mi)
% 1.68/1.56 % (32182)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/18Mi)
% 1.68/1.56 % (32181)Instruction limit reached!
% 1.68/1.56 % (32181)------------------------------
% 1.68/1.56 % (32181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.56 % (32181)Termination reason: Unknown
% 1.68/1.56 % (32181)Termination phase: Saturation
% 1.68/1.56
% 1.68/1.56 % (32181)Memory used [KB]: 5500
% 1.68/1.56 % (32181)Time elapsed: 0.004 s
% 1.68/1.56 % (32181)Instructions burned: 4 (million)
% 1.68/1.56 % (32181)------------------------------
% 1.68/1.56 % (32181)------------------------------
% 1.68/1.56 % (32183)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/710Mi)
% 1.68/1.57 % (32184)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/6Mi)
% 1.68/1.57 % (32182)Instruction limit reached!
% 1.68/1.57 % (32182)------------------------------
% 1.68/1.57 % (32182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.57 % (32182)Termination reason: Unknown
% 1.68/1.57 % (32182)Termination phase: Saturation
% 1.68/1.57
% 1.68/1.57 % (32182)Memory used [KB]: 5500
% 1.68/1.57 % (32182)Time elapsed: 0.011 s
% 1.68/1.57 % (32182)Instructions burned: 19 (million)
% 1.68/1.57 % (32182)------------------------------
% 1.68/1.57 % (32182)------------------------------
% 1.68/1.57 % (32184)Instruction limit reached!
% 1.68/1.57 % (32184)------------------------------
% 1.68/1.57 % (32184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.57 % (32184)Termination reason: Unknown
% 1.68/1.57 % (32184)Termination phase: Saturation
% 1.68/1.57
% 1.68/1.57 % (32184)Memory used [KB]: 5500
% 1.68/1.57 % (32184)Time elapsed: 0.005 s
% 1.68/1.57 % (32184)Instructions burned: 7 (million)
% 1.68/1.57 % (32184)------------------------------
% 1.68/1.57 % (32184)------------------------------
% 1.68/1.57 % (32185)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_32051 for (2999ds/902Mi)
% 1.68/1.58 % (32163)Instruction limit reached!
% 1.68/1.58 % (32163)------------------------------
% 1.68/1.58 % (32163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.58 % (32163)Termination reason: Unknown
% 1.68/1.58 % (32163)Termination phase: Saturation
% 1.68/1.58
% 1.68/1.58 % (32163)Memory used [KB]: 6396
% 1.68/1.58 % (32163)Time elapsed: 0.092 s
% 1.68/1.58 % (32163)Instructions burned: 184 (million)
% 1.68/1.58 % (32163)------------------------------
% 1.68/1.58 % (32163)------------------------------
% 1.68/1.58 % (32186)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_32051 for (2999ds/21Mi)
% 1.68/1.59 % (32187)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32051 for (2999ds/5Mi)
% 1.68/1.59 % (32187)Instruction limit reached!
% 1.68/1.59 % (32187)------------------------------
% 1.68/1.59 % (32187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.59 % (32187)Termination reason: Unknown
% 1.68/1.59 % (32187)Termination phase: Saturation
% 1.68/1.59
% 1.68/1.59 % (32187)Memory used [KB]: 5500
% 1.68/1.59 % (32187)Time elapsed: 0.004 s
% 1.68/1.59 % (32187)Instructions burned: 5 (million)
% 1.68/1.59 % (32187)------------------------------
% 1.68/1.59 % (32187)------------------------------
% 1.68/1.59 % (32188)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_32051 for (2999ds/6Mi)
% 1.68/1.59 % (32186)Instruction limit reached!
% 1.68/1.59 % (32186)------------------------------
% 1.68/1.59 % (32186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.59 % (32186)Termination reason: Unknown
% 1.68/1.59 % (32186)Termination phase: Saturation
% 1.68/1.59
% 1.68/1.59 % (32186)Memory used [KB]: 5628
% 1.68/1.59 % (32186)Time elapsed: 0.013 s
% 1.68/1.59 % (32186)Instructions burned: 21 (million)
% 1.68/1.59 % (32186)------------------------------
% 1.68/1.59 % (32186)------------------------------
% 1.68/1.60 % (32188)Instruction limit reached!
% 1.68/1.60 % (32188)------------------------------
% 1.68/1.60 % (32188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.60 % (32188)Termination reason: Unknown
% 1.68/1.60 % (32188)Termination phase: Saturation
% 1.68/1.60
% 1.68/1.60 % (32188)Memory used [KB]: 5500
% 1.68/1.60 % (32188)Time elapsed: 0.005 s
% 1.68/1.60 % (32188)Instructions burned: 7 (million)
% 1.68/1.60 % (32188)------------------------------
% 1.68/1.60 % (32188)------------------------------
% 1.68/1.60 % (32189)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32051 for (2998ds/377Mi)
% 1.68/1.61 % (32190)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_32051 for (2998ds/779Mi)
% 1.68/1.61 % (32191)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_32051 for (2998ds/19Mi)
% 1.68/1.62 % (32191)Refutation not found, incomplete strategy
% 1.68/1.62 % (32191)------------------------------
% 1.68/1.62 % (32191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.62 % (32191)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.62
% 1.68/1.62
% 1.68/1.62 % (32191)Memory used [KB]: 5500
% 1.68/1.62 % (32191)Time elapsed: 0.004 s
% 1.68/1.62 % (32191)Instructions burned: 5 (million)
% 1.68/1.62 % (32191)------------------------------
% 1.68/1.62 % (32191)------------------------------
% 1.68/1.62 % (32174)First to succeed.
% 1.68/1.62 % (32168)Instruction limit reached!
% 1.68/1.62 % (32168)------------------------------
% 1.68/1.62 % (32168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.62 % (32168)Termination reason: Unknown
% 1.68/1.62 % (32168)Termination phase: Saturation
% 1.68/1.62
% 1.68/1.62 % (32168)Memory used [KB]: 6140
% 1.68/1.62 % (32168)Time elapsed: 0.132 s
% 1.68/1.62 % (32168)Instructions burned: 275 (million)
% 1.68/1.62 % (32168)------------------------------
% 1.68/1.62 % (32168)------------------------------
% 1.68/1.62 % (32174)Refutation found. Thanks to Tanya!
% 1.68/1.62 % SZS status Theorem for DTF2THF_32051
% 1.68/1.62 % SZS output start Proof for DTF2THF_32051
% 1.68/1.62 thf(func_def_0, type, cJ: $i > $i).
% 1.68/1.62 thf(func_def_1, type, cP: $i > $i > $i).
% 1.68/1.62 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 1.68/1.62 thf(f641,plain,(
% 1.68/1.62 $false),
% 1.68/1.62 inference(trivial_inequality_removal,[status(thm)],[f640])).
% 1.68/1.62 thf(f640,plain,(
% 1.68/1.62 ($true = $false)),
% 1.68/1.62 inference(boolean_simplification,[status(thm)],[f639])).
% 1.68/1.62 thf(f639,plain,(
% 1.68/1.62 (((cJ @ (cP @ sK3 @ sK2)) = (cJ @ (cP @ sK3 @ sK2))) = $false)),
% 1.68/1.62 inference(backward_demodulation,[status(thm)],[f17,f597])).
% 1.68/1.62 thf(f597,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ X1) @ (cJ @ X0)) = (cJ @ (cP @ X0 @ X1)))) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f167,f71])).
% 1.68/1.62 thf(f71,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = X1)) )),
% 1.68/1.62 inference(forward_demodulation,[status(thm)],[f66,f34])).
% 1.68/1.62 thf(f34,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (((cP @ cE @ X1) = X1)) )),
% 1.68/1.62 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.68/1.62 thf(f33,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = ((cP @ cE @ X1) = X1))) )),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.68/1.62 thf(f32,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((cP @ cE @ Y0) = Y0)) @ X1))) )),
% 1.68/1.62 inference(pi_clausification,[status(thm)],[f24])).
% 1.68/1.62 thf(f24,plain,(
% 1.68/1.62 ($true = (!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))))),
% 1.68/1.62 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.68/1.62 thf(f22,plain,(
% 1.68/1.62 ($true = ((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))))),
% 1.68/1.62 inference(boolean_simplification,[status(thm)],[f21])).
% 1.68/1.62 thf(f21,plain,(
% 1.68/1.62 ($true = (((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))) & $true))),
% 1.68/1.62 inference(backward_demodulation,[status(thm)],[f11,f19])).
% 1.68/1.62 thf(f19,plain,(
% 1.68/1.62 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0))))))))))),
% 1.68/1.62 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.68/1.62 thf(f11,plain,(
% 1.68/1.62 ($true = (((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0)))))))))))),
% 1.68/1.62 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.68/1.62 thf(f7,plain,(
% 1.68/1.62 ($false = ((((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0)))))))))),
% 1.68/1.62 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.68/1.62 thf(f6,plain,(
% 1.68/1.62 ((~ ((((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0))))))))) = $true)),
% 1.68/1.62 inference(cnf_transformation,[status(thm)],[f5])).
% 1.68/1.62 thf(f5,plain,(
% 1.68/1.62 ((~ ((((!! @ $i @ (^[Y0 : $i]: ((cP @ cE @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0)))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0))))))))) = $true)),
% 1.68/1.62 inference(fool_elimination,[status(thm)],[f4])).
% 1.68/1.62 thf(f4,plain,(
% 1.68/1.62 ~((! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X3 : $i] : (cE = (cP @ (cJ @ X3) @ X3)) & ! [X4 : $i] : ((cP @ cE @ X4) = X4)) => ! [X5 : $i,X6 : $i] : ((cP @ (cJ @ X6) @ (cJ @ X5)) = (cJ @ (cP @ X5 @ X6))))),
% 1.68/1.62 inference(rectify,[status(thm)],[f2])).
% 1.68/1.62 thf(f2,negated_conjecture,(
% 1.68/1.62 ~((! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X0 : $i] : ((cP @ cE @ X0) = X0)) => ! [X3 : $i,X4 : $i] : ((cJ @ (cP @ X3 @ X4)) = (cP @ (cJ @ X4) @ (cJ @ X3))))),
% 1.68/1.62 inference(negated_conjecture,[status(cth)],[f1])).
% 1.68/1.62 thf(f1,conjecture,(
% 1.68/1.62 (! [X0 : $i,X1 : $i,X2 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : (cE = (cP @ (cJ @ X1) @ X1)) & ! [X0 : $i] : ((cP @ cE @ X0) = X0)) => ! [X3 : $i,X4 : $i] : ((cJ @ (cP @ X3 @ X4)) = (cP @ (cJ @ X4) @ (cJ @ X3)))),
% 1.68/1.62 file('/export/starexec/sandbox/tmp/tmp.oLyTMbwlcc/DTF2THF_32051.p',cTHM18_pme)).
% 1.68/1.62 thf(f66,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ X0) @ (cP @ X0 @ X1)) = (cP @ cE @ X1))) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f43,f29])).
% 1.68/1.62 thf(f29,plain,(
% 1.68/1.62 ( ! [X1 : $i] : ((cE = (cP @ (cJ @ X1) @ X1))) )),
% 1.68/1.62 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.68/1.62 thf(f28,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = (cE = (cP @ (cJ @ X1) @ X1)))) )),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.68/1.62 thf(f27,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))) @ X1))) )),
% 1.68/1.62 inference(pi_clausification,[status(thm)],[f26])).
% 1.68/1.62 thf(f26,plain,(
% 1.68/1.62 ($true = (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0)))))),
% 1.68/1.62 inference(boolean_simplification,[status(thm)],[f25])).
% 1.68/1.62 thf(f25,plain,(
% 1.68/1.62 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (cE = (cP @ (cJ @ Y0) @ Y0))))))),
% 1.68/1.62 inference(backward_demodulation,[status(thm)],[f22,f24])).
% 1.68/1.62 thf(f43,plain,(
% 1.68/1.62 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((cP @ (cP @ X3 @ X2) @ X1) = (cP @ X3 @ (cP @ X2 @ X1)))) )),
% 1.68/1.62 inference(equality_proxy_clausification,[status(thm)],[f42])).
% 1.68/1.62 thf(f42,plain,(
% 1.68/1.62 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((cP @ (cP @ X3 @ X2) @ X1) = (cP @ X3 @ (cP @ X2 @ X1))))) )),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.68/1.62 thf(f41,plain,(
% 1.68/1.62 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cP @ (cP @ Y0 @ X2) @ X1) = (cP @ Y0 @ (cP @ X2 @ X1)))) @ X3))) )),
% 1.68/1.62 inference(pi_clausification,[status(thm)],[f40])).
% 1.68/1.62 thf(f40,plain,(
% 1.68/1.62 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((cP @ (cP @ Y0 @ X2) @ X1) = (cP @ Y0 @ (cP @ X2 @ X1))))) = $true)) )),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.68/1.62 thf(f39,plain,(
% 1.68/1.62 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cP @ Y1 @ Y0) @ X1) = (cP @ Y1 @ (cP @ Y0 @ X1)))))) @ X2))) )),
% 1.68/1.62 inference(pi_clausification,[status(thm)],[f38])).
% 1.68/1.62 thf(f38,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cP @ Y1 @ Y0) @ X1) = (cP @ Y1 @ (cP @ Y0 @ X1))))))))) )),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.68/1.62 thf(f37,plain,(
% 1.68/1.62 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y2 @ Y1) @ Y0) = (cP @ Y2 @ (cP @ Y1 @ Y0)))))))) @ X1))) )),
% 1.68/1.62 inference(pi_clausification,[status(thm)],[f19])).
% 1.68/1.62 thf(f167,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ (cP @ X1 @ X0)) @ X1) = (cJ @ X0))) )),
% 1.68/1.62 inference(forward_demodulation,[status(thm)],[f161,f88])).
% 1.68/1.62 thf(f88,plain,(
% 1.68/1.62 ( ! [X0 : $i] : (((cP @ X0 @ cE) = X0)) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f77,f74])).
% 1.68/1.62 thf(f74,plain,(
% 1.68/1.62 ( ! [X0 : $i] : (((cP @ (cJ @ (cJ @ X0)) @ cE) = X0)) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f71,f29])).
% 1.68/1.62 thf(f77,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ X1) = (cP @ (cJ @ (cJ @ X0)) @ X1))) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f71,f71])).
% 1.68/1.62 thf(f161,plain,(
% 1.68/1.62 ( ! [X0 : $i,X1 : $i] : (((cP @ (cJ @ (cP @ X1 @ X0)) @ (cP @ X1 @ cE)) = (cJ @ X0))) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f76,f87])).
% 1.68/1.62 thf(f87,plain,(
% 1.68/1.62 ( ! [X0 : $i] : ((cE = (cP @ X0 @ (cJ @ X0)))) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f77,f29])).
% 1.68/1.62 thf(f76,plain,(
% 1.68/1.62 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cP @ (cJ @ (cP @ X0 @ X1)) @ (cP @ X0 @ (cP @ X1 @ X2))) = X2)) )),
% 1.68/1.62 inference(superposition,[status(thm)],[f71,f43])).
% 1.68/1.62 thf(f17,plain,(
% 1.68/1.62 ($false = ((cP @ (cJ @ sK2) @ (cJ @ sK3)) = (cJ @ (cP @ sK3 @ sK2))))),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.68/1.62 thf(f16,plain,(
% 1.68/1.62 (((^[Y0 : $i]: ((cP @ (cJ @ sK2) @ (cJ @ Y0)) = (cJ @ (cP @ Y0 @ sK2)))) @ sK3) = $false)),
% 1.68/1.62 inference(sigma_clausification,[status(thm)],[f15])).
% 1.68/1.62 thf(f15,plain,(
% 1.68/1.62 ((!! @ $i @ (^[Y0 : $i]: ((cP @ (cJ @ sK2) @ (cJ @ Y0)) = (cJ @ (cP @ Y0 @ sK2))))) = $false)),
% 1.68/1.62 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.68/1.62 thf(f14,plain,(
% 1.68/1.62 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0)))))) @ sK2) = $false)),
% 1.68/1.62 inference(sigma_clausification,[status(thm)],[f13])).
% 1.68/1.62 thf(f13,plain,(
% 1.68/1.62 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0))))))))),
% 1.68/1.62 inference(boolean_simplification,[status(thm)],[f12])).
% 1.68/1.62 thf(f12,plain,(
% 1.68/1.62 (($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cJ @ Y0) @ (cJ @ Y1)) = (cJ @ (cP @ Y1 @ Y0)))))))) = $false)),
% 1.68/1.62 inference(backward_demodulation,[status(thm)],[f7,f11])).
% 1.68/1.62 % SZS output end Proof for DTF2THF_32051
% 1.68/1.62 % (32174)------------------------------
% 1.68/1.62 % (32174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.62 % (32174)Termination reason: Refutation
% 1.68/1.62
% 1.68/1.62 % (32174)Memory used [KB]: 6268
% 1.68/1.62 % (32174)Time elapsed: 0.102 s
% 1.68/1.62 % (32174)Instructions burned: 198 (million)
% 1.68/1.62 % (32174)------------------------------
% 1.68/1.62 % (32174)------------------------------
% 1.68/1.62 % (32162)Success in time 0.133 s
%------------------------------------------------------------------------------