%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : GRP001^5 : 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 : n022.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 08:49:17 AM UTC 2026
% Result : Theorem 1.62s 1.35s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 265 ( 109 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 516 ( 4 ~; 0 |; 28 &; 418 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% ( 59 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 127 ( 67 ^; 60 !; 0 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $i ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f171,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
$false = $true,
inference(boolean_simplification,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
= ( ( cP @ sK2 @ sK3 )
= ( cP @ sK2 @ sK3 ) ) ),
inference(backward_demodulation,[status(thm)],[f17,f160]) ).
thf(f160,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ X1 )
= ( cP @ X1 @ X0 ) ),
inference(superposition,[status(thm)],[f100,f139]) ).
thf(f139,plain,
! [X0: $i,X1: $i] :
( ( cP @ X1 @ ( cP @ X0 @ X1 ) )
= X0 ),
inference(forward_demodulation,[status(thm)],[f135,f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( cP @ X1 @ e )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( ( cP @ X1 @ e )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f31,f33]) ).
thf(f33,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& $true )
= $true ),
inference(backward_demodulation,[status(thm)],[f20,f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ e )
= Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( e
= ( cP @ X0 @ X0 ) )
& ! [X1: $i,X2: $i,X3: $i] :
( ( cP @ ( cP @ X3 @ X2 ) @ X1 )
= ( cP @ X3 @ ( cP @ X2 @ X1 ) ) )
& ! [X4: $i] :
( ( cP @ X4 @ e )
= X4 )
& ! [X5: $i] :
( ( cP @ e @ X5 )
= X5 ) )
=> ! [X6: $i,X7: $i] :
( ( cP @ X6 @ X7 )
= ( cP @ X7 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i] :
( e
= ( cP @ X2 @ X2 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 ) )
=> ! [X3: $i,X4: $i] :
( ( cP @ X3 @ X4 )
= ( cP @ X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i] :
( e
= ( cP @ X2 @ X2 ) )
& ! [X2: $i,X1: $i,X0: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) )
& ! [X1: $i] :
( ( cP @ X1 @ e )
= X1 )
& ! [X0: $i] :
( ( cP @ e @ X0 )
= X0 ) )
=> ! [X3: $i,X4: $i] :
( ( cP @ X3 @ X4 )
= ( cP @ X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XXyVxDFIGl/DTF2THF_16694.p',cGRP_COMM2) ).
thf(f135,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ e )
= ( cP @ X1 @ ( cP @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f100,f96]) ).
thf(f96,plain,
! [X0: $i,X1: $i] :
( e
= ( cP @ X0 @ ( cP @ X1 @ ( cP @ X0 @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f58,f25]) ).
thf(f25,plain,
! [X1: $i] :
( e
= ( cP @ X1 @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( e
= ( cP @ X1 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
& ( !! @ $i
@ ^ [Y0: $i] :
( e
= ( cP @ Y0 @ Y0 ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f11,f20]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( cP @ X1 @ ( cP @ X2 @ X3 ) )
= ( cP @ ( cP @ X1 @ X2 ) @ X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( cP @ ( cP @ X1 @ X2 ) @ X3 )
= ( cP @ X1 @ ( cP @ X2 @ X3 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ Y0 )
= ( cP @ X1 @ ( cP @ X2 @ Y0 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ ( cP @ X1 @ X2 ) @ Y0 )
= ( cP @ X1 @ ( cP @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cP @ X1 @ Y0 ) @ Y1 )
= ( cP @ X1 @ ( cP @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ ( cP @ X1 @ Y0 ) @ Y1 )
= ( cP @ X1 @ ( cP @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( cP @ ( cP @ Y0 @ Y1 ) @ Y2 )
= ( cP @ Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f100,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[status(thm)],[f92,f45]) ).
thf(f45,plain,
! [X1: $i] :
( ( cP @ e @ X1 )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( ( cP @ e @ X1 )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cP @ e @ Y0 )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f92,plain,
! [X0: $i,X1: $i] :
( ( cP @ X0 @ ( cP @ X0 @ X1 ) )
= ( cP @ e @ X1 ) ),
inference(superposition,[status(thm)],[f58,f25]) ).
thf(f17,plain,
( $false
= ( ( cP @ sK3 @ sK2 )
= ( cP @ sK2 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $false
= ( ^ [Y0: $i] :
( ( cP @ Y0 @ sK2 )
= ( cP @ sK2 @ Y0 ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( cP @ Y0 @ sK2 )
= ( cP @ sK2 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f12]) ).
thf(f12,plain,
( $false
= ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cP @ Y1 @ Y0 )
= ( cP @ Y0 @ Y1 ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f7,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP001^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n022.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 07:31:51 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : GRP001^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.47 % Domain : Group Theory
% 0.29/0.47 % Problem : TPS problem GRP-COMM2
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : Group is Abelian iff every element has order 2.
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.47 % Source : [Bro09]
% 0.29/0.47 % Names : tps_0516 [Bro09]
% 0.29/0.47 % : GRP-COMM2 [TPS]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 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, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0
% 0.29/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.29/0.47 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.29/0.47 % Number of connectives : 22 ( 0 ~; 0 |; 3 &; 18 @)
% 0.29/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 8 ( 8 avg)
% 0.29/0.47 % Number of types : 1 ( 0 usr)
% 0.29/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.47 % :
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(cP,type,
% 0.29/0.47 cP: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(e,type,
% 0.29/0.47 e: $i ).
% 0.29/0.47
% 0.29/0.47 thf(cGRP_COMM2,conjecture,
% 0.29/0.47 ( ( ! [Xx: $i] :
% 0.29/0.47 ( ( cP @ e @ Xx )
% 0.29/0.47 = Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( cP @ Xy @ e )
% 0.29/0.47 = Xy )
% 0.29/0.47 & ! [Xz: $i] :
% 0.29/0.47 ( ( cP @ Xz @ Xz )
% 0.29/0.47 = e )
% 0.29/0.47 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 0.29/0.47 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
% 0.29/0.47 => ! [Xa: $i,Xb: $i] :
% 0.29/0.47 ( ( cP @ Xa @ Xb )
% 0.29/0.47 = ( cP @ Xb @ Xa ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.46/1.27 ---- Embedded in THF ---
% 1.46/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.27 %%% Generated on Tue Feb 24 07:31:52 EST 2026
% 1.46/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.27 %%% Logic specification used:
% 1.46/1.27 %%% thf(spec, logic, $$dhol).
% 1.46/1.27
% 1.46/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XXyVxDFIGl/DTF2DTF16694.p
% See solution above
% 1.46/1.27 ------------------------
% 1.46/1.28 ---- Cleaned THF ---
% 1.46/1.28 thf(cP,type,
% 1.46/1.28 cP: $i > $i > $i ).
% 1.46/1.28
% 1.46/1.28 thf(e,type,
% 1.46/1.28 e: $i ).
% 1.46/1.28
% 1.46/1.28 thf(cGRP_COMM2,conjecture,
% 1.46/1.28 ( ( ! [Xx: $i] :
% 1.46/1.28 ( ( cP @ e @ Xx )
% 1.46/1.28 = Xx )
% 1.46/1.28 & ! [Xy: $i] :
% 1.46/1.28 ( ( cP @ Xy @ e )
% 1.46/1.28 = Xy )
% 1.46/1.28 & ! [Xz: $i] :
% 1.46/1.28 ( ( cP @ Xz @ Xz )
% 1.46/1.28 = e )
% 1.46/1.28 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.46/1.28 ( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
% 1.46/1.28 = ( cP @ Xx @ ( cP @ Xy @ Xz ) ) ) )
% 1.46/1.28 => ! [Xa: $i,Xb: $i] :
% 1.46/1.28 ( ( cP @ Xa @ Xb )
% 1.46/1.28 = ( cP @ Xb @ Xa ) ) ) ).
% 1.46/1.28 ------------------------
% 1.46/1.29 % (16971)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_16694 for (2999ds/4Mi)
% 1.46/1.29 % (16973)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/2Mi)
% 1.46/1.29 % (16973)Instruction limit reached!
% 1.46/1.29 % (16973)------------------------------
% 1.46/1.29 % (16973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (16973)Termination reason: Unknown
% 1.46/1.29 % (16973)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (16973)Memory used [KB]: 5500
% 1.46/1.29 % (16973)Time elapsed: 0.002 s
% 1.46/1.29 % (16973)Instructions burned: 2 (million)
% 1.46/1.29 % (16973)------------------------------
% 1.46/1.29 % (16973)------------------------------
% 1.46/1.29 % (16971)Instruction limit reached!
% 1.46/1.29 % (16971)------------------------------
% 1.46/1.29 % (16971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (16971)Termination reason: Unknown
% 1.46/1.29 % (16971)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (16971)Memory used [KB]: 5500
% 1.46/1.29 % (16971)Time elapsed: 0.004 s
% 1.46/1.29 % (16971)Instructions burned: 6 (million)
% 1.46/1.29 % (16971)------------------------------
% 1.46/1.29 % (16971)------------------------------
% 1.62/1.30 % (16970)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/183Mi)
% 1.62/1.30 % (16974)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_16694 for (2999ds/2Mi)
% 1.62/1.30 % (16975)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_16694 for (2999ds/275Mi)
% 1.62/1.30 % (16976)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/18Mi)
% 1.62/1.30 % (16972)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_16694 for (2999ds/27Mi)
% 1.62/1.30 % (16974)Instruction limit reached!
% 1.62/1.30 % (16974)------------------------------
% 1.62/1.30 % (16974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (16974)Termination reason: Unknown
% 1.62/1.30 % (16974)Termination phase: Property scanning
% 1.62/1.30
% 1.62/1.30 % (16974)Memory used [KB]: 895
% 1.62/1.30 % (16974)Time elapsed: 0.003 s
% 1.62/1.30 % (16974)Instructions burned: 2 (million)
% 1.62/1.30 % (16974)------------------------------
% 1.62/1.30 % (16974)------------------------------
% 1.62/1.30 % (16978)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_16694 for (2999ds/37Mi)
% 1.62/1.30 % (16977)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/3Mi)
% 1.62/1.30 % (16977)Instruction limit reached!
% 1.62/1.30 % (16977)------------------------------
% 1.62/1.30 % (16977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (16977)Termination reason: Unknown
% 1.62/1.30 % (16977)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (16977)Memory used [KB]: 5500
% 1.62/1.30 % (16977)Time elapsed: 0.003 s
% 1.62/1.30 % (16977)Instructions burned: 3 (million)
% 1.62/1.30 % (16977)------------------------------
% 1.62/1.30 % (16977)------------------------------
% 1.62/1.31 % (16976)Instruction limit reached!
% 1.62/1.31 % (16976)------------------------------
% 1.62/1.31 % (16976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (16976)Termination reason: Unknown
% 1.62/1.31 % (16976)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (16976)Memory used [KB]: 5500
% 1.62/1.31 % (16976)Time elapsed: 0.014 s
% 1.62/1.31 % (16976)Instructions burned: 19 (million)
% 1.62/1.31 % (16976)------------------------------
% 1.62/1.31 % (16976)------------------------------
% 1.62/1.31 % (16980)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_16694 for (2999ds/3Mi)
% 1.62/1.32 % (16978)Instruction limit reached!
% 1.62/1.32 % (16978)------------------------------
% 1.62/1.32 % (16978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16978)Termination reason: Unknown
% 1.62/1.32 % (16978)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (16978)Memory used [KB]: 5628
% 1.62/1.32 % (16978)Time elapsed: 0.013 s
% 1.62/1.32 % (16978)Instructions burned: 38 (million)
% 1.62/1.32 % (16978)------------------------------
% 1.62/1.32 % (16978)------------------------------
% 1.62/1.32 % (16980)Instruction limit reached!
% 1.62/1.32 % (16980)------------------------------
% 1.62/1.32 % (16980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16980)Termination reason: Unknown
% 1.62/1.32 % (16980)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (16980)Memory used [KB]: 5500
% 1.62/1.32 % (16980)Time elapsed: 0.003 s
% 1.62/1.32 % (16980)Instructions burned: 3 (million)
% 1.62/1.32 % (16980)------------------------------
% 1.62/1.32 % (16980)------------------------------
% 1.62/1.32 % (16972)Instruction limit reached!
% 1.62/1.32 % (16972)------------------------------
% 1.62/1.32 % (16972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (16972)Termination reason: Unknown
% 1.62/1.32 % (16972)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (16972)Memory used [KB]: 5628
% 1.62/1.32 % (16972)Time elapsed: 0.018 s
% 1.62/1.32 % (16972)Instructions burned: 28 (million)
% 1.62/1.32 % (16972)------------------------------
% 1.62/1.32 % (16972)------------------------------
% 1.62/1.32 % (16979)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_16694 for (2999ds/15Mi)
% 1.62/1.32 % (16982)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/7Mi)
% 1.62/1.33 % (16983)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/16Mi)
% 1.62/1.33 % (16979)Instruction limit reached!
% 1.62/1.33 % (16979)------------------------------
% 1.62/1.33 % (16979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16979)Termination reason: Unknown
% 1.62/1.33 % (16979)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (16979)Memory used [KB]: 5500
% 1.62/1.33 % (16979)Time elapsed: 0.011 s
% 1.62/1.33 % (16979)Instructions burned: 15 (million)
% 1.62/1.33 % (16979)------------------------------
% 1.62/1.33 % (16979)------------------------------
% 1.62/1.33 % (16982)Instruction limit reached!
% 1.62/1.33 % (16982)------------------------------
% 1.62/1.33 % (16982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16982)Termination reason: Unknown
% 1.62/1.33 % (16982)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (16982)Memory used [KB]: 1023
% 1.62/1.33 % (16982)Time elapsed: 0.004 s
% 1.62/1.33 % (16982)Instructions burned: 9 (million)
% 1.62/1.33 % (16982)------------------------------
% 1.62/1.33 % (16982)------------------------------
% 1.62/1.33 % (16984)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_16694 for (2999ds/3Mi)
% 1.62/1.33 % (16981)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_16694 for (2999ds/1041Mi)
% 1.62/1.33 % (16984)Instruction limit reached!
% 1.62/1.33 % (16984)------------------------------
% 1.62/1.33 % (16984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16984)Termination reason: Unknown
% 1.62/1.33 % (16984)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (16984)Memory used [KB]: 5500
% 1.62/1.33 % (16984)Time elapsed: 0.003 s
% 1.62/1.33 % (16984)Instructions burned: 3 (million)
% 1.62/1.33 % (16984)------------------------------
% 1.62/1.33 % (16984)------------------------------
% 1.62/1.33 % (16983)Instruction limit reached!
% 1.62/1.33 % (16983)------------------------------
% 1.62/1.33 % (16983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (16983)Termination reason: Unknown
% 1.62/1.33 % (16983)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (16983)Memory used [KB]: 5628
% 1.62/1.33 % (16983)Time elapsed: 0.008 s
% 1.62/1.33 % (16983)Instructions burned: 16 (million)
% 1.62/1.33 % (16983)------------------------------
% 1.62/1.33 % (16983)------------------------------
% 1.62/1.34 % (16986)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/7Mi)
% 1.62/1.34 % (16986)Refutation not found, incomplete strategy
% 1.62/1.34 % (16986)------------------------------
% 1.62/1.34 % (16986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (16986)Termination reason: Refutation not found, incomplete strategy
% 1.62/1.34
% 1.62/1.34
% 1.62/1.34 % (16986)Memory used [KB]: 5500
% 1.62/1.34 % (16986)Time elapsed: 0.001 s
% 1.62/1.34 % (16986)Instructions burned: 1 (million)
% 1.62/1.34 % (16986)------------------------------
% 1.62/1.34 % (16986)------------------------------
% 1.62/1.34 % (16987)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/3Mi)
% 1.62/1.34 % (16987)Instruction limit reached!
% 1.62/1.34 % (16987)------------------------------
% 1.62/1.34 % (16987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (16987)Termination reason: Unknown
% 1.62/1.34 % (16987)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (16987)Memory used [KB]: 5500
% 1.62/1.34 % (16987)Time elapsed: 0.003 s
% 1.62/1.34 % (16987)Instructions burned: 4 (million)
% 1.62/1.34 % (16987)------------------------------
% 1.62/1.34 % (16987)------------------------------
% 1.62/1.34 % (16988)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/4Mi)
% 1.62/1.34 % (16985)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_16694 for (2999ds/3Mi)
% 1.62/1.34 % (16988)Instruction limit reached!
% 1.62/1.34 % (16988)------------------------------
% 1.62/1.34 % (16988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (16988)Termination reason: Unknown
% 1.62/1.34 % (16988)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (16988)Memory used [KB]: 5500
% 1.62/1.34 % (16988)Time elapsed: 0.004 s
% 1.62/1.34 % (16988)Instructions burned: 6 (million)
% 1.62/1.34 % (16988)------------------------------
% 1.62/1.34 % (16988)------------------------------
% 1.62/1.35 % (16985)Instruction limit reached!
% 1.62/1.35 % (16985)------------------------------
% 1.62/1.35 % (16985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (16985)Termination reason: Unknown
% 1.62/1.35 % (16985)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (16985)Memory used [KB]: 5500
% 1.62/1.35 % (16985)Time elapsed: 0.004 s
% 1.62/1.35 % (16985)Instructions burned: 3 (million)
% 1.62/1.35 % (16985)------------------------------
% 1.62/1.35 % (16985)------------------------------
% 1.62/1.35 % (16989)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/18Mi)
% 1.62/1.35 % (16981)First to succeed.
% 1.62/1.35 % (16990)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16694 for (2999ds/710Mi)
% 1.62/1.35 % (16981)Refutation found. Thanks to Tanya!
% 1.62/1.35 % SZS status Theorem for DTF2THF_16694
% 1.62/1.35 % SZS output start Proof for DTF2THF_16694
% 1.62/1.35 thf(func_def_0, type, cP: $i > $i > $i).
% 1.62/1.35 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.62/1.35 thf(f171,plain,(
% 1.62/1.35 $false),
% 1.62/1.35 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.62/1.35 thf(f170,plain,(
% 1.62/1.35 ($false = $true)),
% 1.62/1.35 inference(boolean_simplification,[status(thm)],[f169])).
% 1.62/1.35 thf(f169,plain,(
% 1.62/1.35 ($false = ((cP @ sK2 @ sK3) = (cP @ sK2 @ sK3)))),
% 1.62/1.35 inference(backward_demodulation,[status(thm)],[f17,f160])).
% 1.62/1.35 thf(f160,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ X1) = (cP @ X1 @ X0))) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f100,f139])).
% 1.62/1.35 thf(f139,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : (((cP @ X1 @ (cP @ X0 @ X1)) = X0)) )),
% 1.62/1.35 inference(forward_demodulation,[status(thm)],[f135,f38])).
% 1.62/1.35 thf(f38,plain,(
% 1.62/1.35 ( ! [X1 : $i] : (((cP @ X1 @ e) = X1)) )),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.62/1.35 thf(f37,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((cP @ X1 @ e) = X1) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.62/1.35 thf(f36,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)) @ X1) = $true)) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f35])).
% 1.62/1.35 thf(f35,plain,(
% 1.62/1.35 ((!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0))) = $true)),
% 1.62/1.35 inference(boolean_simplification,[status(thm)],[f34])).
% 1.62/1.35 thf(f34,plain,(
% 1.62/1.35 (($true & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) = $true)),
% 1.62/1.35 inference(backward_demodulation,[status(thm)],[f31,f33])).
% 1.62/1.35 thf(f33,plain,(
% 1.62/1.35 ((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) = $true)),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.62/1.35 thf(f31,plain,(
% 1.62/1.35 (((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) = $true)),
% 1.62/1.35 inference(boolean_simplification,[status(thm)],[f30])).
% 1.62/1.35 thf(f30,plain,(
% 1.62/1.35 ((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & $true) = $true)),
% 1.62/1.35 inference(backward_demodulation,[status(thm)],[f20,f28])).
% 1.62/1.35 thf(f28,plain,(
% 1.62/1.35 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2))))))))) = $true)),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.62/1.35 thf(f20,plain,(
% 1.62/1.35 ((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))))) = $true)),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.62/1.35 thf(f11,plain,(
% 1.62/1.35 (((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0))))) = $true)),
% 1.62/1.35 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.62/1.35 thf(f7,plain,(
% 1.62/1.35 ((((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1))))))) = $false)),
% 1.62/1.35 inference(not_proxy_clausification,[status(thm)],[f6])).
% 1.62/1.35 thf(f6,plain,(
% 1.62/1.35 ((~ (((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1)))))))) = $true)),
% 1.62/1.35 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.35 thf(f5,plain,(
% 1.62/1.35 ((~ (((((!! @ $i @ (^[Y0 : $i]: ((cP @ e @ Y0) = Y0))) & (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ e) = Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1)))))))) = $true)),
% 1.62/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.35 thf(f4,plain,(
% 1.62/1.35 ~((! [X0 : $i] : (e = (cP @ X0 @ X0)) & ! [X1 : $i,X2 : $i,X3 : $i] : ((cP @ (cP @ X3 @ X2) @ X1) = (cP @ X3 @ (cP @ X2 @ X1))) & ! [X4 : $i] : ((cP @ X4 @ e) = X4) & ! [X5 : $i] : ((cP @ e @ X5) = X5)) => ! [X6 : $i,X7 : $i] : ((cP @ X6 @ X7) = (cP @ X7 @ X6)))),
% 1.62/1.35 inference(rectify,[status(thm)],[f2])).
% 1.62/1.35 thf(f2,negated_conjecture,(
% 1.62/1.35 ~((! [X2 : $i] : (e = (cP @ X2 @ X2)) & ! [X2 : $i,X1 : $i,X0 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : ((cP @ X1 @ e) = X1) & ! [X0 : $i] : ((cP @ e @ X0) = X0)) => ! [X3 : $i,X4 : $i] : ((cP @ X3 @ X4) = (cP @ X4 @ X3)))),
% 1.62/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.35 thf(f1,conjecture,(
% 1.62/1.35 (! [X2 : $i] : (e = (cP @ X2 @ X2)) & ! [X2 : $i,X1 : $i,X0 : $i] : ((cP @ (cP @ X0 @ X1) @ X2) = (cP @ X0 @ (cP @ X1 @ X2))) & ! [X1 : $i] : ((cP @ X1 @ e) = X1) & ! [X0 : $i] : ((cP @ e @ X0) = X0)) => ! [X3 : $i,X4 : $i] : ((cP @ X3 @ X4) = (cP @ X4 @ X3))),
% 1.62/1.35 file('/export/starexec/sandbox2/tmp/tmp.XXyVxDFIGl/DTF2THF_16694.p',cGRP_COMM2)).
% 1.62/1.35 thf(f135,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ e) = (cP @ X1 @ (cP @ X0 @ X1)))) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f100,f96])).
% 1.62/1.35 thf(f96,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : ((e = (cP @ X0 @ (cP @ X1 @ (cP @ X0 @ X1))))) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f58,f25])).
% 1.62/1.35 thf(f25,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((e = (cP @ X1 @ X1))) )),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.62/1.35 thf(f24,plain,(
% 1.62/1.35 ( ! [X1 : $i] : (((e = (cP @ X1 @ X1)) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.62/1.35 thf(f23,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (e = (cP @ Y0 @ Y0))) @ X1) = $true)) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f22])).
% 1.62/1.35 thf(f22,plain,(
% 1.62/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0)))))),
% 1.62/1.35 inference(boolean_simplification,[status(thm)],[f21])).
% 1.62/1.35 thf(f21,plain,(
% 1.62/1.35 (($true & (!! @ $i @ (^[Y0 : $i]: (e = (cP @ Y0 @ Y0))))) = $true)),
% 1.62/1.35 inference(backward_demodulation,[status(thm)],[f11,f20])).
% 1.62/1.35 thf(f58,plain,(
% 1.62/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((cP @ X1 @ (cP @ X2 @ X3)) = (cP @ (cP @ X1 @ X2) @ X3))) )),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f57])).
% 1.62/1.35 thf(f57,plain,(
% 1.62/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((cP @ (cP @ X1 @ X2) @ X3) = (cP @ X1 @ (cP @ X2 @ X3))) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.62/1.35 thf(f56,plain,(
% 1.62/1.35 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cP @ (cP @ X1 @ X2) @ Y0) = (cP @ X1 @ (cP @ X2 @ Y0)))) @ X3))) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f55])).
% 1.62/1.35 thf(f55,plain,(
% 1.62/1.35 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((cP @ (cP @ X1 @ X2) @ Y0) = (cP @ X1 @ (cP @ X2 @ Y0))))) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f54])).
% 1.62/1.35 thf(f54,plain,(
% 1.62/1.35 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cP @ X1 @ Y0) @ Y1) = (cP @ X1 @ (cP @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f53])).
% 1.62/1.35 thf(f53,plain,(
% 1.62/1.35 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ (cP @ X1 @ Y0) @ Y1) = (cP @ X1 @ (cP @ Y0 @ Y1))))))) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f52])).
% 1.62/1.35 thf(f52,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((cP @ (cP @ Y0 @ Y1) @ Y2) = (cP @ Y0 @ (cP @ Y1 @ Y2)))))))) @ X1) = $true)) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f28])).
% 1.62/1.35 thf(f100,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ (cP @ X0 @ X1)) = X1)) )),
% 1.62/1.35 inference(forward_demodulation,[status(thm)],[f92,f45])).
% 1.62/1.35 thf(f45,plain,(
% 1.62/1.35 ( ! [X1 : $i] : (((cP @ e @ X1) = X1)) )),
% 1.62/1.35 inference(equality_proxy_clausification,[status(thm)],[f44])).
% 1.62/1.35 thf(f44,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((cP @ e @ X1) = X1) = $true)) )),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.62/1.35 thf(f43,plain,(
% 1.62/1.35 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((cP @ e @ Y0) = Y0)) @ X1) = $true)) )),
% 1.62/1.35 inference(pi_clausification,[status(thm)],[f33])).
% 1.62/1.35 thf(f92,plain,(
% 1.62/1.35 ( ! [X0 : $i,X1 : $i] : (((cP @ X0 @ (cP @ X0 @ X1)) = (cP @ e @ X1))) )),
% 1.62/1.35 inference(superposition,[status(thm)],[f58,f25])).
% 1.62/1.35 thf(f17,plain,(
% 1.62/1.35 ($false = ((cP @ sK3 @ sK2) = (cP @ sK2 @ sK3)))),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.62/1.35 thf(f16,plain,(
% 1.62/1.35 ($false = ((^[Y0 : $i]: ((cP @ Y0 @ sK2) = (cP @ sK2 @ Y0))) @ sK3))),
% 1.62/1.35 inference(sigma_clausification,[status(thm)],[f15])).
% 1.62/1.35 thf(f15,plain,(
% 1.62/1.35 ($false = (!! @ $i @ (^[Y0 : $i]: ((cP @ Y0 @ sK2) = (cP @ sK2 @ Y0)))))),
% 1.62/1.35 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.62/1.35 thf(f14,plain,(
% 1.62/1.35 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1))))) @ sK2))),
% 1.62/1.35 inference(sigma_clausification,[status(thm)],[f13])).
% 1.62/1.35 thf(f13,plain,(
% 1.62/1.35 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1)))))))),
% 1.62/1.35 inference(boolean_simplification,[status(thm)],[f12])).
% 1.62/1.35 thf(f12,plain,(
% 1.62/1.35 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cP @ Y1 @ Y0) = (cP @ Y0 @ Y1))))))))),
% 1.62/1.35 inference(backward_demodulation,[status(thm)],[f7,f11])).
% 1.62/1.35 % SZS output end Proof for DTF2THF_16694
% 1.62/1.35 % (16981)------------------------------
% 1.62/1.35 % (16981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (16981)Termination reason: Refutation
% 1.62/1.35
% 1.62/1.35 % (16981)Memory used [KB]: 5628
% 1.62/1.35 % (16981)Time elapsed: 0.024 s
% 1.62/1.35 % (16981)Instructions burned: 33 (million)
% 1.62/1.35 % (16981)------------------------------
% 1.62/1.35 % (16981)------------------------------
% 1.62/1.35 % (16969)Success in time 0.06 s
%------------------------------------------------------------------------------