%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO378^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:54:05 AM UTC 2026
% Result : Theorem 1.61s 1.31s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 154 ( 73 equ; 9 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 127 ( 11 ~; 6 |; 20 &; 71 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 5 usr; 5 con; 0-2 aty)
% ( 0 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 58 ( 33 ^; 17 !; 8 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQDP0: $i > $o ).
thf(func_def_2,type,
cQDP1: ( $i > $o ) > $o ).
thf(func_def_3,type,
cQDP2: ( ( $i > $o ) > $o ) > $o ).
thf(func_def_15,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f33,plain,
$false,
inference(equality_resolution,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $i] : ( c != X0 ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i] :
( ( c = X0 )
= $false ),
inference(equality_resolution,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i > $o,X1: $i] :
( ( ( (=) @ c )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i > $o] :
( ( ( ?? @ $i @ X0 )
= $false )
| ( ( (=) @ c )
!= X0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i > $o] :
( ( ( ( (=) @ c )
= X0 )
= $false )
| ( ( ?? @ $i @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $i > $o] :
( $false
= ( ( ?? @ $i @ X0 )
& ( ( (=) @ c )
= X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i > $o] :
( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) )
@ X0 )
= $false ),
inference(equality_resolution,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
!= X0 )
| ( ( X0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X0: ( $i > $o ) > $o,X1: $i > $o] :
( ( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
= X0 )
= $false )
| ( ( X0 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: ( $i > $o ) > $o] :
( ( ( ?? @ ( $i > $o ) @ X0 )
= $false )
| ( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
= X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: ( $i > $o ) > $o] :
( $true
!= ( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( ( (=) @ c )
= Y0 ) ) )
= X0 )
& ( ?? @ ( $i > $o ) @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: ( $i > $o ) > $o] :
( ( ^ [Y0: ( $i > $o ) > $o] :
( ( ( ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( ( ^ [Y2: $i] : ( c = Y2 ) )
= Y1 ) ) )
= Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) )
@ X0 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f18,f20]) ).
thf(f20,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( ( ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( ( ^ [Y2: $i] : ( c = Y2 ) )
= Y1 ) ) )
= Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f15,f19]) ).
thf(f19,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( ( ^ [Y1: $i] : ( c = Y1 ) )
= Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f16,f17]) ).
thf(f17,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( cQDP0
= ( ^ [Y0: $i] : ( c = Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( cQDP0
= ( ^ [X0: $i] : ( c = X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP0_def) ).
thf(f16,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( cQDP0 = Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( cQDP1
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
& ( cQDP0 = Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ^ [X0: $i > $o] :
( ( cQDP0 = X0 )
& ? [X1: $i] : ( X0 @ X1 ) ) )
= cQDP1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( ( ^ [X0: $i > $o] :
( ( cQDP0 = X0 )
& ? [X1: $i] : ( X0 @ X1 ) ) )
= cQDP1 ),
file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP1_def) ).
thf(f15,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( cQDP1 = Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( cQDP2
= ( ^ [Y0: ( $i > $o ) > $o] :
( ( cQDP1 = Y0 )
& ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
& ( cQDP1 = X0 ) ) )
= cQDP2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: ( $i > $o ) > $o] :
( ? [X1: $i > $o] : ( X0 @ X1 )
& ( cQDP1 = X0 ) ) )
= cQDP2 ),
file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP2_def) ).
thf(f18,plain,
! [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ? [X0: ( $i > $o ) > $o] :
( ( cQDP2 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
~ ? [X0: ( $i > $o ) > $o] : ( cQDP2 @ X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ? [X2: ( $i > $o ) > $o] : ( cQDP2 @ X2 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
? [X2: ( $i > $o ) > $o] : ( cQDP2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDTHM2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO378^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n018.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:29:01 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SYO378^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.19/0.47 % Domain : Syntactic
% 0.19/0.47 % Problem : TPS problem from QUANTDEPTH-THMS
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_0589 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 4 unt; 4 typ; 3 def)
% 0.19/0.47 % Number of atoms : 12 ( 6 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 1 ( 3 avg)
% 0.19/0.47 % Number of connectives : 5 ( 0 ~; 0 |; 2 &; 3 @)
% 0.19/0.47 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 3 ( 2 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 6 ( 3 ^; 0 !; 3 ?; 6 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(c_type,type,
% 0.19/0.47 c: $i ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP0_type,type,
% 0.19/0.47 cQDP0: $i > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP1_type,type,
% 0.19/0.47 cQDP1: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP2_type,type,
% 0.19/0.47 cQDP2: ( ( $i > $o ) > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP0_def,definition,
% 0.19/0.47 ( cQDP0
% 0.19/0.47 = ( ^ [Xz: $i] : ( Xz = c ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP1_def,definition,
% 0.19/0.47 ( cQDP1
% 0.19/0.47 = ( ^ [Xz: $i > $o] :
% 0.19/0.47 ( ( Xz = cQDP0 )
% 0.19/0.47 & ? [Xt: $i] : ( Xz @ Xt ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cQDP2_def,definition,
% 0.19/0.47 ( cQDP2
% 0.19/0.47 = ( ^ [Xz: ( $i > $o ) > $o] :
% 0.19/0.47 ( ( Xz = cQDP1 )
% 0.19/0.47 & ? [Xt: $i > $o] : ( Xz @ Xt ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(cQDTHM2,conjecture,
% 0.19/0.47 ? [Xs: ( $i > $o ) > $o] : ( cQDP2 @ Xs ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.43/1.28 ---- Embedded in THF ---
% 1.43/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.43/1.29 %%% Generated on Tue Feb 24 14:29:02 EST 2026
% 1.43/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.43/1.29 %%% Logic specification used:
% 1.43/1.29 %%% thf(spec, logic, $$dhol).
% 1.43/1.29
% 1.43/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2DTF13592.p
% See solution above
% 1.43/1.29 ------------------------
% 1.43/1.29 ---- Cleaned THF ---
% 1.43/1.30 thf(c_type,type,
% 1.43/1.30 c: $i ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP0_type,type,
% 1.43/1.30 cQDP0: $i > $o ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP1_type,type,
% 1.43/1.30 cQDP1: ( $i > $o ) > $o ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP2_type,type,
% 1.43/1.30 cQDP2: ( ( $i > $o ) > $o ) > $o ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP0_def,definition,
% 1.43/1.30 ( cQDP0
% 1.43/1.30 = ( ^ [Xz: $i] : ( Xz = c ) ) ) ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP1_def,definition,
% 1.43/1.30 ( cQDP1
% 1.43/1.30 = ( ^ [Xz: $i > $o] :
% 1.43/1.30 ( ( Xz = cQDP0 )
% 1.43/1.30 & ? [Xt: $i] : ( Xz @ Xt ) ) ) ) ).
% 1.43/1.30
% 1.43/1.30 thf(cQDP2_def,definition,
% 1.43/1.30 ( cQDP2
% 1.43/1.30 = ( ^ [Xz: ( $i > $o ) > $o] :
% 1.43/1.30 ( ( Xz = cQDP1 )
% 1.43/1.30 & ? [Xt: $i > $o] : ( Xz @ Xt ) ) ) ) ).
% 1.43/1.30
% 1.43/1.30 thf(cQDTHM2,conjecture,
% 1.43/1.30 ? [Xs: ( $i > $o ) > $o] : ( cQDP2 @ Xs ) ).
% 1.61/1.30 ------------------------
% 1.61/1.31 % (13789)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13592 for (2999ds/2Mi)
% 1.61/1.31 % (13789)Instruction limit reached!
% 1.61/1.31 % (13789)------------------------------
% 1.61/1.31 % (13789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (13789)Termination reason: Unknown
% 1.61/1.31 % (13789)Termination phase: Saturation
% 1.61/1.31
% 1.61/1.31 % (13789)Memory used [KB]: 5373
% 1.61/1.31 % (13789)Time elapsed: 0.002 s
% 1.61/1.31 % (13789)Instructions burned: 2 (million)
% 1.61/1.31 % (13789)------------------------------
% 1.61/1.31 % (13789)------------------------------
% 1.61/1.31 % (13787)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_13592 for (2999ds/4Mi)
% 1.61/1.31 % (13792)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13592 for (2999ds/18Mi)
% 1.61/1.31 % (13787)First to succeed.
% 1.61/1.31 % (13792)Also succeeded, but the first one will report.
% 1.61/1.31 % (13787)Refutation found. Thanks to Tanya!
% 1.61/1.31 % SZS status Theorem for DTF2THF_13592
% 1.61/1.31 % SZS output start Proof for DTF2THF_13592
% 1.61/1.31 thf(func_def_1, type, cQDP0: $i > $o).
% 1.61/1.31 thf(func_def_2, type, cQDP1: ($i > $o) > $o).
% 1.61/1.31 thf(func_def_3, type, cQDP2: (($i > $o) > $o) > $o).
% 1.61/1.31 thf(func_def_15, type, ph1: !>[X0: $tType]:(X0)).
% 1.61/1.31 thf(f33,plain,(
% 1.61/1.31 $false),
% 1.61/1.31 inference(equality_resolution,[status(thm)],[f32])).
% 1.61/1.31 thf(f32,plain,(
% 1.61/1.31 ( ! [X0 : $i] : ((c != X0)) )),
% 1.61/1.31 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.61/1.31 thf(f31,plain,(
% 1.61/1.31 ( ! [X0 : $i] : (((c = X0) = $false)) )),
% 1.61/1.31 inference(equality_resolution,[status(thm)],[f30])).
% 1.61/1.31 thf(f30,plain,(
% 1.61/1.31 ( ! [X0 : $i > $o,X1 : $i] : (((= @ c) != X0) | ((X0 @ X1) = $false)) )),
% 1.61/1.31 inference(pi_clausification,[status(thm)],[f29])).
% 1.61/1.31 thf(f29,plain,(
% 1.61/1.31 ( ! [X0 : $i > $o] : (((?? @ $i @ X0) = $false) | ((= @ c) != X0)) )),
% 1.61/1.31 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.61/1.31 thf(f28,plain,(
% 1.61/1.31 ( ! [X0 : $i > $o] : ((((= @ c) = X0) = $false) | ((?? @ $i @ X0) = $false)) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.61/1.31 thf(f27,plain,(
% 1.61/1.31 ( ! [X0 : $i > $o] : (($false = ((?? @ $i @ X0) & ((= @ c) = X0)))) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.61/1.31 thf(f26,plain,(
% 1.61/1.31 ( ! [X0 : $i > $o] : ((((^[Y0 : $i > $o]: ((?? @ $i @ Y0) & ((= @ c) = Y0))) @ X0) = $false)) )),
% 1.61/1.31 inference(equality_resolution,[status(thm)],[f25])).
% 1.61/1.31 thf(f25,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o,X1 : $i > $o] : (((^[Y0 : $i > $o]: ((?? @ $i @ Y0) & ((= @ c) = Y0))) != X0) | ((X0 @ X1) = $false)) )),
% 1.61/1.31 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.61/1.31 thf(f24,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o,X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((?? @ $i @ Y0) & ((= @ c) = Y0))) = X0) = $false) | ((X0 @ X1) = $false)) )),
% 1.61/1.31 inference(pi_clausification,[status(thm)],[f23])).
% 1.61/1.31 thf(f23,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o] : (((?? @ ($i > $o) @ X0) = $false) | (((^[Y0 : $i > $o]: ((?? @ $i @ Y0) & ((= @ c) = Y0))) = X0) = $false)) )),
% 1.61/1.31 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.61/1.31 thf(f22,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o] : (($true != (((^[Y0 : $i > $o]: ((?? @ $i @ Y0) & ((= @ c) = Y0))) = X0) & (?? @ ($i > $o) @ X0)))) )),
% 1.61/1.31 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.61/1.31 thf(f21,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: (((^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) & ((^[Y2 : $i]: (c = Y2)) = Y1))) = Y0) & (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1))))) @ X0) != $true)) )),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f18,f20])).
% 1.61/1.31 thf(f20,plain,(
% 1.61/1.31 (cQDP2 = (^[Y0 : ($i > $o) > $o]: (((^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2))) & ((^[Y2 : $i]: (c = Y2)) = Y1))) = Y0) & (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1))))))),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f15,f19])).
% 1.61/1.31 thf(f19,plain,(
% 1.61/1.31 (cQDP1 = (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) & ((^[Y1 : $i]: (c = Y1)) = Y0))))),
% 1.61/1.31 inference(definition_unfolding,[status(thm)],[f16,f17])).
% 1.61/1.31 thf(f17,plain,(
% 1.61/1.31 (cQDP0 = (^[Y0 : $i]: (c = Y0)))),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.61/1.31 thf(f7,plain,(
% 1.61/1.31 (cQDP0 = (^[Y0 : $i]: (c = Y0)))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f1])).
% 1.61/1.31 thf(f1,axiom,(
% 1.61/1.31 (cQDP0 = (^[X0 : $i] : ((c = X0))))),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP0_def)).
% 1.61/1.31 thf(f16,plain,(
% 1.61/1.31 (cQDP1 = (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) & (cQDP0 = Y0))))),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 1.61/1.31 thf(f11,plain,(
% 1.61/1.31 (cQDP1 = (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) & (cQDP0 = Y0))))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f10])).
% 1.61/1.31 thf(f10,plain,(
% 1.61/1.31 ((^[X0 : $i > $o] : ((cQDP0 = X0) & ? [X1 : $i] : (X0 @ X1))) = cQDP1)),
% 1.61/1.31 inference(rectify,[status(thm)],[f2])).
% 1.61/1.31 thf(f2,axiom,(
% 1.61/1.31 ((^[X0 : $i > $o] : ((cQDP0 = X0) & ? [X1 : $i] : (X0 @ X1))) = cQDP1)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP1_def)).
% 1.61/1.31 thf(f15,plain,(
% 1.61/1.31 (cQDP2 = (^[Y0 : ($i > $o) > $o]: ((cQDP1 = Y0) & (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1))))))),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f9])).
% 1.61/1.31 thf(f9,plain,(
% 1.61/1.31 (cQDP2 = (^[Y0 : ($i > $o) > $o]: ((cQDP1 = Y0) & (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (Y0 @ Y1))))))),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.31 thf(f8,plain,(
% 1.61/1.31 ((^[X0 : ($i > $o) > $o] : (? [X1 : $i > $o] : (X0 @ X1) & (cQDP1 = X0))) = cQDP2)),
% 1.61/1.31 inference(rectify,[status(thm)],[f3])).
% 1.61/1.31 thf(f3,axiom,(
% 1.61/1.31 ((^[X0 : ($i > $o) > $o] : (? [X1 : $i > $o] : (X0 @ X1) & (cQDP1 = X0))) = cQDP2)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDP2_def)).
% 1.61/1.31 thf(f18,plain,(
% 1.61/1.31 ( ! [X0 : ($i > $o) > $o] : (((cQDP2 @ X0) != $true)) )),
% 1.61/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.31 thf(f14,plain,(
% 1.61/1.31 ! [X0 : ($i > $o) > $o] : ((cQDP2 @ X0) != $true)),
% 1.61/1.31 inference(ennf_transformation,[status(thm)],[f13])).
% 1.61/1.31 thf(f13,plain,(
% 1.61/1.31 ~? [X0 : ($i > $o) > $o] : ((cQDP2 @ X0) = $true)),
% 1.61/1.31 inference(fool_elimination,[status(thm)],[f12])).
% 1.61/1.31 thf(f12,plain,(
% 1.61/1.31 ~? [X0 : ($i > $o) > $o] : (cQDP2 @ X0)),
% 1.61/1.31 inference(rectify,[status(thm)],[f5])).
% 1.61/1.31 thf(f5,negated_conjecture,(
% 1.61/1.31 ~? [X2 : ($i > $o) > $o] : (cQDP2 @ X2)),
% 1.61/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.61/1.31 thf(f4,conjecture,(
% 1.61/1.31 ? [X2 : ($i > $o) > $o] : (cQDP2 @ X2)),
% 1.61/1.31 file('/export/starexec/sandbox/tmp/tmp.lgVd4pVTtd/DTF2THF_13592.p',cQDTHM2)).
% 1.61/1.31 % SZS output end Proof for DTF2THF_13592
% 1.61/1.31 % (13787)------------------------------
% 1.61/1.31 % (13787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.31 % (13787)Termination reason: Refutation
% 1.61/1.31
% 1.61/1.31 % (13787)Memory used [KB]: 5500
% 1.61/1.31 % (13787)Time elapsed: 0.003 s
% 1.61/1.31 % (13787)Instructions burned: 2 (million)
% 1.61/1.31 % (13787)------------------------------
% 1.61/1.31 % (13787)------------------------------
% 1.61/1.31 % (13785)Success in time 0.005 s
%------------------------------------------------------------------------------