%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO317^5 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:56 AM UTC 2026
% Result : Theorem 1.63s 1.32s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 280 ( 83 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 338 ( 41 ~; 28 |; 42 &; 210 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 0 ^; 70 !; 12 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cEQ: $i > $i > $o ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_8,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_10,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f59,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
$true != $true,
inference(superposition,[status(thm)],[f55,f13]) ).
thf(f13,plain,
! [X5: $i] :
( ( cEQ @ X5 @ X5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ) )
& ! [X3: $i,X4: $i] :
( ( $true
= ( cEQ @ X4 @ X3 ) )
| ( ( cEQ @ ( f @ X4 ) @ ( f @ X3 ) )
!= $true ) )
& ! [X5: $i] :
( ( cEQ @ X5 @ X5 )
= $true )
& ( ( cP @ a )
= $true )
& ! [X6: $i,X7: $i] :
( ( $true
= ( cP @ X7 ) )
| ( $true
!= ( cEQ @ X6 @ X7 ) )
| ( $true
!= ( cP @ X6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ? [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
& ( $true
= ( X0 @ ( f @ X2 ) ) ) )
=> ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ? [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
& ( $true
= ( X0 @ ( f @ X2 ) ) ) ) )
& ! [X3: $i,X4: $i] :
( ( $true
= ( cEQ @ X4 @ X3 ) )
| ( ( cEQ @ ( f @ X4 ) @ ( f @ X3 ) )
!= $true ) )
& ! [X5: $i] :
( ( cEQ @ X5 @ X5 )
= $true )
& ( ( cP @ a )
= $true )
& ! [X6: $i,X7: $i] :
( ( $true
= ( cP @ X7 ) )
| ( $true
!= ( cEQ @ X6 @ X7 ) )
| ( $true
!= ( cP @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X5: $i > $o] :
( ! [X7: $i] :
( ( X5 @ X7 )
!= $true )
| ? [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
& ( ( X5 @ ( f @ X6 ) )
= $true ) ) )
& ! [X1: $i,X0: $i] :
( ( ( cEQ @ X0 @ X1 )
= $true )
| ( $true
!= ( cEQ @ ( f @ X0 ) @ ( f @ X1 ) ) ) )
& ! [X2: $i] :
( $true
= ( cEQ @ X2 @ X2 ) )
& ( ( cP @ a )
= $true )
& ! [X4: $i,X3: $i] :
( ( $true
= ( cP @ X3 ) )
| ( $true
!= ( cEQ @ X4 @ X3 ) )
| ( $true
!= ( cP @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X5: $i > $o] :
( ! [X7: $i] :
( ( X5 @ X7 )
!= $true )
| ? [X6: $i] :
( ( $true
!= ( cP @ X6 ) )
& ( ( X5 @ ( f @ X6 ) )
= $true ) ) )
& ( ( cP @ a )
= $true )
& ! [X3: $i,X4: $i] :
( ( $true
= ( cP @ X3 ) )
| ( $true
!= ( cP @ X4 ) )
| ( $true
!= ( cEQ @ X4 @ X3 ) ) )
& ! [X1: $i,X0: $i] :
( ( ( cEQ @ X0 @ X1 )
= $true )
| ( $true
!= ( cEQ @ ( f @ X0 ) @ ( f @ X1 ) ) ) )
& ! [X2: $i] :
( $true
= ( cEQ @ X2 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cP @ a )
= $true )
& ! [X3: $i,X4: $i] :
( ( ( $true
= ( cP @ X4 ) )
& ( $true
= ( cEQ @ X4 @ X3 ) ) )
=> ( $true
= ( cP @ X3 ) ) )
& ! [X0: $i,X1: $i] :
( ( $true
= ( cEQ @ ( f @ X0 ) @ ( f @ X1 ) ) )
=> ( ( cEQ @ X0 @ X1 )
= $true ) )
& ! [X2: $i] :
( $true
= ( cEQ @ X2 @ X2 ) ) )
=> ? [X5: $i > $o] :
( ! [X6: $i] :
( ( ( X5 @ ( f @ X6 ) )
= $true )
=> ( $true
= ( cP @ X6 ) ) )
& ? [X7: $i] :
( ( X5 @ X7 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cEQ @ ( f @ X0 ) @ ( f @ X1 ) )
=> ( cEQ @ X0 @ X1 ) )
& ( cP @ a )
& ! [X2: $i] : ( cEQ @ X2 @ X2 )
& ! [X3: $i,X4: $i] :
( ( ( cEQ @ X4 @ X3 )
& ( cP @ X4 ) )
=> ( cP @ X3 ) ) )
=> ? [X5: $i > $o] :
( ! [X6: $i] :
( ( X5 @ ( f @ X6 ) )
=> ( cP @ X6 ) )
& ? [X7: $i] : ( X5 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i] :
( ( cEQ @ ( f @ X1 ) @ ( f @ X2 ) )
=> ( cEQ @ X1 @ X2 ) )
& ( cP @ a )
& ! [X0: $i] : ( cEQ @ X0 @ X0 )
& ! [X1: $i,X0: $i] :
( ( ( cEQ @ X0 @ X1 )
& ( cP @ X0 ) )
=> ( cP @ X1 ) ) )
=> ? [X3: $i > $o] :
( ! [X0: $i] :
( ( X3 @ ( f @ X0 ) )
=> ( cP @ X0 ) )
& ? [X2: $i] : ( X3 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X2: $i] :
( ( cEQ @ ( f @ X1 ) @ ( f @ X2 ) )
=> ( cEQ @ X1 @ X2 ) )
& ( cP @ a )
& ! [X0: $i] : ( cEQ @ X0 @ X0 )
& ! [X1: $i,X0: $i] :
( ( ( cEQ @ X0 @ X1 )
& ( cP @ X0 ) )
=> ( cP @ X1 ) ) )
=> ? [X3: $i > $o] :
( ! [X0: $i] :
( ( X3 @ ( f @ X0 ) )
=> ( cP @ X0 ) )
& ? [X2: $i] : ( X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CbyjHvliT1/DTF2THF_7279.p',cTHM304) ).
thf(f55,plain,
! [X0: $i] :
( $true
!= ( cEQ @ ( f @ a ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cEQ @ ( f @ a ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f16,f46]) ).
thf(f46,plain,
( $true
= ( cP @ ( sK0 @ ( cEQ @ ( f @ a ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
= ( cP @ ( sK0 @ ( cEQ @ ( f @ a ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f33,f12]) ).
thf(f12,plain,
( ( cP @ a )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f33,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cP @ ( sK0 @ ( cEQ @ ( f @ X0 ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cP @ ( sK0 @ ( cEQ @ ( f @ X0 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f11,f29]) ).
thf(f29,plain,
! [X0: $i] :
( $true
= ( cEQ @ X0 @ ( sK0 @ ( cEQ @ ( f @ X0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( $true
= ( cEQ @ X0 @ ( sK0 @ ( cEQ @ ( f @ X0 ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f22]) ).
thf(f22,plain,
! [X0: $i] :
( ( cEQ @ X0 @ ( f @ ( sK0 @ ( cEQ @ X0 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cEQ @ X0 @ ( f @ ( sK0 @ ( cEQ @ X0 ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f15,f13]) ).
thf(f15,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( $true
= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f14,plain,
! [X3: $i,X4: $i] :
( ( ( cEQ @ ( f @ X4 ) @ ( f @ X3 ) )
!= $true )
| ( $true
= ( cEQ @ X4 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f11,plain,
! [X6: $i,X7: $i] :
( ( $true
!= ( cEQ @ X6 @ X7 ) )
| ( $true
!= ( cP @ X6 ) )
| ( $true
= ( cP @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( ( X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO317^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n020.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 14:28:12 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.33/0.47 ---- Original DTF file ---
% 0.33/0.47 thf(spec,logic,$$dhol).
% 0.33/0.47 %------------------------------------------------------------------------------
% 0.33/0.47 % File : SYO317^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.47 % Domain : Syntactic
% 0.33/0.47 % Problem : TPS problem from BASIC-HO-THMS
% 0.33/0.47 % Version : Especial.
% 0.33/0.47 % English :
% 0.33/0.47
% 0.33/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.47 % Source : [Bro09]
% 0.33/0.47 % Names : tps_0946 [Bro09]
% 0.33/0.47
% 0.33/0.47 % Status : Theorem
% 0.33/0.47 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.33/0.47 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.33/0.47 % Number of atoms : 8 ( 0 equ; 0 cnn)
% 0.33/0.47 % Maximal formula atoms : 8 ( 8 avg)
% 0.33/0.47 % Number of connectives : 26 ( 0 ~; 0 |; 5 &; 17 @)
% 0.33/0.47 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.33/0.47 % Maximal formula depth : 11 ( 11 avg)
% 0.33/0.47 % Number of types : 2 ( 0 usr)
% 0.33/0.47 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.33/0.47 % Number of symbols : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.33/0.47 % Number of variables : 8 ( 0 ^; 6 !; 2 ?; 8 :)
% 0.33/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.47
% 0.33/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.47 %------------------------------------------------------------------------------
% 0.33/0.47 thf(cP,type,
% 0.33/0.47 cP: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(f,type,
% 0.33/0.47 f: $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(cEQ,type,
% 0.33/0.47 cEQ: $i > $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(a,type,
% 0.33/0.47 a: $i ).
% 0.33/0.47
% 0.33/0.47 thf(cTHM304,conjecture,
% 0.33/0.47 ( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx )
% 0.33/0.47 & ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( ( cEQ @ Xx @ Xy )
% 0.33/0.47 & ( cP @ Xx ) )
% 0.33/0.47 => ( cP @ Xy ) )
% 0.33/0.47 & ( cP @ a )
% 0.33/0.47 & ! [Xy: $i,Xz: $i] :
% 0.33/0.47 ( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
% 0.33/0.47 => ( cEQ @ Xy @ Xz ) ) )
% 0.33/0.47 => ? [A: $i > $o] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( A @ ( f @ Xx ) )
% 0.33/0.47 => ( cP @ Xx ) )
% 0.33/0.47 & ? [Xz: $i] : ( A @ Xz ) ) ) ).
% 0.33/0.47
% 0.33/0.47 %------------------------------------------------------------------------------
% 0.33/0.47 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 14:28:13 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CbyjHvliT1/DTF2DTF7279.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.29 ---- Cleaned THF ---
% 1.45/1.29 thf(cP,type,
% 1.45/1.29 cP: $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(f,type,
% 1.45/1.29 f: $i > $i ).
% 1.45/1.29
% 1.45/1.29 thf(cEQ,type,
% 1.45/1.29 cEQ: $i > $i > $o ).
% 1.45/1.29
% 1.45/1.29 thf(a,type,
% 1.45/1.29 a: $i ).
% 1.45/1.29
% 1.45/1.29 thf(cTHM304,conjecture,
% 1.45/1.29 ( ( ! [Xx: $i] : ( cEQ @ Xx @ Xx )
% 1.45/1.29 & ! [Xx: $i,Xy: $i] :
% 1.45/1.29 ( ( ( cEQ @ Xx @ Xy )
% 1.45/1.29 & ( cP @ Xx ) )
% 1.45/1.29 => ( cP @ Xy ) )
% 1.45/1.29 & ( cP @ a )
% 1.45/1.29 & ! [Xy: $i,Xz: $i] :
% 1.45/1.29 ( ( cEQ @ ( f @ Xy ) @ ( f @ Xz ) )
% 1.45/1.29 => ( cEQ @ Xy @ Xz ) ) )
% 1.45/1.29 => ? [A: $i > $o] :
% 1.45/1.29 ( ! [Xx: $i] :
% 1.45/1.29 ( ( A @ ( f @ Xx ) )
% 1.45/1.29 => ( cP @ Xx ) )
% 1.45/1.29 & ? [Xz: $i] : ( A @ Xz ) ) ) ).
% 1.45/1.29 ------------------------
% 1.63/1.30 % (7610)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_7279 for (2999ds/2Mi)
% 1.63/1.30 % (7609)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7279 for (2999ds/2Mi)
% 1.63/1.30 % (7609)Instruction limit reached!
% 1.63/1.30 % (7609)------------------------------
% 1.63/1.30 % (7609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (7609)Termination reason: Unknown
% 1.63/1.30 % (7609)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (7609)Memory used [KB]: 5500
% 1.63/1.30 % (7609)Time elapsed: 0.002 s
% 1.63/1.30 % (7609)Instructions burned: 2 (million)
% 1.63/1.30 % (7609)------------------------------
% 1.63/1.30 % (7609)------------------------------
% 1.63/1.30 % (7610)Instruction limit reached!
% 1.63/1.30 % (7610)------------------------------
% 1.63/1.30 % (7610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.30 % (7610)Termination reason: Unknown
% 1.63/1.30 % (7610)Termination phase: Saturation
% 1.63/1.30
% 1.63/1.30 % (7610)Memory used [KB]: 5500
% 1.63/1.30 % (7610)Time elapsed: 0.002 s
% 1.63/1.30 % (7610)Instructions burned: 3 (million)
% 1.63/1.30 % (7610)------------------------------
% 1.63/1.30 % (7610)------------------------------
% 1.63/1.31 % (7606)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7279 for (2999ds/183Mi)
% 1.63/1.31 % (7607)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_7279 for (2999ds/4Mi)
% 1.63/1.31 % (7608)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_7279 for (2999ds/27Mi)
% 1.63/1.31 % (7611)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_7279 for (2999ds/275Mi)
% 1.63/1.31 % (7612)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7279 for (2999ds/18Mi)
% 1.63/1.31 % (7607)Instruction limit reached!
% 1.63/1.31 % (7607)------------------------------
% 1.63/1.31 % (7607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7607)Termination reason: Unknown
% 1.63/1.31 % (7607)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7607)Memory used [KB]: 5500
% 1.63/1.31 % (7607)Time elapsed: 0.005 s
% 1.63/1.31 % (7607)Instructions burned: 4 (million)
% 1.63/1.31 % (7607)------------------------------
% 1.63/1.31 % (7607)------------------------------
% 1.63/1.31 % (7614)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_7279 for (2999ds/37Mi)
% 1.63/1.31 % (7613)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7279 for (2999ds/3Mi)
% 1.63/1.31 % (7613)Instruction limit reached!
% 1.63/1.31 % (7613)------------------------------
% 1.63/1.31 % (7613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.31 % (7613)Termination reason: Unknown
% 1.63/1.31 % (7613)Termination phase: Saturation
% 1.63/1.31
% 1.63/1.31 % (7613)Memory used [KB]: 5500
% 1.63/1.31 % (7613)Time elapsed: 0.003 s
% 1.63/1.31 % (7613)Instructions burned: 3 (million)
% 1.63/1.31 % (7613)------------------------------
% 1.63/1.31 % (7613)------------------------------
% 1.63/1.32 % (7608)First to succeed.
% 1.63/1.32 % (7608)Refutation found. Thanks to Tanya!
% 1.63/1.32 % SZS status Theorem for DTF2THF_7279
% 1.63/1.32 % SZS output start Proof for DTF2THF_7279
% 1.63/1.32 thf(func_def_0, type, cP: $i > $o).
% 1.63/1.32 thf(func_def_1, type, f: $i > $i).
% 1.63/1.32 thf(func_def_2, type, cEQ: $i > $i > $o).
% 1.63/1.32 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.63/1.32 thf(func_def_8, type, sK0: ($i > $o) > $i).
% 1.63/1.32 thf(func_def_10, type, ph2: !>[X0: $tType]:(X0)).
% 1.63/1.32 thf(f59,plain,(
% 1.63/1.32 $false),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.63/1.32 thf(f56,plain,(
% 1.63/1.32 ($true != $true)),
% 1.63/1.32 inference(superposition,[status(thm)],[f55,f13])).
% 1.63/1.32 thf(f13,plain,(
% 1.63/1.32 ( ! [X5 : $i] : (((cEQ @ X5 @ X5) = $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f10,plain,(
% 1.63/1.32 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | (($true != (cP @ (sK0 @ X0))) & ($true = (X0 @ (f @ (sK0 @ X0)))))) & ! [X3 : $i,X4 : $i] : (($true = (cEQ @ X4 @ X3)) | ((cEQ @ (f @ X4) @ (f @ X3)) != $true)) & ! [X5 : $i] : ((cEQ @ X5 @ X5) = $true) & ((cP @ a) = $true) & ! [X6 : $i,X7 : $i] : (($true = (cP @ X7)) | ($true != (cEQ @ X6 @ X7)) | ($true != (cP @ X6)))),
% 1.63/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.63/1.32 thf(f9,plain,(
% 1.63/1.32 ! [X0 : $i > $o] : (? [X2 : $i] : (($true != (cP @ X2)) & ($true = (X0 @ (f @ X2)))) => (($true != (cP @ (sK0 @ X0))) & ($true = (X0 @ (f @ (sK0 @ X0))))))),
% 1.63/1.32 introduced(definition,[],[choice_axiom])).
% 1.63/1.32 thf(f8,plain,(
% 1.63/1.32 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) != $true) | ? [X2 : $i] : (($true != (cP @ X2)) & ($true = (X0 @ (f @ X2))))) & ! [X3 : $i,X4 : $i] : (($true = (cEQ @ X4 @ X3)) | ((cEQ @ (f @ X4) @ (f @ X3)) != $true)) & ! [X5 : $i] : ((cEQ @ X5 @ X5) = $true) & ((cP @ a) = $true) & ! [X6 : $i,X7 : $i] : (($true = (cP @ X7)) | ($true != (cEQ @ X6 @ X7)) | ($true != (cP @ X6)))),
% 1.63/1.32 inference(rectify,[status(thm)],[f7])).
% 1.63/1.32 thf(f7,plain,(
% 1.63/1.32 ! [X5 : $i > $o] : (! [X7 : $i] : ((X5 @ X7) != $true) | ? [X6 : $i] : (($true != (cP @ X6)) & ((X5 @ (f @ X6)) = $true))) & ! [X1 : $i,X0 : $i] : (((cEQ @ X0 @ X1) = $true) | ($true != (cEQ @ (f @ X0) @ (f @ X1)))) & ! [X2 : $i] : ($true = (cEQ @ X2 @ X2)) & ((cP @ a) = $true) & ! [X4 : $i,X3 : $i] : (($true = (cP @ X3)) | ($true != (cEQ @ X4 @ X3)) | ($true != (cP @ X4)))),
% 1.63/1.32 inference(flattening,[status(thm)],[f6])).
% 1.63/1.32 thf(f6,plain,(
% 1.63/1.32 ! [X5 : $i > $o] : (! [X7 : $i] : ((X5 @ X7) != $true) | ? [X6 : $i] : (($true != (cP @ X6)) & ((X5 @ (f @ X6)) = $true))) & (((cP @ a) = $true) & ! [X3 : $i,X4 : $i] : (($true = (cP @ X3)) | (($true != (cP @ X4)) | ($true != (cEQ @ X4 @ X3)))) & ! [X1 : $i,X0 : $i] : (((cEQ @ X0 @ X1) = $true) | ($true != (cEQ @ (f @ X0) @ (f @ X1)))) & ! [X2 : $i] : ($true = (cEQ @ X2 @ X2)))),
% 1.63/1.32 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.32 thf(f5,plain,(
% 1.63/1.32 ~((((cP @ a) = $true) & ! [X3 : $i,X4 : $i] : ((($true = (cP @ X4)) & ($true = (cEQ @ X4 @ X3))) => ($true = (cP @ X3))) & ! [X0 : $i,X1 : $i] : (($true = (cEQ @ (f @ X0) @ (f @ X1))) => ((cEQ @ X0 @ X1) = $true)) & ! [X2 : $i] : ($true = (cEQ @ X2 @ X2))) => ? [X5 : $i > $o] : (! [X6 : $i] : (((X5 @ (f @ X6)) = $true) => ($true = (cP @ X6))) & ? [X7 : $i] : ((X5 @ X7) = $true)))),
% 1.63/1.32 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.32 thf(f4,plain,(
% 1.63/1.32 ~((! [X0 : $i,X1 : $i] : ((cEQ @ (f @ X0) @ (f @ X1)) => (cEQ @ X0 @ X1)) & (cP @ a) & ! [X2 : $i] : (cEQ @ X2 @ X2) & ! [X3 : $i,X4 : $i] : (((cEQ @ X4 @ X3) & (cP @ X4)) => (cP @ X3))) => ? [X5 : $i > $o] : (! [X6 : $i] : ((X5 @ (f @ X6)) => (cP @ X6)) & ? [X7 : $i] : (X5 @ X7)))),
% 1.63/1.32 inference(rectify,[status(thm)],[f2])).
% 1.63/1.32 thf(f2,negated_conjecture,(
% 1.63/1.32 ~((! [X1 : $i,X2 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2)) & (cP @ a) & ! [X0 : $i] : (cEQ @ X0 @ X0) & ! [X1 : $i,X0 : $i] : (((cEQ @ X0 @ X1) & (cP @ X0)) => (cP @ X1))) => ? [X3 : $i > $o] : (! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0)) & ? [X2 : $i] : (X3 @ X2)))),
% 1.63/1.32 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.32 thf(f1,conjecture,(
% 1.63/1.32 (! [X1 : $i,X2 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2)) & (cP @ a) & ! [X0 : $i] : (cEQ @ X0 @ X0) & ! [X1 : $i,X0 : $i] : (((cEQ @ X0 @ X1) & (cP @ X0)) => (cP @ X1))) => ? [X3 : $i > $o] : (! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0)) & ? [X2 : $i] : (X3 @ X2))),
% 1.63/1.32 file('/export/starexec/sandbox/tmp/tmp.CbyjHvliT1/DTF2THF_7279.p',cTHM304)).
% 1.63/1.32 thf(f55,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (($true != (cEQ @ (f @ a) @ X0))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.63/1.32 thf(f48,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (($true != $true) | ($true != (cEQ @ (f @ a) @ X0))) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f16,f46])).
% 1.63/1.32 thf(f46,plain,(
% 1.63/1.32 ($true = (cP @ (sK0 @ (cEQ @ (f @ a)))))),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.63/1.32 thf(f42,plain,(
% 1.63/1.32 ($true = (cP @ (sK0 @ (cEQ @ (f @ a))))) | ($true != $true)),
% 1.63/1.32 inference(superposition,[status(thm)],[f33,f12])).
% 1.63/1.32 thf(f12,plain,(
% 1.63/1.32 ((cP @ a) = $true)),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f33,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cP @ (sK0 @ (cEQ @ (f @ X0)))) = $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 1.63/1.32 thf(f30,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cP @ (sK0 @ (cEQ @ (f @ X0)))) = $true) | ($true != $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f11,f29])).
% 1.63/1.32 thf(f29,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (($true = (cEQ @ X0 @ (sK0 @ (cEQ @ (f @ X0)))))) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.63/1.32 thf(f26,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (($true = (cEQ @ X0 @ (sK0 @ (cEQ @ (f @ X0))))) | ($true != $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f14,f22])).
% 1.63/1.32 thf(f22,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (((cEQ @ X0 @ (f @ (sK0 @ (cEQ @ X0)))) = $true)) )),
% 1.63/1.32 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.63/1.32 thf(f21,plain,(
% 1.63/1.32 ( ! [X0 : $i] : (($true != $true) | ((cEQ @ X0 @ (f @ (sK0 @ (cEQ @ X0)))) = $true)) )),
% 1.63/1.32 inference(superposition,[status(thm)],[f15,f13])).
% 1.63/1.32 thf(f15,plain,(
% 1.63/1.32 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ X1) != $true) | ($true = (X0 @ (f @ (sK0 @ X0))))) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f14,plain,(
% 1.63/1.32 ( ! [X3 : $i,X4 : $i] : (((cEQ @ (f @ X4) @ (f @ X3)) != $true) | ($true = (cEQ @ X4 @ X3))) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f11,plain,(
% 1.63/1.32 ( ! [X6 : $i,X7 : $i] : (($true != (cEQ @ X6 @ X7)) | ($true != (cP @ X6)) | ($true = (cP @ X7))) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 thf(f16,plain,(
% 1.63/1.32 ( ! [X0 : $i > $o,X1 : $i] : (($true != (cP @ (sK0 @ X0))) | ((X0 @ X1) != $true)) )),
% 1.63/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.32 % SZS output end Proof for DTF2THF_7279
% 1.63/1.32 % (7608)------------------------------
% 1.63/1.32 % (7608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (7608)Termination reason: Refutation
% 1.63/1.32
% 1.63/1.32 % (7608)Memory used [KB]: 5500
% 1.63/1.32 % (7608)Time elapsed: 0.010 s
% 1.63/1.32 % (7608)Instructions burned: 8 (million)
% 1.63/1.32 % (7608)------------------------------
% 1.63/1.32 % (7608)------------------------------
% 1.63/1.32 % (7605)Success in time 0.025 s
%------------------------------------------------------------------------------