%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO103^5 : 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 : n015.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 09:53:23 AM UTC 2026
% Result : Theorem 1.59s 1.36s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 201 ( 57 equ; 0 cnn)
% Maximal formula atoms : 7 ( 9 avg)
% Number of connectives : 446 ( 48 ~; 28 |; 28 &; 341 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 ^; 88 !; 7 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
imp: $i > $i > $i ).
thf(func_def_1,type,
cT: $i > $o ).
thf(func_def_2,type,
nt: $i > $i ).
thf(f93,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
$true != $true,
inference(superposition,[status(thm)],[f84,f11]) ).
thf(f11,plain,
! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ( ( cT @ ( imp @ sK0 @ sK0 ) )
!= $true )
& ! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X5 @ X3 ) ) @ ( imp @ ( imp @ X4 @ X5 ) @ ( imp @ X4 @ X3 ) ) ) ) )
& ! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cT @ X9 ) )
| ( $true
= ( cT @ X8 ) )
| ( ( cT @ ( imp @ X9 @ X8 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
( ? [X2: $i] :
( ( cT @ ( imp @ X2 @ X2 ) )
!= $true )
=> ( ( cT @ ( imp @ sK0 @ sK0 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ? [X2: $i] :
( ( cT @ ( imp @ X2 @ X2 ) )
!= $true )
& ! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X5 @ X3 ) ) @ ( imp @ ( imp @ X4 @ X5 ) @ ( imp @ X4 @ X3 ) ) ) ) )
& ! [X6: $i,X7: $i] :
( ( cT @ ( imp @ X6 @ ( imp @ X7 @ X6 ) ) )
= $true )
& ! [X8: $i,X9: $i] :
( ( $true
!= ( cT @ X9 ) )
| ( $true
= ( cT @ X8 ) )
| ( ( cT @ ( imp @ X9 @ X8 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ? [X9: $i] :
( $true
!= ( cT @ ( imp @ X9 @ X9 ) ) )
& ! [X2: $i,X3: $i,X4: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X2 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X2 ) ) ) ) )
& ! [X5: $i,X6: $i] :
( $true
= ( cT @ ( imp @ X5 @ ( imp @ X6 @ X5 ) ) ) )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cT @ X8 ) )
| ( ( cT @ X7 )
= $true )
| ( $true
!= ( cT @ ( imp @ X8 @ X7 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i,X1: $i] :
( $true
= ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) ) )
& ! [X2: $i,X3: $i,X4: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X2 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X2 ) ) ) ) )
& ! [X5: $i,X6: $i] :
( $true
= ( cT @ ( imp @ X5 @ ( imp @ X6 @ X5 ) ) ) )
& ! [X7: $i,X8: $i] :
( ( $true
!= ( cT @ X8 ) )
| ( ( cT @ X7 )
= $true )
| ( $true
!= ( cT @ ( imp @ X8 @ X7 ) ) ) )
& ? [X9: $i] :
( $true
!= ( cT @ ( imp @ X9 @ X9 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X1 ) @ ( nt @ X0 ) ) @ ( imp @ X0 @ X1 ) ) )
& ! [X2: $i,X3: $i,X4: $i] : ( cT @ ( imp @ ( imp @ X3 @ ( imp @ X4 @ X2 ) ) @ ( imp @ ( imp @ X3 @ X4 ) @ ( imp @ X3 @ X2 ) ) ) )
& ! [X5: $i,X6: $i] : ( cT @ ( imp @ X5 @ ( imp @ X6 @ X5 ) ) )
& ! [X7: $i,X8: $i] :
( ~ ( cT @ X8 )
| ( cT @ X7 )
| ~ ( cT @ ( imp @ X8 @ X7 ) ) )
& ? [X9: $i] :
~ ( cT @ ( imp @ X9 @ X9 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X2: $i,X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X1: $i,X0: $i] : ( cT @ ( imp @ ( imp @ ( nt @ X0 ) @ ( nt @ X1 ) ) @ ( imp @ X1 @ X0 ) ) )
& ! [X2: $i,X0: $i,X1: $i] : ( cT @ ( imp @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) ) )
& ! [X0: $i,X1: $i] : ( cT @ ( imp @ X0 @ ( imp @ X1 @ X0 ) ) )
& ! [X1: $i,X0: $i] :
( ~ ( cT @ X0 )
| ( cT @ X1 )
| ~ ( cT @ ( imp @ X0 @ X1 ) ) )
& ? [X3: $i] :
~ ( cT @ ( imp @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5YicK8KWtM/DTF2THF_16499.p',cTHM147) ).
thf(f84,plain,
! [X0: $i] :
( ( cT @ ( imp @ sK0 @ X0 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
! [X0: $i] :
( ( ( cT @ ( imp @ sK0 @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f76]) ).
thf(f76,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true
= ( cT @ ( imp @ X0 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f63,f11]) ).
thf(f63,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X2 ) )
= $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cT @ ( imp @ X0 @ X2 ) )
= $true )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true )
| ( ( cT @ ( imp @ X0 @ X1 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f10,f48]) ).
thf(f48,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) )
= $true )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true != $true )
| ( ( cT @ ( imp @ X0 @ ( imp @ X1 @ X2 ) ) )
!= $true )
| ( ( cT @ ( imp @ ( imp @ X0 @ X1 ) @ ( imp @ X0 @ X2 ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f10,f12]) ).
thf(f12,plain,
! [X3: $i,X4: $i,X5: $i] :
( $true
= ( cT @ ( imp @ ( imp @ X4 @ ( imp @ X5 @ X3 ) ) @ ( imp @ ( imp @ X4 @ X5 ) @ ( imp @ X4 @ X3 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f10,plain,
! [X8: $i,X9: $i] :
( ( ( cT @ ( imp @ X9 @ X8 ) )
!= $true )
| ( $true
!= ( cT @ X9 ) )
| ( $true
= ( cT @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f13,plain,
( ( cT @ ( imp @ sK0 @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO103^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.30 % Computer : n015.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Feb 24 14:24:31 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO103^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem THM147
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English : Theorem 211 on page 120 of [Chu56].
% 0.16/0.39
% 0.16/0.39 % Refs : [Chu56] Church (1956), Introduction to Mathematical Logic I
% 0.16/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0367 [Bro09]
% 0.16/0.39 % : THM147 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.39 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 7 ( 7 avg)
% 0.16/0.39 % Number of connectives : 45 ( 4 ~; 2 |; 4 &; 35 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 14 ( 14 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.16/0.39 % Number of variables : 10 ( 0 ^; 9 !; 1 ?; 10 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(imp,type,
% 0.16/0.39 imp: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cT,type,
% 0.16/0.39 cT: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(nt,type,
% 0.16/0.39 nt: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM147,conjecture,
% 0.16/0.39 ~ ( ! [Xp: $i,Xq: $i] :
% 0.16/0.39 ( ~ ( cT @ ( imp @ Xp @ Xq ) )
% 0.16/0.39 | ~ ( cT @ Xp )
% 0.16/0.39 | ( cT @ Xq ) )
% 0.16/0.39 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
% 0.16/0.39 & ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
% 0.16/0.39 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
% 0.16/0.39 & ? [Xa: $i] :
% 0.16/0.39 ~ ( cT @ ( imp @ Xa @ Xa ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.59/1.31 ---- Embedded in THF ---
% 1.59/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.59/1.31 %%% Generated on Tue Feb 24 14:24:32 EST 2026
% 1.59/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.59/1.31 %%% Logic specification used:
% 1.59/1.31 %%% thf(spec, logic, $$dhol).
% 1.59/1.31
% 1.59/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5YicK8KWtM/DTF2DTF16499.p
% See solution above
% 1.59/1.31 ------------------------
% 1.59/1.32 ---- Cleaned THF ---
% 1.59/1.32 thf(imp,type,
% 1.59/1.32 imp: $i > $i > $i ).
% 1.59/1.32
% 1.59/1.32 thf(cT,type,
% 1.59/1.32 cT: $i > $o ).
% 1.59/1.32
% 1.59/1.32 thf(nt,type,
% 1.59/1.32 nt: $i > $i ).
% 1.59/1.32
% 1.59/1.32 thf(cTHM147,conjecture,
% 1.59/1.32 ~ ( ! [Xp: $i,Xq: $i] :
% 1.59/1.32 ( ~ ( cT @ ( imp @ Xp @ Xq ) )
% 1.59/1.32 | ~ ( cT @ Xp )
% 1.59/1.32 | ( cT @ Xq ) )
% 1.59/1.32 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ Xp @ ( imp @ Xq @ Xp ) ) )
% 1.59/1.32 & ! [Xp: $i,Xq: $i,Xr: $i] : ( cT @ ( imp @ ( imp @ Xp @ ( imp @ Xq @ Xr ) ) @ ( imp @ ( imp @ Xp @ Xq ) @ ( imp @ Xp @ Xr ) ) ) )
% 1.59/1.32 & ! [Xp: $i,Xq: $i] : ( cT @ ( imp @ ( imp @ ( nt @ Xp ) @ ( nt @ Xq ) ) @ ( imp @ Xq @ Xp ) ) )
% 1.59/1.32 & ? [Xa: $i] :
% 1.59/1.32 ~ ( cT @ ( imp @ Xa @ Xa ) ) ) ).
% 1.59/1.32 ------------------------
% 1.59/1.34 % (16602)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16499 for (2999ds/18Mi)
% 1.59/1.34 % (16598)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_16499 for (2999ds/27Mi)
% 1.59/1.34 % (16596)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16499 for (2999ds/183Mi)
% 1.59/1.34 % (16599)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16499 for (2999ds/2Mi)
% 1.59/1.34 % (16600)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_16499 for (2999ds/2Mi)
% 1.59/1.34 % (16601)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_16499 for (2999ds/275Mi)
% 1.59/1.34 % (16597)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_16499 for (2999ds/4Mi)
% 1.59/1.35 % (16599)Instruction limit reached!
% 1.59/1.35 % (16599)------------------------------
% 1.59/1.35 % (16599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (16599)Termination reason: Unknown
% 1.59/1.35 % (16599)Termination phase: Saturation
% 1.59/1.35 % (16600)Instruction limit reached!
% 1.59/1.35 % (16600)------------------------------
% 1.59/1.35 % (16600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (16600)Termination reason: Unknown
% 1.59/1.35 % (16600)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (16600)Memory used [KB]: 895
% 1.59/1.35 % (16600)Time elapsed: 0.003 s
% 1.59/1.35 % (16600)Instructions burned: 2 (million)
% 1.59/1.35 % (16600)------------------------------
% 1.59/1.35 % (16600)------------------------------
% 1.59/1.35
% 1.59/1.35 % (16599)Memory used [KB]: 895
% 1.59/1.35 % (16599)Time elapsed: 0.003 s
% 1.59/1.35 % (16599)Instructions burned: 2 (million)
% 1.59/1.35 % (16599)------------------------------
% 1.59/1.35 % (16599)------------------------------
% 1.59/1.35 % (16597)Instruction limit reached!
% 1.59/1.35 % (16597)------------------------------
% 1.59/1.35 % (16597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (16597)Termination reason: Unknown
% 1.59/1.35 % (16597)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (16597)Memory used [KB]: 5500
% 1.59/1.35 % (16597)Time elapsed: 0.004 s
% 1.59/1.35 % (16597)Instructions burned: 4 (million)
% 1.59/1.35 % (16597)------------------------------
% 1.59/1.35 % (16597)------------------------------
% 1.59/1.35 % (16602)Instruction limit reached!
% 1.59/1.35 % (16602)------------------------------
% 1.59/1.35 % (16602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (16602)Termination reason: Unknown
% 1.59/1.35 % (16602)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (16602)Memory used [KB]: 5628
% 1.59/1.35 % (16602)Time elapsed: 0.011 s
% 1.59/1.35 % (16602)Instructions burned: 18 (million)
% 1.59/1.35 % (16602)------------------------------
% 1.59/1.35 % (16602)------------------------------
% 1.59/1.36 % (16596)First to succeed.
% 1.59/1.36 % (16598)Also succeeded, but the first one will report.
% 1.59/1.36 % (16601)Also succeeded, but the first one will report.
% 1.59/1.36 % (16596)Refutation found. Thanks to Tanya!
% 1.59/1.36 % SZS status Theorem for DTF2THF_16499
% 1.59/1.36 % SZS output start Proof for DTF2THF_16499
% 1.59/1.36 thf(func_def_0, type, imp: $i > $i > $i).
% 1.59/1.36 thf(func_def_1, type, cT: $i > $o).
% 1.59/1.36 thf(func_def_2, type, nt: $i > $i).
% 1.59/1.36 thf(f93,plain,(
% 1.59/1.36 $false),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.59/1.36 thf(f85,plain,(
% 1.59/1.36 ($true != $true)),
% 1.59/1.36 inference(superposition,[status(thm)],[f84,f11])).
% 1.59/1.36 thf(f11,plain,(
% 1.59/1.36 ( ! [X6 : $i,X7 : $i] : (((cT @ (imp @ X6 @ (imp @ X7 @ X6))) = $true)) )),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.36 thf(f9,plain,(
% 1.59/1.36 ! [X0 : $i,X1 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X0)) @ (imp @ X0 @ X1)))) & ((cT @ (imp @ sK0 @ sK0)) != $true) & ! [X3 : $i,X4 : $i,X5 : $i] : ($true = (cT @ (imp @ (imp @ X4 @ (imp @ X5 @ X3)) @ (imp @ (imp @ X4 @ X5) @ (imp @ X4 @ X3))))) & ! [X6 : $i,X7 : $i] : ((cT @ (imp @ X6 @ (imp @ X7 @ X6))) = $true) & ! [X8 : $i,X9 : $i] : (($true != (cT @ X9)) | ($true = (cT @ X8)) | ((cT @ (imp @ X9 @ X8)) != $true))),
% 1.59/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.59/1.36 thf(f8,plain,(
% 1.59/1.36 ? [X2 : $i] : ((cT @ (imp @ X2 @ X2)) != $true) => ((cT @ (imp @ sK0 @ sK0)) != $true)),
% 1.59/1.36 introduced(definition,[],[choice_axiom])).
% 1.59/1.36 thf(f7,plain,(
% 1.59/1.36 ! [X0 : $i,X1 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X0)) @ (imp @ X0 @ X1)))) & ? [X2 : $i] : ((cT @ (imp @ X2 @ X2)) != $true) & ! [X3 : $i,X4 : $i,X5 : $i] : ($true = (cT @ (imp @ (imp @ X4 @ (imp @ X5 @ X3)) @ (imp @ (imp @ X4 @ X5) @ (imp @ X4 @ X3))))) & ! [X6 : $i,X7 : $i] : ((cT @ (imp @ X6 @ (imp @ X7 @ X6))) = $true) & ! [X8 : $i,X9 : $i] : (($true != (cT @ X9)) | ($true = (cT @ X8)) | ((cT @ (imp @ X9 @ X8)) != $true))),
% 1.59/1.36 inference(rectify,[status(thm)],[f6])).
% 1.59/1.36 thf(f6,plain,(
% 1.59/1.36 ! [X0 : $i,X1 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X0)) @ (imp @ X0 @ X1)))) & ? [X9 : $i] : ($true != (cT @ (imp @ X9 @ X9))) & ! [X2 : $i,X3 : $i,X4 : $i] : ($true = (cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X2)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X2))))) & ! [X5 : $i,X6 : $i] : ($true = (cT @ (imp @ X5 @ (imp @ X6 @ X5)))) & ! [X7 : $i,X8 : $i] : (($true != (cT @ X8)) | ((cT @ X7) = $true) | ($true != (cT @ (imp @ X8 @ X7))))),
% 1.59/1.36 inference(flattening,[status(thm)],[f5])).
% 1.59/1.36 thf(f5,plain,(
% 1.59/1.36 ~~(! [X0 : $i,X1 : $i] : ($true = (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X0)) @ (imp @ X0 @ X1)))) & ! [X2 : $i,X3 : $i,X4 : $i] : ($true = (cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X2)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X2))))) & ! [X5 : $i,X6 : $i] : ($true = (cT @ (imp @ X5 @ (imp @ X6 @ X5)))) & ! [X7 : $i,X8 : $i] : (~($true = (cT @ X8)) | ((cT @ X7) = $true) | ~($true = (cT @ (imp @ X8 @ X7)))) & ? [X9 : $i] : ~($true = (cT @ (imp @ X9 @ X9))))),
% 1.59/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.36 thf(f4,plain,(
% 1.59/1.36 ~~(! [X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ (nt @ X1) @ (nt @ X0)) @ (imp @ X0 @ X1))) & ! [X2 : $i,X3 : $i,X4 : $i] : (cT @ (imp @ (imp @ X3 @ (imp @ X4 @ X2)) @ (imp @ (imp @ X3 @ X4) @ (imp @ X3 @ X2)))) & ! [X5 : $i,X6 : $i] : (cT @ (imp @ X5 @ (imp @ X6 @ X5))) & ! [X7 : $i,X8 : $i] : (~(cT @ X8) | (cT @ X7) | ~(cT @ (imp @ X8 @ X7))) & ? [X9 : $i] : ~(cT @ (imp @ X9 @ X9)))),
% 1.59/1.36 inference(rectify,[status(thm)],[f2])).
% 1.59/1.36 thf(f2,negated_conjecture,(
% 1.59/1.36 ~~(! [X1 : $i,X0 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X2 : $i,X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X1 : $i,X0 : $i] : (~(cT @ X0) | (cT @ X1) | ~(cT @ (imp @ X0 @ X1))) & ? [X3 : $i] : ~(cT @ (imp @ X3 @ X3)))),
% 1.59/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.36 thf(f1,conjecture,(
% 1.59/1.36 ~(! [X1 : $i,X0 : $i] : (cT @ (imp @ (imp @ (nt @ X0) @ (nt @ X1)) @ (imp @ X1 @ X0))) & ! [X2 : $i,X0 : $i,X1 : $i] : (cT @ (imp @ (imp @ X0 @ (imp @ X1 @ X2)) @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2)))) & ! [X0 : $i,X1 : $i] : (cT @ (imp @ X0 @ (imp @ X1 @ X0))) & ! [X1 : $i,X0 : $i] : (~(cT @ X0) | (cT @ X1) | ~(cT @ (imp @ X0 @ X1))) & ? [X3 : $i] : ~(cT @ (imp @ X3 @ X3)))),
% 1.59/1.36 file('/export/starexec/sandbox/tmp/tmp.5YicK8KWtM/DTF2THF_16499.p',cTHM147)).
% 1.59/1.36 thf(f84,plain,(
% 1.59/1.36 ( ! [X0 : $i] : (((cT @ (imp @ sK0 @ X0)) != $true)) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.59/1.36 thf(f78,plain,(
% 1.59/1.36 ( ! [X0 : $i] : (((cT @ (imp @ sK0 @ X0)) != $true) | ($true != $true)) )),
% 1.59/1.36 inference(superposition,[status(thm)],[f13,f76])).
% 1.59/1.36 thf(f76,plain,(
% 1.59/1.36 ( ! [X0 : $i,X1 : $i] : (($true = (cT @ (imp @ X0 @ X0))) | ((cT @ (imp @ X0 @ X1)) != $true)) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.59/1.36 thf(f64,plain,(
% 1.59/1.36 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((cT @ (imp @ X0 @ X1)) != $true) | ($true = (cT @ (imp @ X0 @ X0)))) )),
% 1.59/1.36 inference(superposition,[status(thm)],[f63,f11])).
% 1.59/1.36 thf(f63,plain,(
% 1.59/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true) | ((cT @ (imp @ X0 @ X2)) = $true) | ((cT @ (imp @ X0 @ X1)) != $true)) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.59/1.36 thf(f62,plain,(
% 1.59/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cT @ (imp @ X0 @ X2)) = $true) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true) | ((cT @ (imp @ X0 @ X1)) != $true) | ($true != $true)) )),
% 1.59/1.36 inference(superposition,[status(thm)],[f10,f48])).
% 1.59/1.36 thf(f48,plain,(
% 1.59/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))) = $true) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true)) )),
% 1.59/1.36 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.59/1.36 thf(f47,plain,(
% 1.59/1.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((cT @ (imp @ X0 @ (imp @ X1 @ X2))) != $true) | ((cT @ (imp @ (imp @ X0 @ X1) @ (imp @ X0 @ X2))) = $true)) )),
% 1.59/1.36 inference(superposition,[status(thm)],[f10,f12])).
% 1.59/1.36 thf(f12,plain,(
% 1.59/1.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (cT @ (imp @ (imp @ X4 @ (imp @ X5 @ X3)) @ (imp @ (imp @ X4 @ X5) @ (imp @ X4 @ X3)))))) )),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.36 thf(f10,plain,(
% 1.59/1.36 ( ! [X8 : $i,X9 : $i] : (((cT @ (imp @ X9 @ X8)) != $true) | ($true != (cT @ X9)) | ($true = (cT @ X8))) )),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.36 thf(f13,plain,(
% 1.59/1.36 ((cT @ (imp @ sK0 @ sK0)) != $true)),
% 1.59/1.36 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.36 % SZS output end Proof for DTF2THF_16499
% 1.59/1.36 % (16596)------------------------------
% 1.59/1.36 % (16596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (16596)Termination reason: Refutation
% 1.59/1.36
% 1.59/1.36 % (16596)Memory used [KB]: 5628
% 1.59/1.36 % (16596)Time elapsed: 0.015 s
% 1.59/1.36 % (16596)Instructions burned: 20 (million)
% 1.59/1.36 % (16596)------------------------------
% 1.59/1.36 % (16596)------------------------------
% 1.59/1.36 % (16595)Success in time 0.027 s
%------------------------------------------------------------------------------