%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO102^5 : 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 : n028.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 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 248 ( 64 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 261 ( 36 ~; 18 |; 32 &; 162 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 52 !; 12 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(f34,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f33,f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X3 @ X2 )
= $true )
| ( ( cP @ X3 @ X1 )
!= $true )
| ( ( cP @ X2 @ X1 )
!= $true ) )
& ( ( cP @ sK2 @ sK0 )
!= $true )
& ( ( cP @ sK1 @ sK0 )
= $true )
& ( ( cP @ sK2 @ sK1 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X6 @ X4 )
!= $true )
& ( ( cP @ X5 @ X4 )
= $true )
& ( ( cP @ X6 @ X5 )
= $true ) )
=> ( ( ( cP @ sK2 @ sK0 )
!= $true )
& ( ( cP @ sK1 @ sK0 )
= $true )
& ( ( cP @ sK2 @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( cP @ X0 @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( ( ( cP @ X3 @ X2 )
= $true )
| ( ( cP @ X3 @ X1 )
!= $true )
| ( ( cP @ X2 @ X1 )
!= $true ) )
& ? [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X6 @ X4 )
!= $true )
& ( ( cP @ X5 @ X4 )
= $true )
& ( ( cP @ X6 @ X5 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X2 @ X1 )
= $true )
| ( ( cP @ X2 @ X0 )
!= $true )
| ( ( cP @ X1 @ X0 )
!= $true ) )
& ? [X5: $i,X6: $i,X4: $i] :
( ( ( cP @ X4 @ X5 )
!= $true )
& ( ( cP @ X6 @ X5 )
= $true )
& ( ( cP @ X4 @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X4 @ X5 )
!= $true )
& ( ( cP @ X6 @ X5 )
= $true )
& ( ( cP @ X4 @ X6 )
= $true ) )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cP @ X2 @ X1 )
= $true )
| ( ( cP @ X2 @ X0 )
!= $true )
| ( ( cP @ X1 @ X0 )
!= $true ) )
& ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( ( cP @ X2 @ X0 )
= $true )
& ( ( cP @ X1 @ X0 )
= $true ) )
=> ( ( cP @ X2 @ X1 )
= $true ) )
& ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( ( ( cP @ X6 @ X5 )
= $true )
& ( ( cP @ X4 @ X6 )
= $true ) )
=> ( ( cP @ X4 @ X5 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cP @ X2 @ X0 )
& ( cP @ X1 @ X0 ) )
=> ( cP @ X2 @ X1 ) )
& ! [X3: $i] : ( cP @ X3 @ X3 ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ( ( cP @ X4 @ X6 )
& ( cP @ X6 @ X5 ) )
=> ( cP @ X4 @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X2 @ X1 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X0: $i] : ( cP @ X0 @ X0 ) )
=> ! [X3: $i,X5: $i,X4: $i] :
( ( ( cP @ X3 @ X4 )
& ( cP @ X4 @ X5 ) )
=> ( cP @ X3 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( cP @ X0 @ X1 )
& ( cP @ X2 @ X1 ) )
=> ( cP @ X0 @ X2 ) )
& ! [X0: $i] : ( cP @ X0 @ X0 ) )
=> ! [X3: $i,X5: $i,X4: $i] :
( ( ( cP @ X3 @ X4 )
& ( cP @ X4 @ X5 ) )
=> ( cP @ X3 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OYa2kCvr5t/DTF2THF_11253.p',cTHM101) ).
thf(f33,plain,
( ( cP @ sK0 @ sK0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( cP @ sK0 @ sK0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f27,f12]) ).
thf(f12,plain,
( ( cP @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( cP @ sK1 @ X0 )
!= $true )
| ( ( cP @ sK0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cP @ sK1 @ X0 )
!= $true )
| ( ( cP @ sK0 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f22,f14]) ).
thf(f14,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( cP @ X3 @ X2 )
= $true )
| ( ( cP @ X2 @ X1 )
!= $true )
| ( ( cP @ X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f22,plain,
( ( cP @ sK0 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( cP @ sK0 @ sK1 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f11]) ).
thf(f11,plain,
( ( cP @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( cP @ sK2 @ X0 )
!= $true )
| ( ( cP @ sK0 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( cP @ sK0 @ X0 )
!= $true )
| ( ( cP @ sK2 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f13,f14]) ).
thf(f13,plain,
( ( cP @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO102^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:24:27 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO102^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem THM101
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0362 [Bro09]
% 0.30/0.46 % : THM101 [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 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
% 0.30/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.46 % Number of atoms : 7 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 7 avg)
% 0.30/0.46 % Number of connectives : 20 ( 0 ~; 0 |; 3 &; 14 @)
% 0.30/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 10 ( 10 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cP,type,
% 0.30/0.46 cP: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(cTHM101,conjecture,
% 0.30/0.46 ( ( ! [Xx: $i] : ( cP @ Xx @ Xx )
% 0.30/0.46 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( ( cP @ Xx @ Xy )
% 0.30/0.46 & ( cP @ Xz @ Xy ) )
% 0.30/0.46 => ( cP @ Xx @ Xz ) ) )
% 0.30/0.46 => ! [Xu: $i,Xv: $i,Xw: $i] :
% 0.30/0.46 ( ( ( cP @ Xu @ Xv )
% 0.30/0.46 & ( cP @ Xv @ Xw ) )
% 0.30/0.46 => ( cP @ Xu @ Xw ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.48/1.24 ---- Embedded in THF ---
% 1.48/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.24 %%% Generated on Tue Feb 24 14:24:28 EST 2026
% 1.48/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.24 %%% Logic specification used:
% 1.48/1.24 %%% thf(spec, logic, $$dhol).
% 1.48/1.24
% 1.48/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OYa2kCvr5t/DTF2DTF11253.p
% See solution above
% 1.48/1.24 ------------------------
% 1.48/1.25 ---- Cleaned THF ---
% 1.48/1.25 thf(cP,type,
% 1.48/1.25 cP: $i > $i > $o ).
% 1.48/1.25
% 1.48/1.25 thf(cTHM101,conjecture,
% 1.48/1.25 ( ( ! [Xx: $i] : ( cP @ Xx @ Xx )
% 1.48/1.25 & ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.48/1.25 ( ( ( cP @ Xx @ Xy )
% 1.48/1.25 & ( cP @ Xz @ Xy ) )
% 1.48/1.25 => ( cP @ Xx @ Xz ) ) )
% 1.48/1.25 => ! [Xu: $i,Xv: $i,Xw: $i] :
% 1.48/1.25 ( ( ( cP @ Xu @ Xv )
% 1.48/1.25 & ( cP @ Xv @ Xw ) )
% 1.48/1.25 => ( cP @ Xu @ Xw ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.26 % (11412)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_11253 for (2999ds/2Mi)
% 1.48/1.26 % (11409)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_11253 for (2999ds/4Mi)
% 1.48/1.26 % (11412)Instruction limit reached!
% 1.48/1.26 % (11412)------------------------------
% 1.48/1.26 % (11412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (11412)Termination reason: Unknown
% 1.48/1.26 % (11412)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (11412)Memory used [KB]: 5373
% 1.48/1.26 % (11412)Time elapsed: 0.002 s
% 1.48/1.26 % (11412)Instructions burned: 2 (million)
% 1.48/1.26 % (11412)------------------------------
% 1.48/1.26 % (11412)------------------------------
% 1.48/1.27 % (11409)Instruction limit reached!
% 1.48/1.27 % (11409)------------------------------
% 1.48/1.27 % (11409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (11409)Termination reason: Unknown
% 1.48/1.27 % (11409)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (11409)Memory used [KB]: 5500
% 1.48/1.27 % (11409)Time elapsed: 0.003 s
% 1.48/1.27 % (11409)Instructions burned: 4 (million)
% 1.48/1.27 % (11409)------------------------------
% 1.48/1.27 % (11409)------------------------------
% 1.48/1.27 % (11408)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11253 for (2999ds/183Mi)
% 1.48/1.27 % (11413)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_11253 for (2999ds/275Mi)
% 1.48/1.27 % (11411)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11253 for (2999ds/2Mi)
% 1.48/1.27 % (11414)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11253 for (2999ds/18Mi)
% 1.48/1.27 % (11411)Instruction limit reached!
% 1.48/1.27 % (11411)------------------------------
% 1.48/1.27 % (11411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (11411)Termination reason: Unknown
% 1.48/1.27 % (11411)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (11411)Memory used [KB]: 5500
% 1.48/1.27 % (11411)Time elapsed: 0.004 s
% 1.48/1.27 % (11411)Instructions burned: 2 (million)
% 1.48/1.27 % (11411)------------------------------
% 1.48/1.27 % (11411)------------------------------
% 1.48/1.27 % (11415)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11253 for (2999ds/3Mi)
% 1.48/1.27 % (11408)First to succeed.
% 1.48/1.28 % (11413)Also succeeded, but the first one will report.
% 1.48/1.28 % (11416)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_11253 for (2999ds/37Mi)
% 1.48/1.28 % (11414)Also succeeded, but the first one will report.
% 1.48/1.28 % (11408)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_11253
% 1.48/1.28 % SZS output start Proof for DTF2THF_11253
% 1.48/1.28 thf(func_def_0, type, cP: $i > $i > $o).
% 1.48/1.28 thf(f34,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(subsumption_resolution,[status(thm)],[f33,f15])).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ X0 @ X0) = $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ! [X0 : $i] : ((cP @ X0 @ X0) = $true) & ! [X1 : $i,X2 : $i,X3 : $i] : (((cP @ X3 @ X2) = $true) | ((cP @ X3 @ X1) != $true) | ((cP @ X2 @ X1) != $true)) & (((cP @ sK2 @ sK0) != $true) & ((cP @ sK1 @ sK0) = $true) & ((cP @ sK2 @ sK1) = $true))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ? [X4 : $i,X5 : $i,X6 : $i] : (((cP @ X6 @ X4) != $true) & ((cP @ X5 @ X4) = $true) & ((cP @ X6 @ X5) = $true)) => (((cP @ sK2 @ sK0) != $true) & ((cP @ sK1 @ sK0) = $true) & ((cP @ sK2 @ sK1) = $true))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ! [X0 : $i] : ((cP @ X0 @ X0) = $true) & ! [X1 : $i,X2 : $i,X3 : $i] : (((cP @ X3 @ X2) = $true) | ((cP @ X3 @ X1) != $true) | ((cP @ X2 @ X1) != $true)) & ? [X4 : $i,X5 : $i,X6 : $i] : (((cP @ X6 @ X4) != $true) & ((cP @ X5 @ X4) = $true) & ((cP @ X6 @ X5) = $true))),
% 1.48/1.28 inference(rectify,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ! [X3 : $i] : ((cP @ X3 @ X3) = $true) & ! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X2 @ X1) = $true) | ((cP @ X2 @ X0) != $true) | ((cP @ X1 @ X0) != $true)) & ? [X5 : $i,X6 : $i,X4 : $i] : (((cP @ X4 @ X5) != $true) & ((cP @ X6 @ X5) = $true) & ((cP @ X4 @ X6) = $true))),
% 1.48/1.28 inference(flattening,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ? [X4 : $i,X5 : $i,X6 : $i] : (((cP @ X4 @ X5) != $true) & (((cP @ X6 @ X5) = $true) & ((cP @ X4 @ X6) = $true))) & (! [X1 : $i,X0 : $i,X2 : $i] : (((cP @ X2 @ X1) = $true) | (((cP @ X2 @ X0) != $true) | ((cP @ X1 @ X0) != $true))) & ! [X3 : $i] : ((cP @ X3 @ X3) = $true))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~((! [X1 : $i,X0 : $i,X2 : $i] : ((((cP @ X2 @ X0) = $true) & ((cP @ X1 @ X0) = $true)) => ((cP @ X2 @ X1) = $true)) & ! [X3 : $i] : ((cP @ X3 @ X3) = $true)) => ! [X4 : $i,X5 : $i,X6 : $i] : ((((cP @ X6 @ X5) = $true) & ((cP @ X4 @ X6) = $true)) => ((cP @ X4 @ X5) = $true)))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~((! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X2 @ X0) & (cP @ X1 @ X0)) => (cP @ X2 @ X1)) & ! [X3 : $i] : (cP @ X3 @ X3)) => ! [X4 : $i,X5 : $i,X6 : $i] : (((cP @ X4 @ X6) & (cP @ X6 @ X5)) => (cP @ X4 @ X5)))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~((! [X1 : $i,X2 : $i,X0 : $i] : (((cP @ X0 @ X1) & (cP @ X2 @ X1)) => (cP @ X0 @ X2)) & ! [X0 : $i] : (cP @ X0 @ X0)) => ! [X3 : $i,X5 : $i,X4 : $i] : (((cP @ X3 @ X4) & (cP @ X4 @ X5)) => (cP @ X3 @ X5)))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 (! [X1 : $i,X2 : $i,X0 : $i] : (((cP @ X0 @ X1) & (cP @ X2 @ X1)) => (cP @ X0 @ X2)) & ! [X0 : $i] : (cP @ X0 @ X0)) => ! [X3 : $i,X5 : $i,X4 : $i] : (((cP @ X3 @ X4) & (cP @ X4 @ X5)) => (cP @ X3 @ X5))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.OYa2kCvr5t/DTF2THF_11253.p',cTHM101)).
% 1.48/1.28 thf(f33,plain,(
% 1.48/1.28 ((cP @ sK0 @ sK0) != $true)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.48/1.28 thf(f28,plain,(
% 1.48/1.28 ((cP @ sK0 @ sK0) != $true) | ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f27,f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ((cP @ sK1 @ sK0) = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.28 thf(f27,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ sK1 @ X0) != $true) | ((cP @ sK0 @ X0) != $true)) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.48/1.28 thf(f26,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (($true != $true) | ((cP @ sK1 @ X0) != $true) | ((cP @ sK0 @ X0) != $true)) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f22,f14])).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((cP @ X3 @ X2) = $true) | ((cP @ X2 @ X1) != $true) | ((cP @ X3 @ X1) != $true)) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.28 thf(f22,plain,(
% 1.48/1.28 ((cP @ sK0 @ sK1) != $true)),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ((cP @ sK0 @ sK1) != $true) | ($true != $true)),
% 1.48/1.28 inference(superposition,[status(thm)],[f17,f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ((cP @ sK2 @ sK1) = $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ sK2 @ X0) != $true) | ((cP @ sK0 @ X0) != $true)) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 ( ! [X0 : $i] : (((cP @ sK0 @ X0) != $true) | ((cP @ sK2 @ X0) != $true) | ($true != $true)) )),
% 1.48/1.28 inference(superposition,[status(thm)],[f13,f14])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 ((cP @ sK2 @ sK0) != $true)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_11253
% 1.48/1.28 % (11408)------------------------------
% 1.48/1.28 % (11408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (11408)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (11408)Memory used [KB]: 5500
% 1.48/1.28 % (11408)Time elapsed: 0.007 s
% 1.48/1.28 % (11408)Instructions burned: 4 (million)
% 1.48/1.28 % (11408)------------------------------
% 1.48/1.28 % (11408)------------------------------
% 1.48/1.28 % (11407)Success in time 0.022 s
%------------------------------------------------------------------------------