%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV059^5 : 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 : n003.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 09:40:11 AM UTC 2026
% Result : Theorem 1.80s 1.52s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 312 ( 31 ~; 14 |; 27 &; 229 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 11 ^; 47 !; 4 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_7,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_2,type,
cG: b > b ).
thf(func_def_3,type,
cA: b > a ).
thf(func_def_4,type,
c_less_: a > a > $o ).
thf(func_def_5,type,
cF: b > b ).
thf(func_def_11,type,
sK0: b ).
thf(f24,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f23,f14]) ).
thf(f14,plain,
! [X1: b] :
( ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cF @ X1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) )
!= $true )
& ! [X1: b] :
( ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cF @ X1 ) ) )
= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X2 @ X4 )
= $true )
| ( ( c_less_ @ X2 @ X3 )
!= $true )
| ( ( c_less_ @ X3 @ X4 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cG @ X0 ) ) )
!= $true )
=> ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cG @ X0 ) ) )
!= $true )
& ! [X1: b] :
( ( c_less_ @ ( cA @ X1 ) @ ( cA @ ( cF @ X1 ) ) )
= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X2 @ X4 )
= $true )
| ( ( c_less_ @ X2 @ X3 )
!= $true )
| ( ( c_less_ @ X3 @ X4 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ? [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
!= $true )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( $true
= ( c_less_ @ X1 @ X3 ) )
| ( ( c_less_ @ X1 @ X2 )
!= $true )
| ( ( c_less_ @ X2 @ X3 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
!= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ! [X1: a,X2: a,X3: a] :
( ( $true
= ( c_less_ @ X1 @ X3 ) )
| ( ( c_less_ @ X1 @ X2 )
!= $true )
| ( ( c_less_ @ X2 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ( ( c_less_ @ X1 @ X2 )
= $true )
& ( ( c_less_ @ X2 @ X3 )
= $true ) )
=> ( $true
= ( c_less_ @ X1 @ X3 ) ) ) )
=> ! [X4: b] :
( ( c_less_ @ ( cA @ X4 ) @ ( cA @ ( cG @ X4 ) ) )
= $true ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: b] :
( ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( ( c_less_ @ X3 @ X4 )
= $true )
& ( ( c_less_ @ X2 @ X3 )
= $true ) )
=> ( ( c_less_ @ X2 @ X4 )
= $true ) ) )
=> ! [X5: b] :
( ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: b] : ( c_less_ @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
& ( ( ^ [X1: b] : ( cF @ ( cF @ X1 ) ) )
= cG )
& ! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X3 @ X4 )
& ( c_less_ @ X2 @ X3 ) )
=> ( c_less_ @ X2 @ X4 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) )
= cG )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: b] : ( c_less_ @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ( ( ^ [X4: b] : ( cF @ ( cF @ X4 ) ) )
= cG )
& ! [X0: a,X1: a,X2: a] :
( ( ( c_less_ @ X1 @ X2 )
& ( c_less_ @ X0 @ X1 ) )
=> ( c_less_ @ X0 @ X2 ) ) )
=> ! [X5: b] : ( c_less_ @ ( cA @ X5 ) @ ( cA @ ( cG @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x76c0FfWll/DTF2THF_21813.p',cTHM89A_pme) ).
thf(f23,plain,
( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ sK0 ) ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f19,f14]) ).
thf(f19,plain,
! [X0: a] :
( ( ( c_less_ @ X0 @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) )
!= $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: a] :
( ( ( c_less_ @ X0 @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) )
!= $true )
| ( $true != $true )
| ( ( c_less_ @ ( cA @ sK0 ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f17,f12]) ).
thf(f12,plain,
! [X2: a,X3: a,X4: a] :
( ( ( c_less_ @ X2 @ X4 )
= $true )
| ( ( c_less_ @ X3 @ X4 )
!= $true )
| ( ( c_less_ @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f17,plain,
( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( c_less_ @ ( cA @ sK0 )
@ ( cA
@ ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) )
@ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f15,f13]) ).
thf(f13,plain,
( cG
= ( ^ [Y0: b] : ( cF @ ( cF @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f15,plain,
( ( c_less_ @ ( cA @ sK0 ) @ ( cA @ ( cG @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV059^5 : 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
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:39:25 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
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SEV059^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.49 % Domain : Set Theory (Relations)
% 0.32/0.49 % Problem : TPS problem THM89A
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Bro09]
% 0.32/0.49 % Names : tps_0326 [Bro09]
% 0.32/0.49 % : THM89 [TPS]
% 0.32/0.49 % : THM89A [TPS]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.32/0.49 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.32/0.49 % Number of atoms : 6 ( 1 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 6 ( 6 avg)
% 0.32/0.49 % Number of connectives : 23 ( 0 ~; 0 |; 3 &; 18 @)
% 0.32/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 10 ( 10 avg)
% 0.32/0.49 % Number of types : 3 ( 2 usr)
% 0.32/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 5 ( 4 usr; 0 con; 1-2 aty)
% 0.32/0.49 % Number of variables : 6 ( 1 ^; 5 !; 0 ?; 6 :)
% 0.32/0.49 % SPC : TH0_THM_EQU_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.49 % : Polymorphic definitions expanded.
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(b_type,type,
% 0.32/0.49 b: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(a_type,type,
% 0.32/0.49 a: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(cG,type,
% 0.32/0.49 cG: b > b ).
% 0.32/0.49
% 0.32/0.49 thf(cA,type,
% 0.32/0.49 cA: b > a ).
% 0.32/0.49
% 0.32/0.49 thf(c_less_,type,
% 0.32/0.49 c_less_: a > a > $o ).
% 0.32/0.49
% 0.32/0.49 thf(cF,type,
% 0.32/0.49 cF: b > b ).
% 0.32/0.49
% 0.32/0.49 thf(cTHM89A_pme,conjecture,
% 0.32/0.49 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 0.32/0.49 ( ( ( c_less_ @ Xx @ Xy )
% 0.32/0.49 & ( c_less_ @ Xy @ Xz ) )
% 0.32/0.49 => ( c_less_ @ Xx @ Xz ) )
% 0.32/0.49 & ! [X: b] : ( c_less_ @ ( cA @ X ) @ ( cA @ ( cF @ X ) ) )
% 0.32/0.49 & ( cG
% 0.32/0.49 = ( ^ [Z: b] : ( cF @ ( cF @ Z ) ) ) ) )
% 0.32/0.49 => ! [Y: b] : ( c_less_ @ ( cA @ Y ) @ ( cA @ ( cG @ Y ) ) ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.61/1.48 ---- Embedded in THF ---
% 1.61/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.48 %%% Generated on Tue Feb 24 12:39:26 EST 2026
% 1.61/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.48 %%% Logic specification used:
% 1.61/1.48 %%% thf(spec, logic, $$dhol).
% 1.61/1.48
% 1.61/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.x76c0FfWll/DTF2DTF21813.p
% See solution above
% 1.61/1.48 ------------------------
% 1.61/1.49 ---- Cleaned THF ---
% 1.61/1.49 thf(b_type,type,
% 1.61/1.49 b: $tType ).
% 1.61/1.49
% 1.61/1.49 thf(a_type,type,
% 1.61/1.49 a: $tType ).
% 1.61/1.49
% 1.61/1.49 thf(cG,type,
% 1.61/1.49 cG: b > b ).
% 1.61/1.49
% 1.61/1.49 thf(cA,type,
% 1.61/1.49 cA: b > a ).
% 1.61/1.49
% 1.61/1.49 thf(c_less_,type,
% 1.61/1.49 c_less_: a > a > $o ).
% 1.61/1.49
% 1.61/1.49 thf(cF,type,
% 1.61/1.49 cF: b > b ).
% 1.61/1.49
% 1.61/1.49 thf(cTHM89A_pme,conjecture,
% 1.61/1.49 ( ( ! [Xx: a,Xy: a,Xz: a] :
% 1.61/1.49 ( ( ( c_less_ @ Xx @ Xy )
% 1.61/1.49 & ( c_less_ @ Xy @ Xz ) )
% 1.61/1.49 => ( c_less_ @ Xx @ Xz ) )
% 1.61/1.49 & ! [X: b] : ( c_less_ @ ( cA @ X ) @ ( cA @ ( cF @ X ) ) )
% 1.61/1.49 & ( cG
% 1.61/1.49 = ( ^ [Z: b] : ( cF @ ( cF @ Z ) ) ) ) )
% 1.61/1.49 => ! [Y: b] : ( c_less_ @ ( cA @ Y ) @ ( cA @ ( cG @ Y ) ) ) ) ).
% 1.61/1.49 ------------------------
% 1.80/1.51 % (21934)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_21813 for (2999ds/4Mi)
% 1.80/1.51 % (21938)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_21813 for (2999ds/275Mi)
% 1.80/1.51 % (21937)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_21813 for (2999ds/2Mi)
% 1.80/1.51 % (21933)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21813 for (2999ds/183Mi)
% 1.80/1.51 % (21939)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21813 for (2999ds/18Mi)
% 1.80/1.51 % (21936)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21813 for (2999ds/2Mi)
% 1.80/1.51 % (21935)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_21813 for (2999ds/27Mi)
% 1.80/1.51 % (21936)Instruction limit reached!
% 1.80/1.51 % (21936)------------------------------
% 1.80/1.51 % (21936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (21936)Termination reason: Unknown
% 1.80/1.51 % (21936)Termination phase: Saturation
% 1.80/1.51
% 1.80/1.51 % (21936)Memory used [KB]: 5373
% 1.80/1.51 % (21936)Time elapsed: 0.003 s
% 1.80/1.51 % (21936)Instructions burned: 2 (million)
% 1.80/1.51 % (21936)------------------------------
% 1.80/1.51 % (21936)------------------------------
% 1.80/1.51 % (21937)Instruction limit reached!
% 1.80/1.51 % (21937)------------------------------
% 1.80/1.51 % (21937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (21937)Termination reason: Unknown
% 1.80/1.51 % (21937)Termination phase: Saturation
% 1.80/1.51
% 1.80/1.51 % (21937)Memory used [KB]: 5500
% 1.80/1.51 % (21937)Time elapsed: 0.003 s
% 1.80/1.51 % (21937)Instructions burned: 2 (million)
% 1.80/1.51 % (21937)------------------------------
% 1.80/1.51 % (21937)------------------------------
% 1.80/1.51 % (21933)First to succeed.
% 1.80/1.51 % (21934)Instruction limit reached!
% 1.80/1.51 % (21934)------------------------------
% 1.80/1.51 % (21934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.51 % (21934)Termination reason: Unknown
% 1.80/1.51 % (21934)Termination phase: Saturation
% 1.80/1.51
% 1.80/1.51 % (21934)Memory used [KB]: 5500
% 1.80/1.51 % (21934)Time elapsed: 0.005 s
% 1.80/1.51 % (21934)Instructions burned: 5 (million)
% 1.80/1.51 % (21934)------------------------------
% 1.80/1.51 % (21934)------------------------------
% 1.80/1.52 % (21935)Also succeeded, but the first one will report.
% 1.80/1.52 % (21933)Refutation found. Thanks to Tanya!
% 1.80/1.52 % SZS status Theorem for DTF2THF_21813
% 1.80/1.52 % SZS output start Proof for DTF2THF_21813
% 1.80/1.52 thf(type_def_5, type, b: $tType).
% 1.80/1.52 thf(type_def_7, type, a: $tType).
% 1.80/1.52 thf(func_def_0, type, b: $tType).
% 1.80/1.52 thf(func_def_1, type, a: $tType).
% 1.80/1.52 thf(func_def_2, type, cG: b > b).
% 1.80/1.52 thf(func_def_3, type, cA: b > a).
% 1.80/1.52 thf(func_def_4, type, c_less_: a > a > $o).
% 1.80/1.52 thf(func_def_5, type, cF: b > b).
% 1.80/1.52 thf(func_def_11, type, sK0: b).
% 1.80/1.52 thf(f24,plain,(
% 1.80/1.52 $false),
% 1.80/1.52 inference(subsumption_resolution,[status(thm)],[f23,f14])).
% 1.80/1.52 thf(f14,plain,(
% 1.80/1.52 ( ! [X1 : b] : (((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1))) = $true)) )),
% 1.80/1.52 inference(cnf_transformation,[status(thm)],[f11])).
% 1.80/1.52 thf(f11,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ (cG @ sK0))) != $true) & ! [X1 : b] : ((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1))) = $true) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X2 : a,X3 : a,X4 : a] : (((c_less_ @ X2 @ X4) = $true) | ((c_less_ @ X2 @ X3) != $true) | ((c_less_ @ X3 @ X4) != $true))),
% 1.80/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 1.80/1.52 thf(f10,plain,(
% 1.80/1.52 ? [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cG @ X0))) != $true) => ((c_less_ @ (cA @ sK0) @ (cA @ (cG @ sK0))) != $true)),
% 1.80/1.52 introduced(definition,[],[choice_axiom])).
% 1.80/1.52 thf(f9,plain,(
% 1.80/1.52 ? [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cG @ X0))) != $true) & ! [X1 : b] : ((c_less_ @ (cA @ X1) @ (cA @ (cF @ X1))) = $true) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X2 : a,X3 : a,X4 : a] : (((c_less_ @ X2 @ X4) = $true) | ((c_less_ @ X2 @ X3) != $true) | ((c_less_ @ X3 @ X4) != $true))),
% 1.80/1.52 inference(rectify,[status(thm)],[f8])).
% 1.80/1.52 thf(f8,plain,(
% 1.80/1.52 ? [X4 : b] : ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))) != $true) & ! [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))) = $true) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X1 : a,X2 : a,X3 : a] : (($true = (c_less_ @ X1 @ X3)) | ((c_less_ @ X1 @ X2) != $true) | ((c_less_ @ X2 @ X3) != $true))),
% 1.80/1.52 inference(flattening,[status(thm)],[f7])).
% 1.80/1.52 thf(f7,plain,(
% 1.80/1.52 ? [X4 : b] : ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))) != $true) & ((cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))) = $true) & ! [X1 : a,X2 : a,X3 : a] : (($true = (c_less_ @ X1 @ X3)) | (((c_less_ @ X1 @ X2) != $true) | ((c_less_ @ X2 @ X3) != $true))))),
% 1.80/1.52 inference(ennf_transformation,[status(thm)],[f6])).
% 1.80/1.52 thf(f6,plain,(
% 1.80/1.52 ~(((cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((c_less_ @ X1 @ X2) = $true) & ((c_less_ @ X2 @ X3) = $true)) => ($true = (c_less_ @ X1 @ X3)))) => ! [X4 : b] : ((c_less_ @ (cA @ X4) @ (cA @ (cG @ X4))) = $true))),
% 1.80/1.52 inference(rectify,[status(thm)],[f5])).
% 1.80/1.52 thf(f5,plain,(
% 1.80/1.52 ~((! [X0 : b] : ((c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))) = $true) & (cG = (^[Y0 : b]: (cF @ (cF @ Y0)))) & ! [X2 : a,X3 : a,X4 : a] : ((((c_less_ @ X3 @ X4) = $true) & ((c_less_ @ X2 @ X3) = $true)) => ((c_less_ @ X2 @ X4) = $true))) => ! [X5 : b] : ((c_less_ @ (cA @ X5) @ (cA @ (cG @ X5))) = $true))),
% 1.80/1.52 inference(fool_elimination,[status(thm)],[f4])).
% 1.80/1.52 thf(f4,plain,(
% 1.80/1.52 ~((! [X0 : b] : (c_less_ @ (cA @ X0) @ (cA @ (cF @ X0))) & ((^[X1 : b] : (cF @ (cF @ X1))) = cG) & ! [X2 : a,X3 : a,X4 : a] : (((c_less_ @ X3 @ X4) & (c_less_ @ X2 @ X3)) => (c_less_ @ X2 @ X4))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5))))),
% 1.80/1.52 inference(rectify,[status(thm)],[f2])).
% 1.80/1.52 thf(f2,negated_conjecture,(
% 1.80/1.52 ~((! [X3 : b] : (c_less_ @ (cA @ X3) @ (cA @ (cF @ X3))) & ((^[X4 : b] : (cF @ (cF @ X4))) = cG) & ! [X0 : a,X1 : a,X2 : a] : (((c_less_ @ X1 @ X2) & (c_less_ @ X0 @ X1)) => (c_less_ @ X0 @ X2))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5))))),
% 1.80/1.52 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.52 thf(f1,conjecture,(
% 1.80/1.52 (! [X3 : b] : (c_less_ @ (cA @ X3) @ (cA @ (cF @ X3))) & ((^[X4 : b] : (cF @ (cF @ X4))) = cG) & ! [X0 : a,X1 : a,X2 : a] : (((c_less_ @ X1 @ X2) & (c_less_ @ X0 @ X1)) => (c_less_ @ X0 @ X2))) => ! [X5 : b] : (c_less_ @ (cA @ X5) @ (cA @ (cG @ X5)))),
% 1.80/1.52 file('/export/starexec/sandbox/tmp/tmp.x76c0FfWll/DTF2THF_21813.p',cTHM89A_pme)).
% 1.80/1.52 thf(f23,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ sK0))) != $true)),
% 1.80/1.52 inference(trivial_inequality_removal,[status(thm)],[f20])).
% 1.80/1.52 thf(f20,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ sK0))) != $true) | ($true != $true)),
% 1.80/1.52 inference(superposition,[status(thm)],[f19,f14])).
% 1.80/1.52 thf(f19,plain,(
% 1.80/1.52 ( ! [X0 : a] : (((c_less_ @ X0 @ (cA @ (cF @ (cF @ sK0)))) != $true) | ((c_less_ @ (cA @ sK0) @ X0) != $true)) )),
% 1.80/1.52 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.80/1.52 thf(f18,plain,(
% 1.80/1.52 ( ! [X0 : a] : (((c_less_ @ X0 @ (cA @ (cF @ (cF @ sK0)))) != $true) | ($true != $true) | ((c_less_ @ (cA @ sK0) @ X0) != $true)) )),
% 1.80/1.52 inference(superposition,[status(thm)],[f17,f12])).
% 1.80/1.52 thf(f12,plain,(
% 1.80/1.52 ( ! [X2 : a,X3 : a,X4 : a] : (((c_less_ @ X2 @ X4) = $true) | ((c_less_ @ X3 @ X4) != $true) | ((c_less_ @ X2 @ X3) != $true)) )),
% 1.80/1.52 inference(cnf_transformation,[status(thm)],[f11])).
% 1.80/1.52 thf(f17,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ (cF @ (cF @ sK0)))) != $true)),
% 1.80/1.52 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.80/1.52 thf(f16,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ ((^[Y0 : b]: (cF @ (cF @ Y0))) @ sK0))) != $true)),
% 1.80/1.52 inference(definition_unfolding,[status(thm)],[f15,f13])).
% 1.80/1.52 thf(f13,plain,(
% 1.80/1.52 (cG = (^[Y0 : b]: (cF @ (cF @ Y0))))),
% 1.80/1.52 inference(cnf_transformation,[status(thm)],[f11])).
% 1.80/1.52 thf(f15,plain,(
% 1.80/1.52 ((c_less_ @ (cA @ sK0) @ (cA @ (cG @ sK0))) != $true)),
% 1.80/1.52 inference(cnf_transformation,[status(thm)],[f11])).
% 1.80/1.52 % SZS output end Proof for DTF2THF_21813
% 1.80/1.52 % (21933)------------------------------
% 1.80/1.52 % (21933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (21933)Termination reason: Refutation
% 1.80/1.52
% 1.80/1.52 % (21933)Memory used [KB]: 5500
% 1.80/1.52 % (21933)Time elapsed: 0.005 s
% 1.80/1.52 % (21933)Instructions burned: 3 (million)
% 1.80/1.52 % (21933)------------------------------
% 1.80/1.52 % (21933)------------------------------
% 1.80/1.52 % (21932)Success in time 0.017 s
%------------------------------------------------------------------------------