%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV060^5 : 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 : n001.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 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 90 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 266 ( 40 ~; 27 |; 36 &; 146 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 56 !; 28 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_1,type,
a: $tType ).
thf(func_def_5,type,
sK0: b > a > $o ).
thf(func_def_6,type,
sK1: b ).
thf(func_def_7,type,
sK2: b > a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: b ).
thf(func_def_10,type,
sK5: a ).
thf(f33,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f30,f13]) ).
thf(f13,plain,
( ( sK0 @ sK1 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X4: b,X5: a] :
( ( ( sK3 = X5 )
& ( sK1 = X4 ) )
| ( ( sK2 @ X4 @ X5 )
= $true )
| ( ( sK0 @ X4 @ X5 )
!= $true ) )
& ( ( sK0 @ sK4 @ sK5 )
= $true )
& ( ( sK2 @ sK4 @ sK5 )
!= $true )
& ( ( sK0 @ sK1 @ sK3 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: b > a > $o,X1: b,X2: b > a > $o,X3: a] :
( ! [X4: b,X5: a] :
( ( ( X3 = X5 )
& ( X1 = X4 ) )
| ( ( X2 @ X4 @ X5 )
= $true )
| ( ( X0 @ X4 @ X5 )
!= $true ) )
& ? [X6: b,X7: a] :
( ( $true
= ( X0 @ X6 @ X7 ) )
& ( ( X2 @ X6 @ X7 )
!= $true ) )
& ( ( X0 @ X1 @ X3 )
!= $true ) )
=> ( ! [X5: a,X4: b] :
( ( ( sK3 = X5 )
& ( sK1 = X4 ) )
| ( ( sK2 @ X4 @ X5 )
= $true )
| ( ( sK0 @ X4 @ X5 )
!= $true ) )
& ? [X7: a,X6: b] :
( ( ( sK0 @ X6 @ X7 )
= $true )
& ( ( sK2 @ X6 @ X7 )
!= $true ) )
& ( ( sK0 @ sK1 @ sK3 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X7: a,X6: b] :
( ( ( sK0 @ X6 @ X7 )
= $true )
& ( ( sK2 @ X6 @ X7 )
!= $true ) )
=> ( ( ( sK0 @ sK4 @ sK5 )
= $true )
& ( ( sK2 @ sK4 @ sK5 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: b > a > $o,X1: b,X2: b > a > $o,X3: a] :
( ! [X4: b,X5: a] :
( ( ( X3 = X5 )
& ( X1 = X4 ) )
| ( ( X2 @ X4 @ X5 )
= $true )
| ( ( X0 @ X4 @ X5 )
!= $true ) )
& ? [X6: b,X7: a] :
( ( $true
= ( X0 @ X6 @ X7 ) )
& ( ( X2 @ X6 @ X7 )
!= $true ) )
& ( ( X0 @ X1 @ X3 )
!= $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X1: b > a > $o,X2: b,X3: b > a > $o,X0: a] :
( ! [X5: b,X4: a] :
( ( ( X0 = X4 )
& ( X2 = X5 ) )
| ( $true
= ( X3 @ X5 @ X4 ) )
| ( $true
!= ( X1 @ X5 @ X4 ) ) )
& ? [X7: b,X6: a] :
( ( ( X1 @ X7 @ X6 )
= $true )
& ( ( X3 @ X7 @ X6 )
!= $true ) )
& ( ( X1 @ X2 @ X0 )
!= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a,X1: b > a > $o,X3: b > a > $o,X2: b] :
( ? [X7: b,X6: a] :
( ( ( X1 @ X7 @ X6 )
= $true )
& ( ( X3 @ X7 @ X6 )
!= $true ) )
& ( ( X1 @ X2 @ X0 )
!= $true )
& ! [X4: a,X5: b] :
( ( $true
= ( X3 @ X5 @ X4 ) )
| ( ( X0 = X4 )
& ( X2 = X5 ) )
| ( $true
!= ( X1 @ X5 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a,X1: b > a > $o,X3: b > a > $o,X2: b] :
( ( ( ( X1 @ X2 @ X0 )
!= $true )
& ! [X4: a,X5: b] :
( ( $true
= ( X1 @ X5 @ X4 ) )
=> ( ( $true
= ( X3 @ X5 @ X4 ) )
| ( ( X0 = X4 )
& ( X2 = X5 ) ) ) ) )
=> ! [X6: a,X7: b] :
( ( ( X1 @ X7 @ X6 )
= $true )
=> ( ( X3 @ X7 @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a,X1: b > a > $o,X2: b,X3: b > a > $o] :
( ( ( ( X1 @ X2 @ X0 )
!= $true )
& ! [X4: a,X5: b] :
( ( $true
= ( X1 @ X5 @ X4 ) )
=> ( ( $true
= ( X3 @ X5 @ X4 ) )
| ( ( X0 = X4 )
& ( X2 = X5 ) ) ) ) )
=> ! [X6: a,X7: b] :
( ( ( X1 @ X7 @ X6 )
= $true )
=> ( ( X3 @ X7 @ X6 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a,X1: b > a > $o,X2: b,X3: b > a > $o] :
( ( ~ ( X1 @ X2 @ X0 )
& ! [X4: a,X5: b] :
( ( X1 @ X5 @ X4 )
=> ( ( X3 @ X5 @ X4 )
| ( ( X2 = X5 )
& ( X0 = X4 ) ) ) ) )
=> ! [X6: a,X7: b] :
( ( X1 @ X7 @ X6 )
=> ( X3 @ X7 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a,X3: b > a > $o,X0: b,X2: b > a > $o] :
( ( ~ ( X3 @ X0 @ X1 )
& ! [X5: a,X4: b] :
( ( X3 @ X4 @ X5 )
=> ( ( X2 @ X4 @ X5 )
| ( ( X0 = X4 )
& ( X1 = X5 ) ) ) ) )
=> ! [X7: a,X6: b] :
( ( X3 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a,X3: b > a > $o,X0: b,X2: b > a > $o] :
( ( ~ ( X3 @ X0 @ X1 )
& ! [X5: a,X4: b] :
( ( X3 @ X4 @ X5 )
=> ( ( X2 @ X4 @ X5 )
| ( ( X0 = X4 )
& ( X1 = X5 ) ) ) ) )
=> ! [X7: a,X6: b] :
( ( X3 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.e1yiKFOKnO/DTF2THF_1698.p',cTHM173_pme) ).
thf(f30,plain,
( ( sK0 @ sK1 @ sK3 )
= $true ),
inference(superposition,[status(thm)],[f21,f28]) ).
thf(f28,plain,
sK3 = sK5,
inference(subsumption_resolution,[status(thm)],[f27,f21]) ).
thf(f27,plain,
( ( ( sK0 @ sK1 @ sK5 )
!= $true )
| ( sK3 = sK5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK3 = sK5 )
| ( $true != $true )
| ( ( sK0 @ sK1 @ sK5 )
!= $true ) ),
inference(superposition,[status(thm)],[f22,f17]) ).
thf(f17,plain,
! [X4: b,X5: a] :
( ( ( sK2 @ X4 @ X5 )
= $true )
| ( ( sK0 @ X4 @ X5 )
!= $true )
| ( sK3 = X5 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f22,plain,
( ( sK2 @ sK1 @ sK5 )
!= $true ),
inference(superposition,[status(thm)],[f14,f20]) ).
thf(f20,plain,
sK4 = sK1,
inference(subsumption_resolution,[status(thm)],[f19,f15]) ).
thf(f15,plain,
( ( sK0 @ sK4 @ sK5 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f19,plain,
( ( sK4 = sK1 )
| ( ( sK0 @ sK4 @ sK5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK0 @ sK4 @ sK5 )
!= $true )
| ( $true != $true )
| ( sK4 = sK1 ) ),
inference(superposition,[status(thm)],[f14,f16]) ).
thf(f16,plain,
! [X4: b,X5: a] :
( ( ( sK2 @ X4 @ X5 )
= $true )
| ( ( sK0 @ X4 @ X5 )
!= $true )
| ( sK1 = X4 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
( ( sK2 @ sK4 @ sK5 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f21,plain,
( ( sK0 @ sK1 @ sK5 )
= $true ),
inference(superposition,[status(thm)],[f15,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV060^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.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 12:40:20 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV060^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory (Relations)
% 0.29/0.46 % Problem : TPS problem THM173
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro09]
% 0.29/0.46 % Names : tps_0329 [Bro09]
% 0.29/0.46 % : THM173 [TPS]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.29/0.46 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.29/0.46 % Number of connectives : 17 ( 1 ~; 1 |; 2 &; 10 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 13 ( 13 avg)
% 0.29/0.46 % Number of types : 3 ( 2 usr)
% 0.29/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.46 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.46 % : Polymorphic definitions expanded.
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(b_type,type,
% 0.29/0.46 b: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(cTHM173_pme,conjecture,
% 0.29/0.46 ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
% 0.29/0.46 ( ( ! [Xx_0: b,Xy_9: a] :
% 0.29/0.46 ( ( Xk @ Xx_0 @ Xy_9 )
% 0.29/0.46 => ( ( Xs @ Xx_0 @ Xy_9 )
% 0.29/0.46 | ( ( Xx_0 = Xx )
% 0.29/0.46 & ( Xy_9 = Xy ) ) ) )
% 0.29/0.46 & ~ ( Xk @ Xx @ Xy ) )
% 0.29/0.46 => ! [Xx0: b,Xy0: a] :
% 0.29/0.46 ( ( Xk @ Xx0 @ Xy0 )
% 0.29/0.46 => ( Xs @ Xx0 @ Xy0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.49/1.23 ---- Embedded in THF ---
% 1.49/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.23 %%% Generated on Tue Feb 24 12:40:21 EST 2026
% 1.49/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.23 %%% Logic specification used:
% 1.49/1.23 %%% thf(spec, logic, $$dhol).
% 1.49/1.23
% 1.49/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.e1yiKFOKnO/DTF2DTF1698.p
% See solution above
% 1.49/1.23 ------------------------
% 1.49/1.24 ---- Cleaned THF ---
% 1.49/1.24 thf(b_type,type,
% 1.49/1.24 b: $tType ).
% 1.49/1.24
% 1.49/1.24 thf(a_type,type,
% 1.49/1.24 a: $tType ).
% 1.49/1.24
% 1.49/1.24 thf(cTHM173_pme,conjecture,
% 1.49/1.24 ! [Xx: b,Xy: a,Xs: b > a > $o,Xk: b > a > $o] :
% 1.49/1.24 ( ( ! [Xx_0: b,Xy_9: a] :
% 1.49/1.24 ( ( Xk @ Xx_0 @ Xy_9 )
% 1.49/1.24 => ( ( Xs @ Xx_0 @ Xy_9 )
% 1.49/1.24 | ( ( Xx_0 = Xx )
% 1.49/1.24 & ( Xy_9 = Xy ) ) ) )
% 1.49/1.24 & ~ ( Xk @ Xx @ Xy ) )
% 1.49/1.24 => ! [Xx0: b,Xy0: a] :
% 1.49/1.24 ( ( Xk @ Xx0 @ Xy0 )
% 1.49/1.24 => ( Xs @ Xx0 @ Xy0 ) ) ) ).
% 1.49/1.24 ------------------------
% 1.49/1.26 % (1931)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1698 for (2999ds/2Mi)
% 1.49/1.26 % (1929)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_1698 for (2999ds/4Mi)
% 1.49/1.26 % (1931)Instruction limit reached!
% 1.49/1.26 % (1931)------------------------------
% 1.49/1.26 % (1931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (1931)Termination reason: Unknown
% 1.49/1.26 % (1931)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (1931)Memory used [KB]: 5500
% 1.49/1.26 % (1931)Time elapsed: 0.002 s
% 1.49/1.26 % (1931)Instructions burned: 2 (million)
% 1.49/1.26 % (1931)------------------------------
% 1.49/1.26 % (1931)------------------------------
% 1.49/1.26 % (1929)Instruction limit reached!
% 1.49/1.26 % (1929)------------------------------
% 1.49/1.26 % (1929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (1929)Termination reason: Unknown
% 1.49/1.26 % (1929)Termination phase: Saturation
% 1.49/1.26
% 1.49/1.26 % (1929)Memory used [KB]: 5500
% 1.49/1.26 % (1929)Time elapsed: 0.003 s
% 1.49/1.26 % (1929)Instructions burned: 4 (million)
% 1.49/1.26 % (1929)------------------------------
% 1.49/1.26 % (1929)------------------------------
% 1.49/1.26 % (1928)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1698 for (2999ds/183Mi)
% 1.49/1.26 % (1930)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_1698 for (2999ds/27Mi)
% 1.49/1.26 % (1932)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_1698 for (2999ds/2Mi)
% 1.49/1.26 % (1933)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_1698 for (2999ds/275Mi)
% 1.49/1.26 % (1934)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1698 for (2999ds/18Mi)
% 1.49/1.26 % (1932)Instruction limit reached!
% 1.49/1.26 % (1932)------------------------------
% 1.49/1.26 % (1932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.26 % (1932)Termination reason: Unknown
% 1.49/1.26 % (1932)Termination phase: Property scanning
% 1.49/1.26
% 1.49/1.26 % (1932)Memory used [KB]: 895
% 1.49/1.26 % (1932)Time elapsed: 0.003 s
% 1.49/1.26 % (1932)Instructions burned: 2 (million)
% 1.49/1.26 % (1932)------------------------------
% 1.49/1.26 % (1932)------------------------------
% 1.49/1.27 % (1935)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1698 for (2999ds/3Mi)
% 1.49/1.27 % (1928)First to succeed.
% 1.49/1.27 % (1935)Instruction limit reached!
% 1.49/1.27 % (1935)------------------------------
% 1.49/1.27 % (1935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (1935)Termination reason: Unknown
% 1.49/1.27 % (1935)Termination phase: Saturation
% 1.49/1.27
% 1.49/1.27 % (1935)Memory used [KB]: 5500
% 1.49/1.27 % (1935)Time elapsed: 0.002 s
% 1.49/1.27 % (1935)Instructions burned: 3 (million)
% 1.49/1.27 % (1935)------------------------------
% 1.49/1.27 % (1935)------------------------------
% 1.49/1.27 % (1933)Also succeeded, but the first one will report.
% 1.49/1.27 % (1928)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_1698
% 1.49/1.27 % SZS output start Proof for DTF2THF_1698
% 1.49/1.27 thf(type_def_5, type, b: $tType).
% 1.49/1.27 thf(type_def_6, type, a: $tType).
% 1.49/1.27 thf(func_def_0, type, b: $tType).
% 1.49/1.27 thf(func_def_1, type, a: $tType).
% 1.49/1.27 thf(func_def_5, type, sK0: b > a > $o).
% 1.49/1.27 thf(func_def_6, type, sK1: b).
% 1.49/1.27 thf(func_def_7, type, sK2: b > a > $o).
% 1.49/1.27 thf(func_def_8, type, sK3: a).
% 1.49/1.27 thf(func_def_9, type, sK4: b).
% 1.49/1.27 thf(func_def_10, type, sK5: a).
% 1.49/1.27 thf(f33,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f30,f13])).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 ((sK0 @ sK1 @ sK3) != $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 ! [X4 : b,X5 : a] : (((sK3 = X5) & (sK1 = X4)) | ((sK2 @ X4 @ X5) = $true) | ((sK0 @ X4 @ X5) != $true)) & (((sK0 @ sK4 @ sK5) = $true) & ((sK2 @ sK4 @ sK5) != $true)) & ((sK0 @ sK1 @ sK3) != $true)),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f11,f10])).
% 1.49/1.27 thf(f10,plain,(
% 1.49/1.27 ? [X0 : b > a > $o,X1 : b,X2 : b > a > $o,X3 : a] : (! [X4 : b,X5 : a] : (((X3 = X5) & (X1 = X4)) | ((X2 @ X4 @ X5) = $true) | ((X0 @ X4 @ X5) != $true)) & ? [X6 : b,X7 : a] : (($true = (X0 @ X6 @ X7)) & ((X2 @ X6 @ X7) != $true)) & ((X0 @ X1 @ X3) != $true)) => (! [X5 : a,X4 : b] : (((sK3 = X5) & (sK1 = X4)) | ((sK2 @ X4 @ X5) = $true) | ((sK0 @ X4 @ X5) != $true)) & ? [X7 : a,X6 : b] : (((sK0 @ X6 @ X7) = $true) & ((sK2 @ X6 @ X7) != $true)) & ((sK0 @ sK1 @ sK3) != $true))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 ? [X7 : a,X6 : b] : (((sK0 @ X6 @ X7) = $true) & ((sK2 @ X6 @ X7) != $true)) => (((sK0 @ sK4 @ sK5) = $true) & ((sK2 @ sK4 @ sK5) != $true))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 ? [X0 : b > a > $o,X1 : b,X2 : b > a > $o,X3 : a] : (! [X4 : b,X5 : a] : (((X3 = X5) & (X1 = X4)) | ((X2 @ X4 @ X5) = $true) | ((X0 @ X4 @ X5) != $true)) & ? [X6 : b,X7 : a] : (($true = (X0 @ X6 @ X7)) & ((X2 @ X6 @ X7) != $true)) & ((X0 @ X1 @ X3) != $true))),
% 1.49/1.27 inference(rectify,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 ? [X1 : b > a > $o,X2 : b,X3 : b > a > $o,X0 : a] : (! [X5 : b,X4 : a] : (((X0 = X4) & (X2 = X5)) | ($true = (X3 @ X5 @ X4)) | ($true != (X1 @ X5 @ X4))) & ? [X7 : b,X6 : a] : (((X1 @ X7 @ X6) = $true) & ((X3 @ X7 @ X6) != $true)) & ((X1 @ X2 @ X0) != $true))),
% 1.49/1.27 inference(flattening,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 ? [X0 : a,X1 : b > a > $o,X3 : b > a > $o,X2 : b] : (? [X7 : b,X6 : a] : (((X1 @ X7 @ X6) = $true) & ((X3 @ X7 @ X6) != $true)) & (((X1 @ X2 @ X0) != $true) & ! [X4 : a,X5 : b] : ((($true = (X3 @ X5 @ X4)) | ((X0 = X4) & (X2 = X5))) | ($true != (X1 @ X5 @ X4)))))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.27 thf(f6,plain,(
% 1.49/1.27 ~! [X0 : a,X1 : b > a > $o,X3 : b > a > $o,X2 : b] : ((((X1 @ X2 @ X0) != $true) & ! [X4 : a,X5 : b] : (($true = (X1 @ X5 @ X4)) => (($true = (X3 @ X5 @ X4)) | ((X0 = X4) & (X2 = X5))))) => ! [X6 : a,X7 : b] : (((X1 @ X7 @ X6) = $true) => ((X3 @ X7 @ X6) = $true)))),
% 1.49/1.27 inference(flattening,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,plain,(
% 1.49/1.27 ~! [X0 : a,X1 : b > a > $o,X2 : b,X3 : b > a > $o] : ((~((X1 @ X2 @ X0) = $true) & ! [X4 : a,X5 : b] : (($true = (X1 @ X5 @ X4)) => (($true = (X3 @ X5 @ X4)) | ((X0 = X4) & (X2 = X5))))) => ! [X6 : a,X7 : b] : (((X1 @ X7 @ X6) = $true) => ((X3 @ X7 @ X6) = $true)))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.27 thf(f4,plain,(
% 1.49/1.27 ~! [X0 : a,X1 : b > a > $o,X2 : b,X3 : b > a > $o] : ((~(X1 @ X2 @ X0) & ! [X4 : a,X5 : b] : ((X1 @ X5 @ X4) => ((X3 @ X5 @ X4) | ((X2 = X5) & (X0 = X4))))) => ! [X6 : a,X7 : b] : ((X1 @ X7 @ X6) => (X3 @ X7 @ X6)))),
% 1.49/1.27 inference(rectify,[status(thm)],[f2])).
% 1.49/1.27 thf(f2,negated_conjecture,(
% 1.49/1.27 ~! [X1 : a,X3 : b > a > $o,X0 : b,X2 : b > a > $o] : ((~(X3 @ X0 @ X1) & ! [X5 : a,X4 : b] : ((X3 @ X4 @ X5) => ((X2 @ X4 @ X5) | ((X0 = X4) & (X1 = X5))))) => ! [X7 : a,X6 : b] : ((X3 @ X6 @ X7) => (X2 @ X6 @ X7)))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.27 thf(f1,conjecture,(
% 1.49/1.27 ! [X1 : a,X3 : b > a > $o,X0 : b,X2 : b > a > $o] : ((~(X3 @ X0 @ X1) & ! [X5 : a,X4 : b] : ((X3 @ X4 @ X5) => ((X2 @ X4 @ X5) | ((X0 = X4) & (X1 = X5))))) => ! [X7 : a,X6 : b] : ((X3 @ X6 @ X7) => (X2 @ X6 @ X7)))),
% 1.49/1.27 file('/export/starexec/sandbox2/tmp/tmp.e1yiKFOKnO/DTF2THF_1698.p',cTHM173_pme)).
% 1.49/1.27 thf(f30,plain,(
% 1.49/1.27 ((sK0 @ sK1 @ sK3) = $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f21,f28])).
% 1.49/1.27 thf(f28,plain,(
% 1.49/1.27 (sK3 = sK5)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f27,f21])).
% 1.49/1.27 thf(f27,plain,(
% 1.49/1.27 ((sK0 @ sK1 @ sK5) != $true) | (sK3 = sK5)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.49/1.27 thf(f25,plain,(
% 1.49/1.27 (sK3 = sK5) | ($true != $true) | ((sK0 @ sK1 @ sK5) != $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f22,f17])).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 ( ! [X4 : b,X5 : a] : (((sK2 @ X4 @ X5) = $true) | ((sK0 @ X4 @ X5) != $true) | (sK3 = X5)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f22,plain,(
% 1.49/1.27 ((sK2 @ sK1 @ sK5) != $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f14,f20])).
% 1.49/1.27 thf(f20,plain,(
% 1.49/1.27 (sK4 = sK1)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f19,f15])).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 ((sK0 @ sK4 @ sK5) = $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 (sK4 = sK1) | ((sK0 @ sK4 @ sK5) != $true)),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 ((sK0 @ sK4 @ sK5) != $true) | ($true != $true) | (sK4 = sK1)),
% 1.49/1.27 inference(superposition,[status(thm)],[f14,f16])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 ( ! [X4 : b,X5 : a] : (((sK2 @ X4 @ X5) = $true) | ((sK0 @ X4 @ X5) != $true) | (sK1 = X4)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 ((sK2 @ sK4 @ sK5) != $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f12])).
% 1.49/1.27 thf(f21,plain,(
% 1.49/1.27 ((sK0 @ sK1 @ sK5) = $true)),
% 1.49/1.27 inference(superposition,[status(thm)],[f15,f20])).
% 1.49/1.27 % SZS output end Proof for DTF2THF_1698
% 1.49/1.27 % (1928)------------------------------
% 1.49/1.27 % (1928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (1928)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (1928)Memory used [KB]: 5500
% 1.49/1.27 % (1928)Time elapsed: 0.006 s
% 1.49/1.27 % (1928)Instructions burned: 2 (million)
% 1.49/1.27 % (1928)------------------------------
% 1.49/1.27 % (1928)------------------------------
% 1.49/1.27 % (1927)Success in time 0.021 s
%------------------------------------------------------------------------------