%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN365^5 : 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 : n018.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 09:50:51 AM UTC 2026
% Result : Theorem 1.46s 1.26s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 294 ( 83 equ; 0 cnn)
% Maximal formula atoms : 9 ( 11 avg)
% Number of connectives : 320 ( 46 ~; 27 |; 40 &; 189 @)
% ( 0 <=>; 18 =>; 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 : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 32 !; 16 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(func_def_2,type,
h: $i > $i ).
thf(func_def_3,type,
g: $i > $i ).
thf(func_def_8,type,
sK1: $i > $i ).
thf(f27,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f26,f15]) ).
thf(f15,plain,
( $true
= ( cP @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( ( $true
= ( cP @ ( h @ X0 ) ) )
& ( $true
= ( cP @ ( g @ X0 ) ) ) )
| ( ( cP @ X0 )
!= $true ) )
& ( $true
= ( cP @ sK0 ) )
& ! [X2: $i] :
( ( $true
!= ( cR @ sK0 @ X2 ) )
| ( ( cP @ X2 )
!= $true ) )
& ! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cR @ X3 @ ( g @ ( h @ ( sK1 @ X3 ) ) ) ) )
& ( $true
= ( cP @ ( sK1 @ X3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( ( cP @ X1 )
= $true )
& ! [X2: $i] :
( ( $true
!= ( cR @ X1 @ X2 ) )
| ( ( cP @ X2 )
!= $true ) ) )
=> ( ( $true
= ( cP @ sK0 ) )
& ! [X2: $i] :
( ( $true
!= ( cR @ sK0 @ X2 ) )
| ( ( cP @ X2 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cR @ X3 @ ( g @ ( h @ X4 ) ) ) )
& ( ( cP @ X4 )
= $true ) ) )
=> ( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cR @ X3 @ ( g @ ( h @ ( sK1 @ X3 ) ) ) ) )
& ( $true
= ( cP @ ( sK1 @ X3 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( $true
= ( cP @ ( h @ X0 ) ) )
& ( $true
= ( cP @ ( g @ X0 ) ) ) )
| ( ( cP @ X0 )
!= $true ) )
& ? [X1: $i] :
( ( ( cP @ X1 )
= $true )
& ! [X2: $i] :
( ( $true
!= ( cR @ X1 @ X2 ) )
| ( ( cP @ X2 )
!= $true ) ) )
& ! [X3: $i] :
? [X4: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cR @ X3 @ ( g @ ( h @ X4 ) ) ) )
& ( ( cP @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X2: $i] :
( ( ( ( cP @ ( h @ X2 ) )
= $true )
& ( ( cP @ ( g @ X2 ) )
= $true ) )
| ( ( cP @ X2 )
!= $true ) )
& ? [X3: $i] :
( ( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( cR @ X3 @ X4 ) )
| ( ( cP @ X4 )
!= $true ) ) )
& ! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( ( cR @ X0 @ ( g @ ( h @ X1 ) ) )
= $true )
& ( ( cP @ X1 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X3: $i] :
( ( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( cR @ X3 @ X4 ) )
| ( ( cP @ X4 )
!= $true ) ) )
& ! [X2: $i] :
( ( ( ( cP @ ( h @ X2 ) )
= $true )
& ( ( cP @ ( g @ X2 ) )
= $true ) )
| ( ( cP @ X2 )
!= $true ) )
& ! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( ( cR @ X0 @ ( g @ ( h @ X1 ) ) )
= $true )
& ( ( cP @ X1 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X2: $i] :
( ( ( cP @ X2 )
= $true )
=> ( ( ( cP @ ( h @ X2 ) )
= $true )
& ( ( cP @ ( g @ X2 ) )
= $true ) ) )
& ! [X0: $i] :
? [X1: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( ( cR @ X0 @ ( g @ ( h @ X1 ) ) )
= $true )
& ( ( cP @ X1 )
= $true ) ) ) )
=> ! [X3: $i] :
( ( $true
= ( cP @ X3 ) )
=> ? [X4: $i] :
( ( $true
= ( cR @ X3 @ X4 ) )
& ( ( cP @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 )
=> ( ( cP @ X1 )
& ( cR @ X0 @ ( g @ ( h @ X1 ) ) ) ) )
& ! [X2: $i] :
( ( cP @ X2 )
=> ( ( cP @ ( h @ X2 ) )
& ( cP @ ( g @ X2 ) ) ) ) )
=> ! [X3: $i] :
( ( cP @ X3 )
=> ? [X4: $i] :
( ( cP @ X4 )
& ( cR @ X3 @ X4 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 )
=> ( ( cP @ X1 )
& ( cR @ X0 @ ( g @ ( h @ X1 ) ) ) ) )
& ! [X2: $i] :
( ( cP @ X2 )
=> ( ( cP @ ( h @ X2 ) )
& ( cP @ ( g @ X2 ) ) ) ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ? [X1: $i] :
( ( cP @ X1 )
& ( cR @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
? [X1: $i] :
( ( cP @ X0 )
=> ( ( cP @ X1 )
& ( cR @ X0 @ ( g @ ( h @ X1 ) ) ) ) )
& ! [X2: $i] :
( ( cP @ X2 )
=> ( ( cP @ ( h @ X2 ) )
& ( cP @ ( g @ X2 ) ) ) ) )
=> ! [X0: $i] :
( ( cP @ X0 )
=> ? [X1: $i] :
( ( cP @ X1 )
& ( cR @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.D69NlLoceb/DTF2THF_26600.p',cX2116) ).
thf(f26,plain,
( $true
!= ( cP @ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $true != $true )
| ( $true
!= ( cP @ sK0 ) ) ),
inference(superposition,[status(thm)],[f24,f12]) ).
thf(f12,plain,
! [X3: $i] :
( ( $true
= ( cP @ ( sK1 @ X3 ) ) )
| ( $true
!= ( cP @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f24,plain,
( $true
!= ( cP @ ( sK1 @ sK0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $true
!= ( cP @ ( sK1 @ sK0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f22,f17]) ).
thf(f17,plain,
! [X0: $i] :
( ( $true
= ( cP @ ( h @ X0 ) ) )
| ( ( cP @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f22,plain,
( $true
!= ( cP @ ( h @ ( sK1 @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $true
!= ( cP @ ( h @ ( sK1 @ sK0 ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f16]) ).
thf(f16,plain,
! [X0: $i] :
( ( $true
= ( cP @ ( g @ X0 ) ) )
| ( ( cP @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f20,plain,
( $true
!= ( cP @ ( g @ ( h @ ( sK1 @ sK0 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f19,f15]) ).
thf(f19,plain,
( ( $true
!= ( cP @ sK0 ) )
| ( $true
!= ( cP @ ( g @ ( h @ ( sK1 @ sK0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
!= ( cP @ sK0 ) )
| ( $true != $true )
| ( $true
!= ( cP @ ( g @ ( h @ ( sK1 @ sK0 ) ) ) ) ) ),
inference(superposition,[status(thm)],[f14,f13]) ).
thf(f13,plain,
! [X3: $i] :
( ( $true
= ( cR @ X3 @ ( g @ ( h @ ( sK1 @ X3 ) ) ) ) )
| ( $true
!= ( cP @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f14,plain,
! [X2: $i] :
( ( $true
!= ( cR @ sK0 @ X2 ) )
| ( ( cP @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN365^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:02:01 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYN365^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : TPS problem X2116
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0160 [Bro09]
% 0.29/0.45 % : tps_0267 [Bro09]
% 0.29/0.45 % : tps_0903 [Bro09]
% 0.29/0.45 % : X2116 [TPS]
% 0.29/0.45 % : THM72 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.29/0.45 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 9 ( 9 avg)
% 0.29/0.45 % Number of connectives : 23 ( 0 ~; 0 |; 4 &; 15 @)
% 0.29/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 10 ( 10 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.29/0.45 % Number of variables : 5 ( 0 ^; 3 !; 2 ?; 5 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 % :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(cP,type,
% 0.29/0.45 cP: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cR,type,
% 0.29/0.45 cR: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(h,type,
% 0.29/0.45 h: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(g,type,
% 0.29/0.45 g: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(cX2116,conjecture,
% 0.29/0.45 ( ( ! [Xx: $i] :
% 0.29/0.45 ? [Xy: $i] :
% 0.29/0.45 ( ( cP @ Xx )
% 0.29/0.45 => ( ( cR @ Xx @ ( g @ ( h @ Xy ) ) )
% 0.29/0.45 & ( cP @ Xy ) ) )
% 0.29/0.45 & ! [Xw: $i] :
% 0.29/0.45 ( ( cP @ Xw )
% 0.29/0.45 => ( ( cP @ ( g @ Xw ) )
% 0.29/0.45 & ( cP @ ( h @ Xw ) ) ) ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( cP @ Xx )
% 0.29/0.45 => ? [Xy: $i] :
% 0.29/0.45 ( ( cR @ Xx @ Xy )
% 0.29/0.45 & ( cP @ Xy ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.46/1.22 ---- Embedded in THF ---
% 1.46/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.23 %%% Generated on Tue Feb 24 14:02:01 EST 2026
% 1.46/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.23 %%% Logic specification used:
% 1.46/1.23 %%% thf(spec, logic, $$dhol).
% 1.46/1.23
% 1.46/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.D69NlLoceb/DTF2DTF26600.p
% See solution above
% 1.46/1.23 ------------------------
% 1.46/1.23 ---- Cleaned THF ---
% 1.46/1.24 thf(cP,type,
% 1.46/1.24 cP: $i > $o ).
% 1.46/1.24
% 1.46/1.24 thf(cR,type,
% 1.46/1.24 cR: $i > $i > $o ).
% 1.46/1.24
% 1.46/1.24 thf(h,type,
% 1.46/1.24 h: $i > $i ).
% 1.46/1.24
% 1.46/1.24 thf(g,type,
% 1.46/1.24 g: $i > $i ).
% 1.46/1.24
% 1.46/1.24 thf(cX2116,conjecture,
% 1.46/1.24 ( ( ! [Xx: $i] :
% 1.46/1.24 ? [Xy: $i] :
% 1.46/1.24 ( ( cP @ Xx )
% 1.46/1.24 => ( ( cR @ Xx @ ( g @ ( h @ Xy ) ) )
% 1.46/1.24 & ( cP @ Xy ) ) )
% 1.46/1.24 & ! [Xw: $i] :
% 1.46/1.24 ( ( cP @ Xw )
% 1.46/1.24 => ( ( cP @ ( g @ Xw ) )
% 1.46/1.24 & ( cP @ ( h @ Xw ) ) ) ) )
% 1.46/1.24 => ! [Xx: $i] :
% 1.46/1.24 ( ( cP @ Xx )
% 1.46/1.24 => ? [Xy: $i] :
% 1.46/1.24 ( ( cR @ Xx @ Xy )
% 1.46/1.24 & ( cP @ Xy ) ) ) ) ).
% 1.46/1.24 ------------------------
% 1.46/1.25 % (26715)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_26600 for (2999ds/4Mi)
% 1.46/1.25 % (26715)Instruction limit reached!
% 1.46/1.25 % (26715)------------------------------
% 1.46/1.25 % (26715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.25 % (26715)Termination reason: Unknown
% 1.46/1.25 % (26715)Termination phase: Saturation
% 1.46/1.25
% 1.46/1.25 % (26715)Memory used [KB]: 5500
% 1.46/1.25 % (26715)Time elapsed: 0.003 s
% 1.46/1.25 % (26715)Instructions burned: 4 (million)
% 1.46/1.25 % (26715)------------------------------
% 1.46/1.25 % (26715)------------------------------
% 1.46/1.26 % (26714)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26600 for (2999ds/183Mi)
% 1.46/1.26 % (26716)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_26600 for (2999ds/27Mi)
% 1.46/1.26 % (26717)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26600 for (2999ds/2Mi)
% 1.46/1.26 % (26719)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_26600 for (2999ds/275Mi)
% 1.46/1.26 % (26718)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_26600 for (2999ds/2Mi)
% 1.46/1.26 % (26717)Instruction limit reached!
% 1.46/1.26 % (26717)------------------------------
% 1.46/1.26 % (26717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (26717)Termination reason: Unknown
% 1.46/1.26 % (26718)Instruction limit reached!
% 1.46/1.26 % (26718)------------------------------
% 1.46/1.26 % (26718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (26717)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (26717)Memory used [KB]: 895
% 1.46/1.26 % (26717)Time elapsed: 0.003 s
% 1.46/1.26 % (26717)Instructions burned: 2 (million)
% 1.46/1.26 % (26717)------------------------------
% 1.46/1.26 % (26717)------------------------------
% 1.46/1.26 % (26718)Termination reason: Unknown
% 1.46/1.26 % (26718)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (26718)Memory used [KB]: 895
% 1.46/1.26 % (26718)Time elapsed: 0.003 s
% 1.46/1.26 % (26718)Instructions burned: 2 (million)
% 1.46/1.26 % (26718)------------------------------
% 1.46/1.26 % (26718)------------------------------
% 1.46/1.26 % (26720)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26600 for (2999ds/18Mi)
% 1.46/1.26 % (26714)First to succeed.
% 1.46/1.26 % (26721)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26600 for (2999ds/3Mi)
% 1.46/1.26 % (26719)Also succeeded, but the first one will report.
% 1.46/1.26 % (26721)Instruction limit reached!
% 1.46/1.26 % (26721)------------------------------
% 1.46/1.26 % (26721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (26721)Termination reason: Unknown
% 1.46/1.26 % (26721)Termination phase: Saturation
% 1.46/1.26
% 1.46/1.26 % (26721)Memory used [KB]: 5500
% 1.46/1.26 % (26721)Time elapsed: 0.002 s
% 1.46/1.26 % (26721)Instructions burned: 3 (million)
% 1.46/1.26 % (26721)------------------------------
% 1.46/1.26 % (26721)------------------------------
% 1.46/1.26 % (26714)Refutation found. Thanks to Tanya!
% 1.46/1.26 % SZS status Theorem for DTF2THF_26600
% 1.46/1.26 % SZS output start Proof for DTF2THF_26600
% 1.46/1.26 thf(func_def_0, type, cP: $i > $o).
% 1.46/1.26 thf(func_def_1, type, cR: $i > $i > $o).
% 1.46/1.26 thf(func_def_2, type, h: $i > $i).
% 1.46/1.26 thf(func_def_3, type, g: $i > $i).
% 1.46/1.26 thf(func_def_8, type, sK1: $i > $i).
% 1.46/1.26 thf(f27,plain,(
% 1.46/1.26 $false),
% 1.46/1.26 inference(subsumption_resolution,[status(thm)],[f26,f15])).
% 1.46/1.26 thf(f15,plain,(
% 1.46/1.26 ($true = (cP @ sK0))),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 thf(f11,plain,(
% 1.46/1.26 ! [X0 : $i] : ((($true = (cP @ (h @ X0))) & ($true = (cP @ (g @ X0)))) | ((cP @ X0) != $true)) & (($true = (cP @ sK0)) & ! [X2 : $i] : (($true != (cR @ sK0 @ X2)) | ((cP @ X2) != $true))) & ! [X3 : $i] : (($true != (cP @ X3)) | (($true = (cR @ X3 @ (g @ (h @ (sK1 @ X3))))) & ($true = (cP @ (sK1 @ X3)))))),
% 1.46/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.46/1.26 thf(f9,plain,(
% 1.46/1.26 ? [X1 : $i] : (((cP @ X1) = $true) & ! [X2 : $i] : (($true != (cR @ X1 @ X2)) | ((cP @ X2) != $true))) => (($true = (cP @ sK0)) & ! [X2 : $i] : (($true != (cR @ sK0 @ X2)) | ((cP @ X2) != $true)))),
% 1.46/1.26 introduced(definition,[],[choice_axiom])).
% 1.46/1.26 thf(f10,plain,(
% 1.46/1.26 ! [X3 : $i] : (? [X4 : $i] : (($true != (cP @ X3)) | (($true = (cR @ X3 @ (g @ (h @ X4)))) & ((cP @ X4) = $true))) => (($true != (cP @ X3)) | (($true = (cR @ X3 @ (g @ (h @ (sK1 @ X3))))) & ($true = (cP @ (sK1 @ X3))))))),
% 1.46/1.26 introduced(definition,[],[choice_axiom])).
% 1.46/1.26 thf(f8,plain,(
% 1.46/1.26 ! [X0 : $i] : ((($true = (cP @ (h @ X0))) & ($true = (cP @ (g @ X0)))) | ((cP @ X0) != $true)) & ? [X1 : $i] : (((cP @ X1) = $true) & ! [X2 : $i] : (($true != (cR @ X1 @ X2)) | ((cP @ X2) != $true))) & ! [X3 : $i] : ? [X4 : $i] : (($true != (cP @ X3)) | (($true = (cR @ X3 @ (g @ (h @ X4)))) & ((cP @ X4) = $true)))),
% 1.46/1.26 inference(rectify,[status(thm)],[f7])).
% 1.46/1.26 thf(f7,plain,(
% 1.46/1.26 ! [X2 : $i] : ((((cP @ (h @ X2)) = $true) & ((cP @ (g @ X2)) = $true)) | ((cP @ X2) != $true)) & ? [X3 : $i] : (($true = (cP @ X3)) & ! [X4 : $i] : (($true != (cR @ X3 @ X4)) | ((cP @ X4) != $true))) & ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) != $true) | (((cR @ X0 @ (g @ (h @ X1))) = $true) & ((cP @ X1) = $true)))),
% 1.46/1.26 inference(flattening,[status(thm)],[f6])).
% 1.46/1.26 thf(f6,plain,(
% 1.46/1.26 ? [X3 : $i] : (($true = (cP @ X3)) & ! [X4 : $i] : (($true != (cR @ X3 @ X4)) | ((cP @ X4) != $true))) & (! [X2 : $i] : ((((cP @ (h @ X2)) = $true) & ((cP @ (g @ X2)) = $true)) | ((cP @ X2) != $true)) & ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) != $true) | (((cR @ X0 @ (g @ (h @ X1))) = $true) & ((cP @ X1) = $true))))),
% 1.46/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.26 thf(f5,plain,(
% 1.46/1.26 ~((! [X2 : $i] : (((cP @ X2) = $true) => (((cP @ (h @ X2)) = $true) & ((cP @ (g @ X2)) = $true))) & ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0) = $true) => (((cR @ X0 @ (g @ (h @ X1))) = $true) & ((cP @ X1) = $true)))) => ! [X3 : $i] : (($true = (cP @ X3)) => ? [X4 : $i] : (($true = (cR @ X3 @ X4)) & ((cP @ X4) = $true))))),
% 1.46/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.26 thf(f4,plain,(
% 1.46/1.26 ~((! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ((cP @ X1) & (cR @ X0 @ (g @ (h @ X1))))) & ! [X2 : $i] : ((cP @ X2) => ((cP @ (h @ X2)) & (cP @ (g @ X2))))) => ! [X3 : $i] : ((cP @ X3) => ? [X4 : $i] : ((cP @ X4) & (cR @ X3 @ X4))))),
% 1.46/1.26 inference(rectify,[status(thm)],[f2])).
% 1.46/1.26 thf(f2,negated_conjecture,(
% 1.46/1.26 ~((! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ((cP @ X1) & (cR @ X0 @ (g @ (h @ X1))))) & ! [X2 : $i] : ((cP @ X2) => ((cP @ (h @ X2)) & (cP @ (g @ X2))))) => ! [X0 : $i] : ((cP @ X0) => ? [X1 : $i] : ((cP @ X1) & (cR @ X0 @ X1))))),
% 1.46/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.26 thf(f1,conjecture,(
% 1.46/1.26 (! [X0 : $i] : ? [X1 : $i] : ((cP @ X0) => ((cP @ X1) & (cR @ X0 @ (g @ (h @ X1))))) & ! [X2 : $i] : ((cP @ X2) => ((cP @ (h @ X2)) & (cP @ (g @ X2))))) => ! [X0 : $i] : ((cP @ X0) => ? [X1 : $i] : ((cP @ X1) & (cR @ X0 @ X1)))),
% 1.46/1.26 file('/export/starexec/sandbox/tmp/tmp.D69NlLoceb/DTF2THF_26600.p',cX2116)).
% 1.46/1.26 thf(f26,plain,(
% 1.46/1.26 ($true != (cP @ sK0))),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.46/1.26 thf(f25,plain,(
% 1.46/1.26 ($true != $true) | ($true != (cP @ sK0))),
% 1.46/1.26 inference(superposition,[status(thm)],[f24,f12])).
% 1.46/1.26 thf(f12,plain,(
% 1.46/1.26 ( ! [X3 : $i] : (($true = (cP @ (sK1 @ X3))) | ($true != (cP @ X3))) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 thf(f24,plain,(
% 1.46/1.26 ($true != (cP @ (sK1 @ sK0)))),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.46/1.26 thf(f23,plain,(
% 1.46/1.26 ($true != (cP @ (sK1 @ sK0))) | ($true != $true)),
% 1.46/1.26 inference(superposition,[status(thm)],[f22,f17])).
% 1.46/1.26 thf(f17,plain,(
% 1.46/1.26 ( ! [X0 : $i] : (($true = (cP @ (h @ X0))) | ((cP @ X0) != $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 thf(f22,plain,(
% 1.46/1.26 ($true != (cP @ (h @ (sK1 @ sK0))))),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.46/1.26 thf(f21,plain,(
% 1.46/1.26 ($true != (cP @ (h @ (sK1 @ sK0)))) | ($true != $true)),
% 1.46/1.26 inference(superposition,[status(thm)],[f20,f16])).
% 1.46/1.26 thf(f16,plain,(
% 1.46/1.26 ( ! [X0 : $i] : (($true = (cP @ (g @ X0))) | ((cP @ X0) != $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 thf(f20,plain,(
% 1.46/1.26 ($true != (cP @ (g @ (h @ (sK1 @ sK0)))))),
% 1.46/1.26 inference(subsumption_resolution,[status(thm)],[f19,f15])).
% 1.46/1.26 thf(f19,plain,(
% 1.46/1.26 ($true != (cP @ sK0)) | ($true != (cP @ (g @ (h @ (sK1 @ sK0)))))),
% 1.46/1.26 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.46/1.26 thf(f18,plain,(
% 1.46/1.26 ($true != (cP @ sK0)) | ($true != $true) | ($true != (cP @ (g @ (h @ (sK1 @ sK0)))))),
% 1.46/1.26 inference(superposition,[status(thm)],[f14,f13])).
% 1.46/1.26 thf(f13,plain,(
% 1.46/1.26 ( ! [X3 : $i] : (($true = (cR @ X3 @ (g @ (h @ (sK1 @ X3))))) | ($true != (cP @ X3))) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 thf(f14,plain,(
% 1.46/1.26 ( ! [X2 : $i] : (($true != (cR @ sK0 @ X2)) | ((cP @ X2) != $true)) )),
% 1.46/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.46/1.26 % SZS output end Proof for DTF2THF_26600
% 1.46/1.26 % (26714)------------------------------
% 1.46/1.26 % (26714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.26 % (26714)Termination reason: Refutation
% 1.46/1.26
% 1.46/1.26 % (26714)Memory used [KB]: 5500
% 1.46/1.26 % (26714)Time elapsed: 0.006 s
% 1.46/1.26 % (26714)Instructions burned: 3 (million)
% 1.46/1.26 % (26714)------------------------------
% 1.46/1.26 % (26714)------------------------------
% 1.46/1.26 % (26713)Success in time 0.013 s
%------------------------------------------------------------------------------