%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN055^5 : 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 : n008.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 09:50:26 AM UTC 2026
% Result : Theorem 1.75s 1.50s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 354 ( 100 equ; 0 cnn)
% Maximal formula atoms : 13 ( 14 avg)
% Number of connectives : 309 ( 50 ~; 34 |; 65 &; 137 @)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 0 ^; 39 !; 23 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(func_def_3,type,
cF: $i > $o ).
thf(func_def_4,type,
cG: $i > $o ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f39,f45]) ).
thf(f45,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( $true != $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f24,f15]) ).
thf(f15,plain,
( $true
= ( cP @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ( ( $true
= ( cP @ sK0 ) )
& ( $true
= ( cR @ sK0 ) ) )
| ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) )
& ! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cF @ X3 ) )
& ( $true
= ( cG @ X3 ) ) ) )
& ( $true
= ( cP @ sK1 ) )
& ! [X5: $i] :
( ( $true
!= ( cF @ X5 ) )
| ( ( $true
!= ( cG @ X5 ) )
& ( ( cR @ X5 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
=> ( ( $true
= ( cP @ sK0 ) )
& ( $true
= ( cR @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X4: $i] :
( $true
= ( cP @ X4 ) )
=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) )
& ! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( ( $true
= ( cF @ X3 ) )
& ( $true
= ( cG @ X3 ) ) ) )
& ? [X4: $i] :
( $true
= ( cP @ X4 ) )
& ! [X5: $i] :
( ( $true
!= ( cF @ X5 ) )
| ( ( $true
!= ( cG @ X5 ) )
& ( ( cR @ X5 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X5: $i] :
( ( $true
!= ( cQ @ X5 ) )
| ( ( cP @ X5 )
!= $true ) )
& ( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( ( cF @ X0 )
= $true )
& ( ( cG @ X0 )
= $true ) ) )
& ? [X3: $i] :
( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( cF @ X4 ) )
| ( ( $true
!= ( cG @ X4 ) )
& ( $true
= ( cR @ X4 ) ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X5: $i] :
( ( $true
!= ( cQ @ X5 ) )
| ( ( cP @ X5 )
!= $true ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( ( cF @ X0 )
= $true )
& ( ( cG @ X0 )
= $true ) ) )
& ? [X3: $i] :
( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
!= ( cF @ X4 ) )
| ( ( $true
!= ( cG @ X4 ) )
& ( $true
= ( cR @ X4 ) ) ) )
& ( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
| ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ( $true
= ( cQ @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( ( cF @ X0 )
= $true )
& ( ( cG @ X0 )
= $true ) ) )
& ? [X3: $i] :
( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
= ( cF @ X4 ) )
=> ( ( $true
!= ( cG @ X4 ) )
& ( $true
= ( cR @ X4 ) ) ) )
& ( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
=> ( $true
= ( cQ @ X2 ) ) ) ) )
=> ? [X5: $i] :
( ( $true
= ( cQ @ X5 ) )
& ( ( cP @ X5 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ( ( ( cF @ X0 )
= $true )
& ( ( cG @ X0 )
= $true ) ) )
& ( ? [X1: $i] :
( ( $true
= ( cP @ X1 ) )
& ( $true
= ( cR @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
=> ( $true
= ( cQ @ X2 ) ) ) )
& ? [X3: $i] :
( $true
= ( cP @ X3 ) )
& ! [X4: $i] :
( ( $true
= ( cF @ X4 ) )
=> ( ( $true
= ( cR @ X4 ) )
& ( $true
!= ( cG @ X4 ) ) ) ) )
=> ? [X5: $i] :
( ( $true
= ( cQ @ X5 ) )
& ( ( cP @ X5 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( ( cF @ X0 )
& ( cG @ X0 ) ) )
& ( ? [X1: $i] :
( ( cR @ X1 )
& ( cP @ X1 ) )
| ! [X2: $i] :
( ( cP @ X2 )
=> ( cQ @ X2 ) ) )
& ? [X3: $i] : ( cP @ X3 )
& ! [X4: $i] :
( ( cF @ X4 )
=> ( ( cR @ X4 )
& ~ ( cG @ X4 ) ) ) )
=> ? [X5: $i] :
( ( cP @ X5 )
& ( cQ @ X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( ( cF @ X0 )
& ( cG @ X0 ) ) )
& ( ? [X0: $i] :
( ( cR @ X0 )
& ( cP @ X0 ) )
| ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) ) )
& ? [X0: $i] : ( cP @ X0 )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( ( cR @ X0 )
& ~ ( cG @ X0 ) ) ) )
=> ? [X0: $i] :
( ( cP @ X0 )
& ( cQ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ X0 )
=> ( ( cF @ X0 )
& ( cG @ X0 ) ) )
& ( ? [X0: $i] :
( ( cR @ X0 )
& ( cP @ X0 ) )
| ! [X0: $i] :
( ( cP @ X0 )
=> ( cQ @ X0 ) ) )
& ? [X0: $i] : ( cP @ X0 )
& ! [X0: $i] :
( ( cF @ X0 )
=> ( ( cR @ X0 )
& ~ ( cG @ X0 ) ) ) )
=> ? [X0: $i] :
( ( cP @ X0 )
& ( cQ @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TReppyD3RS/DTF2THF_2777.p',cPELL25) ).
thf(f24,plain,
( ! [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl2_1
<=> ! [X2: $i] :
( $true
!= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f39,plain,
spl2_1,
inference(avatar_split_clause,[status(thm)],[f38,f23]) ).
thf(f38,plain,
! [X0: $i] :
( ( cP @ X0 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f37,f17]) ).
thf(f17,plain,
! [X3: $i] :
( ( $true
!= ( cP @ X3 ) )
| ( $true
= ( cF @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f37,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( ( cF @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( cF @ X0 )
!= $true )
| ( ( cP @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f14,f16]) ).
thf(f16,plain,
! [X3: $i] :
( ( $true
= ( cG @ X3 ) )
| ( $true
!= ( cP @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f14,plain,
! [X5: $i] :
( ( $true
!= ( cG @ X5 ) )
| ( $true
!= ( cF @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN055^5 : 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
% 0.16/0.34 % Computer : n008.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 13:50:09 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
% 0.33/0.49 ---- Original DTF file ---
% 0.33/0.49 thf(spec,logic,$$dhol).
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 % File : SYN055^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.49 % Domain : Syntactic
% 0.33/0.49 % Problem : TPS problem PELL25
% 0.33/0.49 % Version : Especial.
% 0.33/0.49 % English :
% 0.33/0.49
% 0.33/0.49 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.33/0.49 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.49 % Source : [Bro09]
% 0.33/0.49 % Names : tps_0272 [Bro09]
% 0.33/0.49 % : PELL25 [TPS]
% 0.33/0.49 % : Pelletier 25 [Pel86]
% 0.33/0.49
% 0.33/0.49 % Status : Theorem
% 0.33/0.49 % 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 v4.0.0
% 0.33/0.49 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.33/0.49 % Number of atoms : 13 ( 0 equ; 0 cnn)
% 0.33/0.49 % Maximal formula atoms : 13 ( 13 avg)
% 0.33/0.49 % Number of connectives : 26 ( 1 ~; 1 |; 7 &; 13 @)
% 0.33/0.49 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.33/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.33/0.49 % Number of types : 2 ( 0 usr)
% 0.33/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.33/0.49 % Number of symbols : 5 ( 5 usr; 0 con; 1-1 aty)
% 0.33/0.49 % Number of variables : 6 ( 0 ^; 3 !; 3 ?; 6 :)
% 0.33/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.49
% 0.33/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.49 % :
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 thf(cP,type,
% 0.33/0.49 cP: $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(cQ,type,
% 0.33/0.49 cQ: $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(cR,type,
% 0.33/0.49 cR: $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(cF,type,
% 0.33/0.49 cF: $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(cG,type,
% 0.33/0.49 cG: $i > $o ).
% 0.33/0.49
% 0.33/0.49 thf(cPELL25,conjecture,
% 0.33/0.49 ( ( ? [Xx: $i] : ( cP @ Xx )
% 0.33/0.49 & ! [Xx: $i] :
% 0.33/0.49 ( ( cF @ Xx )
% 0.33/0.49 => ( ~ ( cG @ Xx )
% 0.33/0.49 & ( cR @ Xx ) ) )
% 0.33/0.49 & ! [Xx: $i] :
% 0.33/0.49 ( ( cP @ Xx )
% 0.33/0.49 => ( ( cG @ Xx )
% 0.33/0.49 & ( cF @ Xx ) ) )
% 0.33/0.49 & ( ! [Xx: $i] :
% 0.33/0.49 ( ( cP @ Xx )
% 0.33/0.49 => ( cQ @ Xx ) )
% 0.33/0.49 | ? [Xx: $i] :
% 0.33/0.49 ( ( cP @ Xx )
% 0.33/0.49 & ( cR @ Xx ) ) ) )
% 0.33/0.49 => ? [Xx: $i] :
% 0.33/0.49 ( ( cQ @ Xx )
% 0.33/0.49 & ( cP @ Xx ) ) ) ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 1.61/1.46 ---- Embedded in THF ---
% 1.61/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.46 %%% Generated on Tue Feb 24 13:50:10 EST 2026
% 1.61/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.46 %%% Logic specification used:
% 1.61/1.46 %%% thf(spec, logic, $$dhol).
% 1.61/1.46
% 1.61/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.TReppyD3RS/DTF2DTF2777.p
% See solution above
% 1.61/1.46 ------------------------
% 1.61/1.47 ---- Cleaned THF ---
% 1.61/1.47 thf(cP,type,
% 1.61/1.47 cP: $i > $o ).
% 1.61/1.47
% 1.61/1.47 thf(cQ,type,
% 1.61/1.47 cQ: $i > $o ).
% 1.61/1.47
% 1.61/1.47 thf(cR,type,
% 1.61/1.47 cR: $i > $o ).
% 1.61/1.47
% 1.61/1.47 thf(cF,type,
% 1.61/1.47 cF: $i > $o ).
% 1.61/1.47
% 1.61/1.47 thf(cG,type,
% 1.61/1.47 cG: $i > $o ).
% 1.61/1.47
% 1.61/1.47 thf(cPELL25,conjecture,
% 1.61/1.47 ( ( ? [Xx: $i] : ( cP @ Xx )
% 1.61/1.47 & ! [Xx: $i] :
% 1.61/1.47 ( ( cF @ Xx )
% 1.61/1.47 => ( ~ ( cG @ Xx )
% 1.61/1.47 & ( cR @ Xx ) ) )
% 1.61/1.47 & ! [Xx: $i] :
% 1.61/1.47 ( ( cP @ Xx )
% 1.61/1.47 => ( ( cG @ Xx )
% 1.61/1.47 & ( cF @ Xx ) ) )
% 1.61/1.47 & ( ! [Xx: $i] :
% 1.61/1.47 ( ( cP @ Xx )
% 1.61/1.47 => ( cQ @ Xx ) )
% 1.61/1.47 | ? [Xx: $i] :
% 1.61/1.47 ( ( cP @ Xx )
% 1.61/1.47 & ( cR @ Xx ) ) ) )
% 1.61/1.47 => ? [Xx: $i] :
% 1.61/1.47 ( ( cQ @ Xx )
% 1.61/1.47 & ( cP @ Xx ) ) ) ).
% 1.61/1.47 ------------------------
% 1.61/1.49 % (2926)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_2777 for (3000ds/275Mi)
% 1.61/1.49 % (2923)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_2777 for (3000ds/27Mi)
% 1.61/1.49 % (2921)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2777 for (3000ds/183Mi)
% 1.61/1.49 % (2924)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2777 for (3000ds/2Mi)
% 1.61/1.49 % (2927)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2777 for (3000ds/18Mi)
% 1.61/1.49 % (2922)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_2777 for (3000ds/4Mi)
% 1.61/1.49 % (2925)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_2777 for (3000ds/2Mi)
% 1.61/1.49 % (2925)Instruction limit reached!
% 1.61/1.49 % (2925)------------------------------
% 1.61/1.49 % (2925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.49 % (2925)Termination reason: Unknown
% 1.61/1.49 % (2925)Termination phase: Saturation
% 1.61/1.49
% 1.61/1.49 % (2925)Memory used [KB]: 5373
% 1.61/1.49 % (2925)Time elapsed: 0.003 s
% 1.61/1.49 % (2925)Instructions burned: 2 (million)
% 1.61/1.49 % (2925)------------------------------
% 1.61/1.49 % (2925)------------------------------
% 1.61/1.50 % (2924)Instruction limit reached!
% 1.61/1.50 % (2924)------------------------------
% 1.61/1.50 % (2924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.50 % (2924)Termination reason: Unknown
% 1.61/1.50 % (2924)Termination phase: Saturation
% 1.61/1.50
% 1.61/1.50 % (2924)Memory used [KB]: 5500
% 1.61/1.50 % (2924)Time elapsed: 0.004 s
% 1.61/1.50 % (2924)Instructions burned: 2 (million)
% 1.61/1.50 % (2924)------------------------------
% 1.61/1.50 % (2924)------------------------------
% 1.61/1.50 % (2926)First to succeed.
% 1.61/1.50 % (2922)Instruction limit reached!
% 1.61/1.50 % (2922)------------------------------
% 1.61/1.50 % (2922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.50 % (2922)Termination reason: Unknown
% 1.61/1.50 % (2922)Termination phase: Saturation
% 1.61/1.50
% 1.61/1.50 % (2922)Memory used [KB]: 5500
% 1.61/1.50 % (2922)Time elapsed: 0.005 s
% 1.61/1.50 % (2922)Instructions burned: 5 (million)
% 1.61/1.50 % (2922)------------------------------
% 1.61/1.50 % (2922)------------------------------
% 1.75/1.50 % (2921)Also succeeded, but the first one will report.
% 1.75/1.50 % (2923)Also succeeded, but the first one will report.
% 1.75/1.50 % (2926)Refutation found. Thanks to Tanya!
% 1.75/1.50 % SZS status Theorem for DTF2THF_2777
% 1.75/1.50 % SZS output start Proof for DTF2THF_2777
% 1.75/1.50 thf(func_def_0, type, cP: $i > $o).
% 1.75/1.50 thf(func_def_1, type, cQ: $i > $o).
% 1.75/1.50 thf(func_def_2, type, cR: $i > $o).
% 1.75/1.50 thf(func_def_3, type, cF: $i > $o).
% 1.75/1.50 thf(func_def_4, type, cG: $i > $o).
% 1.75/1.50 thf(f46,plain,(
% 1.75/1.50 $false),
% 1.75/1.50 inference(avatar_sat_refutation,[status(thm)],[f39,f45])).
% 1.75/1.50 thf(f45,plain,(
% 1.75/1.50 ~spl2_1),
% 1.75/1.50 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.75/1.50 thf(f44,plain,(
% 1.75/1.50 $false | ~spl2_1),
% 1.75/1.50 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.75/1.50 thf(f40,plain,(
% 1.75/1.50 ($true != $true) | ~spl2_1),
% 1.75/1.50 inference(superposition,[status(thm)],[f24,f15])).
% 1.75/1.50 thf(f15,plain,(
% 1.75/1.50 ($true = (cP @ sK1))),
% 1.75/1.50 inference(cnf_transformation,[status(thm)],[f12])).
% 1.75/1.50 thf(f12,plain,(
% 1.75/1.50 ! [X0 : $i] : (((cQ @ X0) != $true) | ((cP @ X0) != $true)) & ((($true = (cP @ sK0)) & ($true = (cR @ sK0))) | ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))) & ! [X3 : $i] : (($true != (cP @ X3)) | (($true = (cF @ X3)) & ($true = (cG @ X3)))) & ($true = (cP @ sK1)) & ! [X5 : $i] : (($true != (cF @ X5)) | (($true != (cG @ X5)) & ((cR @ X5) = $true)))),
% 1.75/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.75/1.50 thf(f10,plain,(
% 1.75/1.50 ? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) => (($true = (cP @ sK0)) & ($true = (cR @ sK0)))),
% 1.75/1.50 introduced(definition,[],[choice_axiom])).
% 1.75/1.50 thf(f11,plain,(
% 1.75/1.50 ? [X4 : $i] : ($true = (cP @ X4)) => ($true = (cP @ sK1))),
% 1.75/1.50 introduced(definition,[],[choice_axiom])).
% 1.75/1.50 thf(f9,plain,(
% 1.75/1.50 ! [X0 : $i] : (((cQ @ X0) != $true) | ((cP @ X0) != $true)) & (? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) | ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))) & ! [X3 : $i] : (($true != (cP @ X3)) | (($true = (cF @ X3)) & ($true = (cG @ X3)))) & ? [X4 : $i] : ($true = (cP @ X4)) & ! [X5 : $i] : (($true != (cF @ X5)) | (($true != (cG @ X5)) & ((cR @ X5) = $true)))),
% 1.75/1.50 inference(rectify,[status(thm)],[f8])).
% 1.75/1.50 thf(f8,plain,(
% 1.75/1.50 ! [X5 : $i] : (($true != (cQ @ X5)) | ((cP @ X5) != $true)) & (? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) | ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))) & ! [X0 : $i] : (((cP @ X0) != $true) | (((cF @ X0) = $true) & ((cG @ X0) = $true))) & ? [X3 : $i] : ($true = (cP @ X3)) & ! [X4 : $i] : (($true != (cF @ X4)) | (($true != (cG @ X4)) & ($true = (cR @ X4))))),
% 1.75/1.50 inference(flattening,[status(thm)],[f7])).
% 1.75/1.50 thf(f7,plain,(
% 1.75/1.50 ! [X5 : $i] : (($true != (cQ @ X5)) | ((cP @ X5) != $true)) & (! [X0 : $i] : (((cP @ X0) != $true) | (((cF @ X0) = $true) & ((cG @ X0) = $true))) & ? [X3 : $i] : ($true = (cP @ X3)) & ! [X4 : $i] : (($true != (cF @ X4)) | (($true != (cG @ X4)) & ($true = (cR @ X4)))) & (? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) | ! [X2 : $i] : (($true != (cP @ X2)) | ($true = (cQ @ X2)))))),
% 1.75/1.50 inference(ennf_transformation,[status(thm)],[f6])).
% 1.75/1.50 thf(f6,plain,(
% 1.75/1.50 ~((! [X0 : $i] : (((cP @ X0) = $true) => (((cF @ X0) = $true) & ((cG @ X0) = $true))) & ? [X3 : $i] : ($true = (cP @ X3)) & ! [X4 : $i] : (($true = (cF @ X4)) => (($true != (cG @ X4)) & ($true = (cR @ X4)))) & (? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) | ! [X2 : $i] : (($true = (cP @ X2)) => ($true = (cQ @ X2))))) => ? [X5 : $i] : (($true = (cQ @ X5)) & ((cP @ X5) = $true)))),
% 1.75/1.50 inference(flattening,[status(thm)],[f5])).
% 1.75/1.50 thf(f5,plain,(
% 1.75/1.50 ~((! [X0 : $i] : (((cP @ X0) = $true) => (((cF @ X0) = $true) & ((cG @ X0) = $true))) & (? [X1 : $i] : (($true = (cP @ X1)) & ($true = (cR @ X1))) | ! [X2 : $i] : (($true = (cP @ X2)) => ($true = (cQ @ X2)))) & ? [X3 : $i] : ($true = (cP @ X3)) & ! [X4 : $i] : (($true = (cF @ X4)) => (($true = (cR @ X4)) & ~($true = (cG @ X4))))) => ? [X5 : $i] : (($true = (cQ @ X5)) & ((cP @ X5) = $true)))),
% 1.75/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.75/1.50 thf(f4,plain,(
% 1.75/1.50 ~((! [X0 : $i] : ((cP @ X0) => ((cF @ X0) & (cG @ X0))) & (? [X1 : $i] : ((cR @ X1) & (cP @ X1)) | ! [X2 : $i] : ((cP @ X2) => (cQ @ X2))) & ? [X3 : $i] : (cP @ X3) & ! [X4 : $i] : ((cF @ X4) => ((cR @ X4) & ~(cG @ X4)))) => ? [X5 : $i] : ((cP @ X5) & (cQ @ X5)))),
% 1.75/1.50 inference(rectify,[status(thm)],[f2])).
% 1.75/1.50 thf(f2,negated_conjecture,(
% 1.75/1.50 ~((! [X0 : $i] : ((cP @ X0) => ((cF @ X0) & (cG @ X0))) & (? [X0 : $i] : ((cR @ X0) & (cP @ X0)) | ! [X0 : $i] : ((cP @ X0) => (cQ @ X0))) & ? [X0 : $i] : (cP @ X0) & ! [X0 : $i] : ((cF @ X0) => ((cR @ X0) & ~(cG @ X0)))) => ? [X0 : $i] : ((cP @ X0) & (cQ @ X0)))),
% 1.75/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.75/1.50 thf(f1,conjecture,(
% 1.75/1.50 (! [X0 : $i] : ((cP @ X0) => ((cF @ X0) & (cG @ X0))) & (? [X0 : $i] : ((cR @ X0) & (cP @ X0)) | ! [X0 : $i] : ((cP @ X0) => (cQ @ X0))) & ? [X0 : $i] : (cP @ X0) & ! [X0 : $i] : ((cF @ X0) => ((cR @ X0) & ~(cG @ X0)))) => ? [X0 : $i] : ((cP @ X0) & (cQ @ X0))),
% 1.75/1.50 file('/export/starexec/sandbox/tmp/tmp.TReppyD3RS/DTF2THF_2777.p',cPELL25)).
% 1.75/1.50 thf(f24,plain,(
% 1.75/1.50 ( ! [X2 : $i] : (($true != (cP @ X2))) ) | ~spl2_1),
% 1.75/1.50 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.75/1.50 thf(f23,definition,(
% 1.75/1.50 spl2_1 <=> ! [X2 : $i] : ($true != (cP @ X2))),
% 1.75/1.50 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.75/1.50 thf(f39,plain,(
% 1.75/1.50 spl2_1),
% 1.75/1.50 inference(avatar_split_clause,[status(thm)],[f38,f23])).
% 1.75/1.50 thf(f38,plain,(
% 1.75/1.50 ( ! [X0 : $i] : (((cP @ X0) != $true)) )),
% 1.75/1.50 inference(subsumption_resolution,[status(thm)],[f37,f17])).
% 1.75/1.50 thf(f17,plain,(
% 1.75/1.50 ( ! [X3 : $i] : (($true != (cP @ X3)) | ($true = (cF @ X3))) )),
% 1.75/1.50 inference(cnf_transformation,[status(thm)],[f12])).
% 1.75/1.50 thf(f37,plain,(
% 1.75/1.50 ( ! [X0 : $i] : (((cP @ X0) != $true) | ((cF @ X0) != $true)) )),
% 1.75/1.50 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.75/1.50 thf(f36,plain,(
% 1.75/1.50 ( ! [X0 : $i] : (($true != $true) | ((cF @ X0) != $true) | ((cP @ X0) != $true)) )),
% 1.75/1.50 inference(superposition,[status(thm)],[f14,f16])).
% 1.75/1.50 thf(f16,plain,(
% 1.75/1.50 ( ! [X3 : $i] : (($true = (cG @ X3)) | ($true != (cP @ X3))) )),
% 1.75/1.50 inference(cnf_transformation,[status(thm)],[f12])).
% 1.75/1.50 thf(f14,plain,(
% 1.75/1.50 ( ! [X5 : $i] : (($true != (cG @ X5)) | ($true != (cF @ X5))) )),
% 1.75/1.50 inference(cnf_transformation,[status(thm)],[f12])).
% 1.75/1.50 % SZS output end Proof for DTF2THF_2777
% 1.75/1.50 % (2926)------------------------------
% 1.75/1.50 % (2926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.50 % (2926)Termination reason: Refutation
% 1.75/1.50
% 1.75/1.50 % (2926)Memory used [KB]: 5500
% 1.75/1.50 % (2926)Time elapsed: 0.005 s
% 1.75/1.50 % (2926)Instructions burned: 3 (million)
% 1.75/1.50 % (2926)------------------------------
% 1.75/1.50 % (2926)------------------------------
% 1.75/1.50 % (2920)Success in time 0.018 s
%------------------------------------------------------------------------------