%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV197^5 : 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 09:40:32 AM UTC 2026
% Result : Theorem 1.65s 1.35s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 184 ( 126 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 415 ( 62 ~; 44 |; 62 &; 220 @)
% ( 4 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 13 con; 0-2 aty)
% Number of variables : 143 ( 0 ^; 111 !; 32 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
iS: $tType ).
thf(func_def_0,type,
iS: $tType ).
thf(func_def_1,type,
c0: iS ).
thf(func_def_2,type,
cP: iS > iS > iS ).
thf(func_def_6,type,
sK0: iS ).
thf(func_def_7,type,
sK1: iS ).
thf(func_def_8,type,
sK2: iS ).
thf(func_def_9,type,
sK3: iS ).
thf(func_def_10,type,
sK4: iS ).
thf(func_def_11,type,
sK5: iS ).
thf(func_def_12,type,
sK6: ( iS > $o ) > iS ).
thf(func_def_13,type,
sK7: ( iS > $o ) > iS ).
thf(f57,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f33,f38,f48,f54,f56]) ).
thf(f56,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f55]) ).
thf(f55,plain,
( $false
| ~ spl8_1 ),
inference(subsumption_resolution,[status(thm)],[f24,f15]) ).
thf(f15,plain,
! [X10: iS,X11: iS] :
( c0
!= ( cP @ X11 @ X10 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( c0
= ( cP @ sK0 @ sK1 ) )
| ( ( ( cP @ sK3 @ sK5 )
= ( cP @ sK4 @ sK2 ) )
& ( ( sK5 != sK2 )
| ( sK3 != sK4 ) ) ) )
& ! [X6: iS > $o] :
( ( ( ( X6 @ ( sK7 @ X6 ) )
= $true )
& ( $true
= ( X6 @ ( sK6 @ X6 ) ) )
& ( ( X6 @ ( cP @ ( sK7 @ X6 ) @ ( sK6 @ X6 ) ) )
!= $true ) )
| ( $true
!= ( X6 @ c0 ) )
| ! [X9: iS] :
( $true
= ( X6 @ X9 ) ) )
& ! [X10: iS,X11: iS] :
( c0
!= ( cP @ X11 @ X10 ) )
& ! [X12: iS,X13: iS,X14: iS,X15: iS] :
( ( ( X12 = X15 )
& ( X13 = X14 ) )
| ( ( cP @ X15 @ X14 )
!= ( cP @ X12 @ X13 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
=> ( c0
= ( cP @ sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: iS,X3: iS,X4: iS,X5: iS] :
( ( ( cP @ X4 @ X2 )
= ( cP @ X3 @ X5 ) )
& ( ( X2 != X5 )
| ( X3 != X4 ) ) )
=> ( ( ( cP @ sK3 @ sK5 )
= ( cP @ sK4 @ sK2 ) )
& ( ( sK5 != sK2 )
| ( sK3 != sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X6: iS > $o] :
( ? [X7: iS,X8: iS] :
( ( $true
= ( X6 @ X8 ) )
& ( $true
= ( X6 @ X7 ) )
& ( $true
!= ( X6 @ ( cP @ X8 @ X7 ) ) ) )
=> ( ( ( X6 @ ( sK7 @ X6 ) )
= $true )
& ( $true
= ( X6 @ ( sK6 @ X6 ) ) )
& ( ( X6 @ ( cP @ ( sK7 @ X6 ) @ ( sK6 @ X6 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ? [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
= c0 )
| ? [X2: iS,X3: iS,X4: iS,X5: iS] :
( ( ( cP @ X4 @ X2 )
= ( cP @ X3 @ X5 ) )
& ( ( X2 != X5 )
| ( X3 != X4 ) ) ) )
& ! [X6: iS > $o] :
( ? [X7: iS,X8: iS] :
( ( $true
= ( X6 @ X8 ) )
& ( $true
= ( X6 @ X7 ) )
& ( $true
!= ( X6 @ ( cP @ X8 @ X7 ) ) ) )
| ( $true
!= ( X6 @ c0 ) )
| ! [X9: iS] :
( $true
= ( X6 @ X9 ) ) )
& ! [X10: iS,X11: iS] :
( c0
!= ( cP @ X11 @ X10 ) )
& ! [X12: iS,X13: iS,X14: iS,X15: iS] :
( ( ( X12 = X15 )
& ( X13 = X14 ) )
| ( ( cP @ X15 @ X14 )
!= ( cP @ X12 @ X13 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ? [X15: iS,X14: iS] :
( c0
= ( cP @ X15 @ X14 ) )
| ? [X13: iS,X12: iS,X11: iS,X10: iS] :
( ( ( cP @ X12 @ X10 )
= ( cP @ X11 @ X13 ) )
& ( ( X10 != X13 )
| ( X11 != X12 ) ) ) )
& ! [X0: iS > $o] :
( ? [X1: iS,X2: iS] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X1 ) )
& ( $true
!= ( X0 @ ( cP @ X2 @ X1 ) ) ) )
| ( $true
!= ( X0 @ c0 ) )
| ! [X3: iS] :
( ( X0 @ X3 )
= $true ) )
& ! [X9: iS,X8: iS] :
( c0
!= ( cP @ X8 @ X9 ) )
& ! [X7: iS,X6: iS,X4: iS,X5: iS] :
( ( ( X5 = X7 )
& ( X4 = X6 ) )
| ( ( cP @ X7 @ X6 )
!= ( cP @ X5 @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X15: iS,X14: iS] :
( c0
= ( cP @ X15 @ X14 ) )
| ? [X13: iS,X12: iS,X11: iS,X10: iS] :
( ( ( cP @ X12 @ X10 )
= ( cP @ X11 @ X13 ) )
& ( ( X10 != X13 )
| ( X11 != X12 ) ) ) )
& ! [X0: iS > $o] :
( ! [X3: iS] :
( ( X0 @ X3 )
= $true )
| ? [X1: iS,X2: iS] :
( ( $true
!= ( X0 @ ( cP @ X2 @ X1 ) ) )
& ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
| ( $true
!= ( X0 @ c0 ) ) )
& ! [X9: iS,X8: iS] :
( c0
!= ( cP @ X8 @ X9 ) )
& ! [X7: iS,X6: iS,X4: iS,X5: iS] :
( ( ( X5 = X7 )
& ( X4 = X6 ) )
| ( ( cP @ X7 @ X6 )
!= ( cP @ X5 @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: iS > $o] :
( ( ! [X1: iS,X2: iS] :
( ( ( $true
= ( X0 @ X1 ) )
& ( $true
= ( X0 @ X2 ) ) )
=> ( $true
= ( X0 @ ( cP @ X2 @ X1 ) ) ) )
& ( $true
= ( X0 @ c0 ) ) )
=> ! [X3: iS] :
( ( X0 @ X3 )
= $true ) )
& ! [X9: iS,X8: iS] :
( c0
!= ( cP @ X8 @ X9 ) )
& ! [X5: iS,X6: iS,X7: iS,X4: iS] :
( ( ( cP @ X7 @ X6 )
= ( cP @ X5 @ X4 ) )
=> ( ( X5 = X7 )
& ( X4 = X6 ) ) ) )
=> ( ! [X13: iS,X12: iS,X11: iS,X10: iS] :
( ( ( cP @ X12 @ X10 )
= ( cP @ X11 @ X13 ) )
=> ( ( X11 = X12 )
& ( X10 = X13 ) ) )
& ! [X14: iS,X15: iS] :
( c0
!= ( cP @ X15 @ X14 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: iS > $o] :
( ( ( X0 @ c0 )
& ! [X1: iS,X2: iS] :
( ( ( X0 @ X2 )
& ( X0 @ X1 ) )
=> ( X0 @ ( cP @ X2 @ X1 ) ) ) )
=> ! [X3: iS] : ( X0 @ X3 ) )
& ! [X4: iS,X5: iS,X6: iS,X7: iS] :
( ( ( cP @ X7 @ X6 )
= ( cP @ X5 @ X4 ) )
=> ( ( X5 = X7 )
& ( X4 = X6 ) ) )
& ! [X8: iS,X9: iS] :
( c0
!= ( cP @ X8 @ X9 ) ) )
=> ( ! [X10: iS,X11: iS,X12: iS,X13: iS] :
( ( ( cP @ X12 @ X10 )
= ( cP @ X11 @ X13 ) )
=> ( ( X10 = X13 )
& ( X11 = X12 ) ) )
& ! [X14: iS,X15: iS] :
( c0
!= ( cP @ X15 @ X14 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X1: iS,X0: iS] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X2: iS,X0: iS,X3: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ! [X2: iS,X1: iS,X0: iS,X3: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X1: iS,X0: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X4: iS > $o] :
( ( ( X4 @ c0 )
& ! [X1: iS,X0: iS] :
( ( ( X4 @ X0 )
& ( X4 @ X1 ) )
=> ( X4 @ ( cP @ X0 @ X1 ) ) ) )
=> ! [X0: iS] : ( X4 @ X0 ) )
& ! [X2: iS,X0: iS,X3: iS,X1: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X0 = X1 )
& ( X2 = X3 ) ) )
& ! [X0: iS,X1: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) )
=> ( ! [X2: iS,X1: iS,X0: iS,X3: iS] :
( ( ( cP @ X0 @ X2 )
= ( cP @ X1 @ X3 ) )
=> ( ( X2 = X3 )
& ( X0 = X1 ) ) )
& ! [X1: iS,X0: iS] :
( ( cP @ X0 @ X1 )
!= c0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BtQTpPCvVn/DTF2THF_28822.p',cS_ALG02_pme) ).
thf(f24,plain,
( ( c0
= ( cP @ sK0 @ sK1 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl8_1
<=> ( c0
= ( cP @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f54,plain,
( spl8_2
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f53]) ).
thf(f53,plain,
( $false
| spl8_2
| ~ spl8_4 ),
inference(subsumption_resolution,[status(thm)],[f52,f28]) ).
thf(f28,plain,
( ( sK3 != sK4 )
| spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl8_2
<=> ( sK3 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f52,plain,
( ( sK3 = sK4 )
| ~ spl8_4 ),
inference(equality_resolution,[status(thm)],[f44]) ).
thf(f44,plain,
( ! [X0: iS,X1: iS] :
( ( ( cP @ X0 @ X1 )
!= ( cP @ sK3 @ sK5 ) )
| ( sK4 = X0 ) )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f14,f37]) ).
thf(f37,plain,
( ( ( cP @ sK3 @ sK5 )
= ( cP @ sK4 @ sK2 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl8_4
<=> ( ( cP @ sK3 @ sK5 )
= ( cP @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f14,plain,
! [X14: iS,X15: iS,X12: iS,X13: iS] :
( ( ( cP @ X15 @ X14 )
!= ( cP @ X12 @ X13 ) )
| ( X12 = X15 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f48,plain,
( spl8_3
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f47,f35,f30]) ).
thf(f30,definition,
( spl8_3
<=> ( sK5 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f47,plain,
( ( sK5 = sK2 )
| ~ spl8_4 ),
inference(equality_resolution,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: iS,X1: iS] :
( ( ( cP @ X0 @ X1 )
!= ( cP @ sK3 @ sK5 ) )
| ( sK2 = X1 ) )
| ~ spl8_4 ),
inference(superposition,[status(thm)],[f13,f37]) ).
thf(f13,plain,
! [X14: iS,X15: iS,X12: iS,X13: iS] :
( ( ( cP @ X15 @ X14 )
!= ( cP @ X12 @ X13 ) )
| ( X13 = X14 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f38,plain,
( spl8_1
| spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f20,f35,f22]) ).
thf(f20,plain,
( ( ( cP @ sK3 @ sK5 )
= ( cP @ sK4 @ sK2 ) )
| ( c0
= ( cP @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f33,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f19,f30,f26,f22]) ).
thf(f19,plain,
( ( c0
= ( cP @ sK0 @ sK1 ) )
| ( sK5 != sK2 )
| ( sK3 != sK4 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV197^5 : 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
% 0.15/0.34 % Computer : n003.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:41:40 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV197^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.46 % Domain : Set Theory (Sets of sets)
% 0.29/0.46 % Problem : TPS problem from S-THMS
% 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_1096 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 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
% 0.29/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.46 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 8 ( 8 avg)
% 0.29/0.46 % Number of connectives : 33 ( 2 ~; 0 |; 7 &; 19 @)
% 0.29/0.46 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 13 ( 13 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 2 usr; 1 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 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 %------------------------------------------------------------------------------
% 0.29/0.46 thf(iS_type,type,
% 0.29/0.46 iS: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(c0,type,
% 0.29/0.46 c0: iS ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: iS > iS > iS ).
% 0.29/0.46
% 0.29/0.46 thf(cS_ALG02_pme,conjecture,
% 0.29/0.46 ( ( ! [Xx: iS,Xy: iS] :
% 0.29/0.46 ( ( cP @ Xx @ Xy )
% 0.29/0.46 != c0 )
% 0.29/0.46 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 0.29/0.46 ( ( ( cP @ Xx @ Xu )
% 0.29/0.46 = ( cP @ Xy @ Xv ) )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 & ( Xu = Xv ) ) )
% 0.29/0.46 & ! [X: iS > $o] :
% 0.29/0.46 ( ( ( X @ c0 )
% 0.29/0.46 & ! [Xx: iS,Xy: iS] :
% 0.29/0.46 ( ( ( X @ Xx )
% 0.29/0.46 & ( X @ Xy ) )
% 0.29/0.46 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 0.29/0.46 => ! [Xx: iS] : ( X @ Xx ) ) )
% 0.29/0.46 => ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 0.29/0.46 ( ( ( cP @ Xx @ Xu )
% 0.29/0.46 = ( cP @ Xy @ Xv ) )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 & ( Xu = Xv ) ) )
% 0.29/0.46 & ! [Xx: iS,Xy: iS] :
% 0.29/0.46 ( ( cP @ Xx @ Xy )
% 0.29/0.46 != c0 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.65/1.31 ---- Embedded in THF ---
% 1.65/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.65/1.32 %%% Generated on Tue Feb 24 12:41:41 EST 2026
% 1.65/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.65/1.32 %%% Logic specification used:
% 1.65/1.32 %%% thf(spec, logic, $$dhol).
% 1.65/1.32
% 1.65/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BtQTpPCvVn/DTF2DTF28822.p
% See solution above
% 1.65/1.32 ------------------------
% 1.65/1.32 ---- Cleaned THF ---
% 1.65/1.33 thf(iS_type,type,
% 1.65/1.33 iS: $tType ).
% 1.65/1.33
% 1.65/1.33 thf(c0,type,
% 1.65/1.33 c0: iS ).
% 1.65/1.33
% 1.65/1.33 thf(cP,type,
% 1.65/1.33 cP: iS > iS > iS ).
% 1.65/1.33
% 1.65/1.33 thf(cS_ALG02_pme,conjecture,
% 1.65/1.33 ( ( ! [Xx: iS,Xy: iS] :
% 1.65/1.33 ( ( cP @ Xx @ Xy )
% 1.65/1.33 != c0 )
% 1.65/1.33 & ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 1.65/1.33 ( ( ( cP @ Xx @ Xu )
% 1.65/1.33 = ( cP @ Xy @ Xv ) )
% 1.65/1.33 => ( ( Xx = Xy )
% 1.65/1.33 & ( Xu = Xv ) ) )
% 1.65/1.33 & ! [X: iS > $o] :
% 1.65/1.33 ( ( ( X @ c0 )
% 1.65/1.33 & ! [Xx: iS,Xy: iS] :
% 1.65/1.33 ( ( ( X @ Xx )
% 1.65/1.33 & ( X @ Xy ) )
% 1.65/1.33 => ( X @ ( cP @ Xx @ Xy ) ) ) )
% 1.65/1.33 => ! [Xx: iS] : ( X @ Xx ) ) )
% 1.65/1.33 => ( ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
% 1.65/1.33 ( ( ( cP @ Xx @ Xu )
% 1.65/1.33 = ( cP @ Xy @ Xv ) )
% 1.65/1.33 => ( ( Xx = Xy )
% 1.65/1.33 & ( Xu = Xv ) ) )
% 1.65/1.33 & ! [Xx: iS,Xy: iS] :
% 1.65/1.33 ( ( cP @ Xx @ Xy )
% 1.65/1.33 != c0 ) ) ) ).
% 1.65/1.33 ------------------------
% 1.65/1.34 % (29017)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28822 for (2999ds/183Mi)
% 1.65/1.34 % (29020)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28822 for (2999ds/2Mi)
% 1.65/1.34 % (29018)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_28822 for (2999ds/4Mi)
% 1.65/1.34 % (29020)Instruction limit reached!
% 1.65/1.34 % (29020)------------------------------
% 1.65/1.34 % (29020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (29020)Termination reason: Unknown
% 1.65/1.34 % (29020)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (29020)Memory used [KB]: 5500
% 1.65/1.34 % (29020)Time elapsed: 0.003 s
% 1.65/1.34 % (29020)Instructions burned: 3 (million)
% 1.65/1.34 % (29020)------------------------------
% 1.65/1.34 % (29020)------------------------------
% 1.65/1.35 % (29017)First to succeed.
% 1.65/1.35 % (29018)Instruction limit reached!
% 1.65/1.35 % (29018)------------------------------
% 1.65/1.35 % (29018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (29018)Termination reason: Unknown
% 1.65/1.35 % (29018)Termination phase: Saturation
% 1.65/1.35
% 1.65/1.35 % (29018)Memory used [KB]: 5500
% 1.65/1.35 % (29018)Time elapsed: 0.004 s
% 1.65/1.35 % (29018)Instructions burned: 4 (million)
% 1.65/1.35 % (29018)------------------------------
% 1.65/1.35 % (29018)------------------------------
% 1.65/1.35 % (29017)Refutation found. Thanks to Tanya!
% 1.65/1.35 % SZS status Theorem for DTF2THF_28822
% 1.65/1.35 % SZS output start Proof for DTF2THF_28822
% 1.65/1.35 thf(type_def_5, type, iS: $tType).
% 1.65/1.35 thf(func_def_0, type, iS: $tType).
% 1.65/1.35 thf(func_def_1, type, c0: iS).
% 1.65/1.35 thf(func_def_2, type, cP: iS > iS > iS).
% 1.65/1.35 thf(func_def_6, type, sK0: iS).
% 1.65/1.35 thf(func_def_7, type, sK1: iS).
% 1.65/1.35 thf(func_def_8, type, sK2: iS).
% 1.65/1.35 thf(func_def_9, type, sK3: iS).
% 1.65/1.35 thf(func_def_10, type, sK4: iS).
% 1.65/1.35 thf(func_def_11, type, sK5: iS).
% 1.65/1.35 thf(func_def_12, type, sK6: (iS > $o) > iS).
% 1.65/1.35 thf(func_def_13, type, sK7: (iS > $o) > iS).
% 1.65/1.35 thf(f57,plain,(
% 1.65/1.35 $false),
% 1.65/1.35 inference(avatar_sat_refutation,[status(thm)],[f33,f38,f48,f54,f56])).
% 1.65/1.35 thf(f56,plain,(
% 1.65/1.35 ~spl8_1),
% 1.65/1.35 inference(avatar_contradiction_clause,[status(thm)],[f55])).
% 1.65/1.35 thf(f55,plain,(
% 1.65/1.35 $false | ~spl8_1),
% 1.65/1.35 inference(subsumption_resolution,[status(thm)],[f24,f15])).
% 1.65/1.35 thf(f15,plain,(
% 1.65/1.35 ( ! [X10 : iS,X11 : iS] : ((c0 != (cP @ X11 @ X10))) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.35 thf(f12,plain,(
% 1.65/1.35 ((c0 = (cP @ sK0 @ sK1)) | (((cP @ sK3 @ sK5) = (cP @ sK4 @ sK2)) & ((sK5 != sK2) | (sK3 != sK4)))) & ! [X6 : iS > $o] : ((((X6 @ (sK7 @ X6)) = $true) & ($true = (X6 @ (sK6 @ X6))) & ((X6 @ (cP @ (sK7 @ X6) @ (sK6 @ X6))) != $true)) | ($true != (X6 @ c0)) | ! [X9 : iS] : ($true = (X6 @ X9))) & ! [X10 : iS,X11 : iS] : (c0 != (cP @ X11 @ X10)) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X12 = X15) & (X13 = X14)) | ((cP @ X15 @ X14) != (cP @ X12 @ X13)))),
% 1.65/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f8,f11,f10,f9])).
% 1.65/1.35 thf(f9,plain,(
% 1.65/1.35 ? [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) = c0) => (c0 = (cP @ sK0 @ sK1))),
% 1.65/1.35 introduced(definition,[],[choice_axiom])).
% 1.65/1.35 thf(f10,plain,(
% 1.65/1.35 ? [X2 : iS,X3 : iS,X4 : iS,X5 : iS] : (((cP @ X4 @ X2) = (cP @ X3 @ X5)) & ((X2 != X5) | (X3 != X4))) => (((cP @ sK3 @ sK5) = (cP @ sK4 @ sK2)) & ((sK5 != sK2) | (sK3 != sK4)))),
% 1.65/1.35 introduced(definition,[],[choice_axiom])).
% 1.65/1.35 thf(f11,plain,(
% 1.65/1.35 ! [X6 : iS > $o] : (? [X7 : iS,X8 : iS] : (($true = (X6 @ X8)) & ($true = (X6 @ X7)) & ($true != (X6 @ (cP @ X8 @ X7)))) => (((X6 @ (sK7 @ X6)) = $true) & ($true = (X6 @ (sK6 @ X6))) & ((X6 @ (cP @ (sK7 @ X6) @ (sK6 @ X6))) != $true)))),
% 1.65/1.35 introduced(definition,[],[choice_axiom])).
% 1.65/1.35 thf(f8,plain,(
% 1.65/1.35 (? [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) = c0) | ? [X2 : iS,X3 : iS,X4 : iS,X5 : iS] : (((cP @ X4 @ X2) = (cP @ X3 @ X5)) & ((X2 != X5) | (X3 != X4)))) & ! [X6 : iS > $o] : (? [X7 : iS,X8 : iS] : (($true = (X6 @ X8)) & ($true = (X6 @ X7)) & ($true != (X6 @ (cP @ X8 @ X7)))) | ($true != (X6 @ c0)) | ! [X9 : iS] : ($true = (X6 @ X9))) & ! [X10 : iS,X11 : iS] : (c0 != (cP @ X11 @ X10)) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X12 = X15) & (X13 = X14)) | ((cP @ X15 @ X14) != (cP @ X12 @ X13)))),
% 1.65/1.35 inference(rectify,[status(thm)],[f7])).
% 1.65/1.35 thf(f7,plain,(
% 1.65/1.35 (? [X15 : iS,X14 : iS] : (c0 = (cP @ X15 @ X14)) | ? [X13 : iS,X12 : iS,X11 : iS,X10 : iS] : (((cP @ X12 @ X10) = (cP @ X11 @ X13)) & ((X10 != X13) | (X11 != X12)))) & ! [X0 : iS > $o] : (? [X1 : iS,X2 : iS] : (($true = (X0 @ X2)) & ($true = (X0 @ X1)) & ($true != (X0 @ (cP @ X2 @ X1)))) | ($true != (X0 @ c0)) | ! [X3 : iS] : ((X0 @ X3) = $true)) & ! [X9 : iS,X8 : iS] : (c0 != (cP @ X8 @ X9)) & ! [X7 : iS,X6 : iS,X4 : iS,X5 : iS] : (((X5 = X7) & (X4 = X6)) | ((cP @ X7 @ X6) != (cP @ X5 @ X4)))),
% 1.65/1.35 inference(flattening,[status(thm)],[f6])).
% 1.65/1.35 thf(f6,plain,(
% 1.65/1.35 (? [X15 : iS,X14 : iS] : (c0 = (cP @ X15 @ X14)) | ? [X13 : iS,X12 : iS,X11 : iS,X10 : iS] : (((cP @ X12 @ X10) = (cP @ X11 @ X13)) & ((X10 != X13) | (X11 != X12)))) & (! [X0 : iS > $o] : (! [X3 : iS] : ((X0 @ X3) = $true) | (? [X1 : iS,X2 : iS] : (($true != (X0 @ (cP @ X2 @ X1))) & (($true = (X0 @ X1)) & ($true = (X0 @ X2)))) | ($true != (X0 @ c0)))) & ! [X9 : iS,X8 : iS] : (c0 != (cP @ X8 @ X9)) & ! [X7 : iS,X6 : iS,X4 : iS,X5 : iS] : (((X5 = X7) & (X4 = X6)) | ((cP @ X7 @ X6) != (cP @ X5 @ X4))))),
% 1.65/1.35 inference(ennf_transformation,[status(thm)],[f5])).
% 1.65/1.35 thf(f5,plain,(
% 1.65/1.35 ~((! [X0 : iS > $o] : ((! [X1 : iS,X2 : iS] : ((($true = (X0 @ X1)) & ($true = (X0 @ X2))) => ($true = (X0 @ (cP @ X2 @ X1)))) & ($true = (X0 @ c0))) => ! [X3 : iS] : ((X0 @ X3) = $true)) & ! [X9 : iS,X8 : iS] : (c0 != (cP @ X8 @ X9)) & ! [X5 : iS,X6 : iS,X7 : iS,X4 : iS] : (((cP @ X7 @ X6) = (cP @ X5 @ X4)) => ((X5 = X7) & (X4 = X6)))) => (! [X13 : iS,X12 : iS,X11 : iS,X10 : iS] : (((cP @ X12 @ X10) = (cP @ X11 @ X13)) => ((X11 = X12) & (X10 = X13))) & ! [X14 : iS,X15 : iS] : (c0 != (cP @ X15 @ X14))))),
% 1.65/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.65/1.35 thf(f4,plain,(
% 1.65/1.35 ~((! [X0 : iS > $o] : (((X0 @ c0) & ! [X1 : iS,X2 : iS] : (((X0 @ X2) & (X0 @ X1)) => (X0 @ (cP @ X2 @ X1)))) => ! [X3 : iS] : (X0 @ X3)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((cP @ X7 @ X6) = (cP @ X5 @ X4)) => ((X5 = X7) & (X4 = X6))) & ! [X8 : iS,X9 : iS] : (c0 != (cP @ X8 @ X9))) => (! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : (((cP @ X12 @ X10) = (cP @ X11 @ X13)) => ((X10 = X13) & (X11 = X12))) & ! [X14 : iS,X15 : iS] : (c0 != (cP @ X15 @ X14))))),
% 1.65/1.35 inference(rectify,[status(thm)],[f2])).
% 1.65/1.35 thf(f2,negated_conjecture,(
% 1.65/1.35 ~((! [X4 : iS > $o] : (((X4 @ c0) & ! [X1 : iS,X0 : iS] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : iS] : (X4 @ X0)) & ! [X2 : iS,X0 : iS,X3 : iS,X1 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X0 = X1) & (X2 = X3))) & ! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0)) => (! [X2 : iS,X1 : iS,X0 : iS,X3 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X1 : iS,X0 : iS] : ((cP @ X0 @ X1) != c0)))),
% 1.65/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.35 thf(f1,conjecture,(
% 1.65/1.35 (! [X4 : iS > $o] : (((X4 @ c0) & ! [X1 : iS,X0 : iS] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1)))) => ! [X0 : iS] : (X4 @ X0)) & ! [X2 : iS,X0 : iS,X3 : iS,X1 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X0 = X1) & (X2 = X3))) & ! [X0 : iS,X1 : iS] : ((cP @ X0 @ X1) != c0)) => (! [X2 : iS,X1 : iS,X0 : iS,X3 : iS] : (((cP @ X0 @ X2) = (cP @ X1 @ X3)) => ((X2 = X3) & (X0 = X1))) & ! [X1 : iS,X0 : iS] : ((cP @ X0 @ X1) != c0))),
% 1.65/1.35 file('/export/starexec/sandbox/tmp/tmp.BtQTpPCvVn/DTF2THF_28822.p',cS_ALG02_pme)).
% 1.65/1.35 thf(f24,plain,(
% 1.65/1.35 (c0 = (cP @ sK0 @ sK1)) | ~spl8_1),
% 1.65/1.35 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.65/1.35 thf(f22,definition,(
% 1.65/1.35 spl8_1 <=> (c0 = (cP @ sK0 @ sK1))),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.65/1.35 thf(f54,plain,(
% 1.65/1.35 spl8_2 | ~spl8_4),
% 1.65/1.35 inference(avatar_contradiction_clause,[status(thm)],[f53])).
% 1.65/1.35 thf(f53,plain,(
% 1.65/1.35 $false | (spl8_2 | ~spl8_4)),
% 1.65/1.35 inference(subsumption_resolution,[status(thm)],[f52,f28])).
% 1.65/1.35 thf(f28,plain,(
% 1.65/1.35 (sK3 != sK4) | spl8_2),
% 1.65/1.35 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.65/1.35 thf(f26,definition,(
% 1.65/1.35 spl8_2 <=> (sK3 = sK4)),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.65/1.35 thf(f52,plain,(
% 1.65/1.35 (sK3 = sK4) | ~spl8_4),
% 1.65/1.35 inference(equality_resolution,[status(thm)],[f44])).
% 1.65/1.35 thf(f44,plain,(
% 1.65/1.35 ( ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1) != (cP @ sK3 @ sK5)) | (sK4 = X0)) ) | ~spl8_4),
% 1.65/1.35 inference(superposition,[status(thm)],[f14,f37])).
% 1.65/1.35 thf(f37,plain,(
% 1.65/1.35 ((cP @ sK3 @ sK5) = (cP @ sK4 @ sK2)) | ~spl8_4),
% 1.65/1.35 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.65/1.35 thf(f35,definition,(
% 1.65/1.35 spl8_4 <=> ((cP @ sK3 @ sK5) = (cP @ sK4 @ sK2))),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.65/1.35 thf(f14,plain,(
% 1.65/1.35 ( ! [X14 : iS,X15 : iS,X12 : iS,X13 : iS] : (((cP @ X15 @ X14) != (cP @ X12 @ X13)) | (X12 = X15)) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.35 thf(f48,plain,(
% 1.65/1.35 spl8_3 | ~spl8_4),
% 1.65/1.35 inference(avatar_split_clause,[status(thm)],[f47,f35,f30])).
% 1.65/1.35 thf(f30,definition,(
% 1.65/1.35 spl8_3 <=> (sK5 = sK2)),
% 1.65/1.35 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.65/1.35 thf(f47,plain,(
% 1.65/1.35 (sK5 = sK2) | ~spl8_4),
% 1.65/1.35 inference(equality_resolution,[status(thm)],[f41])).
% 1.65/1.35 thf(f41,plain,(
% 1.65/1.35 ( ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1) != (cP @ sK3 @ sK5)) | (sK2 = X1)) ) | ~spl8_4),
% 1.65/1.35 inference(superposition,[status(thm)],[f13,f37])).
% 1.65/1.35 thf(f13,plain,(
% 1.65/1.35 ( ! [X14 : iS,X15 : iS,X12 : iS,X13 : iS] : (((cP @ X15 @ X14) != (cP @ X12 @ X13)) | (X13 = X14)) )),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.35 thf(f38,plain,(
% 1.65/1.35 spl8_1 | spl8_4),
% 1.65/1.35 inference(avatar_split_clause,[status(thm)],[f20,f35,f22])).
% 1.65/1.35 thf(f20,plain,(
% 1.65/1.35 ((cP @ sK3 @ sK5) = (cP @ sK4 @ sK2)) | (c0 = (cP @ sK0 @ sK1))),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.35 thf(f33,plain,(
% 1.65/1.35 spl8_1 | ~spl8_2 | ~spl8_3),
% 1.65/1.35 inference(avatar_split_clause,[status(thm)],[f19,f30,f26,f22])).
% 1.65/1.35 thf(f19,plain,(
% 1.65/1.35 (c0 = (cP @ sK0 @ sK1)) | (sK5 != sK2) | (sK3 != sK4)),
% 1.65/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.35 % SZS output end Proof for DTF2THF_28822
% 1.65/1.35 % (29017)------------------------------
% 1.65/1.35 % (29017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (29017)Termination reason: Refutation
% 1.65/1.35
% 1.65/1.35 % (29017)Memory used [KB]: 5500
% 1.65/1.35 % (29017)Time elapsed: 0.006 s
% 1.65/1.35 % (29017)Instructions burned: 4 (million)
% 1.65/1.35 % (29017)------------------------------
% 1.65/1.35 % (29017)------------------------------
% 1.65/1.35 % (29015)Success in time 0.005 s
%------------------------------------------------------------------------------