%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV196^5 : 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 : n025.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 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 135 equ; 0 cnn)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 551 ( 81 ~; 68 |; 49 &; 342 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 12 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-3 aty)
% Number of variables : 140 ( 0 ^; 107 !; 33 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
y: a ).
thf(func_def_2,type,
x: a ).
thf(func_def_3,type,
cP: a > a > a ).
thf(func_def_4,type,
c0: a ).
thf(func_def_8,type,
sK0: a > a > a > $o ).
thf(f25,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f24,f18]) ).
thf(f18,plain,
! [X2: a] :
( ( sK0 @ X2 @ c0 @ X2 )
= $true ),
inference(equality_resolution,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: a,X1: a] :
( ( X1 != X2 )
| ( $true
= ( sK0 @ X2 @ c0 @ X1 ) ) ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: a,X3: a,X1: a] :
( ( c0 != X3 )
| ( X1 != X2 )
| ( ( sK0 @ X2 @ X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( sK0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ( ( c0 != X2 )
| ( X1 != X3 ) )
& ( ( c0 != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X5 @ X4 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 ) ) )
| ( ( sK0 @ X2 @ X3 @ X1 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > a > a > $o] :
( ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ( ( c0 != X2 )
| ( X1 != X3 ) )
& ( ( c0 != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( X0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( X0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X5 @ X4 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 ) ) )
| ( ( X0 @ X2 @ X3 @ X1 )
= $true ) ) )
=> ( ( ( sK0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true )
& ! [X3: a,X2: a,X1: a] :
( ( ( ( c0 != X2 )
| ( X1 != X3 ) )
& ( ( c0 != X3 )
| ( X1 != X2 ) )
& ! [X9: a,X8: a,X7: a,X6: a,X5: a,X4: a] :
( ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X5 @ X4 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 ) ) )
| ( ( sK0 @ X2 @ X3 @ X1 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > a > $o] :
( ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true )
& ! [X1: a,X2: a,X3: a] :
( ( ( ( c0 != X2 )
| ( X1 != X3 ) )
& ( ( c0 != X3 )
| ( X1 != X2 ) )
& ! [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( ( X0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( X0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X5 @ X4 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 ) ) )
| ( ( X0 @ X2 @ X3 @ X1 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > a > $o] :
( ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true )
& ! [X3: a,X1: a,X2: a] :
( ( ( ( c0 != X1 )
| ( X2 != X3 ) )
& ( ( c0 != X2 )
| ( X1 != X3 ) )
& ! [X8: a,X6: a,X7: a,X9: a,X5: a,X4: a] :
( ( ( X0 @ X6 @ X4 @ X7 )
!= $true )
| ( ( X0 @ X8 @ X5 @ X9 )
!= $true )
| ( ( cP @ X6 @ X8 )
!= X1 )
| ( ( cP @ X7 @ X9 )
!= X3 )
| ( ( cP @ X4 @ X5 )
!= X2 ) ) )
| ( ( X0 @ X1 @ X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > a > a > $o] :
( ! [X2: a,X1: a,X3: a] :
( ( ( ( c0 = X1 )
& ( X2 = X3 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ? [X5: a,X9: a,X7: a,X4: a,X8: a,X6: a] :
( ( ( cP @ X7 @ X9 )
= X3 )
& ( ( X0 @ X8 @ X5 @ X9 )
= $true )
& ( ( cP @ X6 @ X8 )
= X1 )
& ( ( cP @ X4 @ X5 )
= X2 )
& ( ( X0 @ X6 @ X4 @ X7 )
= $true ) ) )
=> ( ( X0 @ X1 @ X2 @ X3 )
= $true ) )
=> ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X2: a,X1: a,X3: a] :
( ( ( ( c0 = X1 )
& ( X2 = X3 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) )
| ? [X5: a,X9: a,X7: a,X4: a,X8: a,X6: a] :
( ( ( cP @ X7 @ X9 )
= X3 )
& ( ( X0 @ X8 @ X5 @ X9 )
= $true )
& ( ( cP @ X6 @ X8 )
= X1 )
& ( ( cP @ X4 @ X5 )
= X2 )
& ( ( X0 @ X6 @ X4 @ X7 )
= $true ) ) )
=> ( ( X0 @ X1 @ X2 @ X3 )
= $true ) )
& $true )
=> ( ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ? [X4: a,X5: a,X6: a,X7: a,X8: a,X9: a] :
( ( X0 @ X6 @ X4 @ X7 )
& ( ( cP @ X4 @ X5 )
= X2 )
& ( X0 @ X8 @ X5 @ X9 )
& ( ( cP @ X6 @ X8 )
= X1 )
& ( ( cP @ X7 @ X9 )
= X3 ) )
| ( ( X2 = X3 )
& ( c0 = X1 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ? [X6: a,X7: a,X4: a,X8: a,X5: a,X9: a] :
( ( X0 @ X4 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X2 )
& ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X4 @ X5 )
= X1 )
& ( ( cP @ X8 @ X9 )
= X3 ) )
| ( ( X2 = X3 )
& ( c0 = X1 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > a > $o] :
( ( ! [X1: a,X2: a,X3: a] :
( ( ? [X6: a,X7: a,X4: a,X8: a,X5: a,X9: a] :
( ( X0 @ X4 @ X6 @ X8 )
& ( ( cP @ X6 @ X7 )
= X2 )
& ( X0 @ X5 @ X7 @ X9 )
& ( ( cP @ X4 @ X5 )
= X1 )
& ( ( cP @ X8 @ X9 )
= X3 ) )
| ( ( X2 = X3 )
& ( c0 = X1 ) )
| ( ( c0 = X2 )
& ( X1 = X3 ) ) )
=> ( X0 @ X1 @ X2 @ X3 ) )
& $true )
=> ( X0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dxINkJ9hSk/DTF2THF_31230.p',cS_JOIN_LEM2_pme) ).
thf(f24,plain,
( ( sK0 @ x @ c0 @ x )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f23,f16]) ).
thf(f16,plain,
! [X3: a] :
( ( sK0 @ c0 @ X3 @ X3 )
= $true ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X3: a,X1: a] :
( ( X1 != X3 )
| ( ( sK0 @ c0 @ X3 @ X1 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f13]) ).
thf(f13,plain,
! [X2: a,X3: a,X1: a] :
( ( c0 != X2 )
| ( X1 != X3 )
| ( ( sK0 @ X2 @ X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f23,plain,
( ( ( sK0 @ c0 @ y @ y )
!= $true )
| ( ( sK0 @ x @ c0 @ x )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( sK0 @ c0 @ y @ y )
!= $true )
| ( ( sK0 @ x @ c0 @ x )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f14,f21]) ).
thf(f21,plain,
! [X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ ( cP @ X5 @ X4 ) @ ( cP @ X9 @ X8 ) @ ( cP @ X6 @ X7 ) )
= $true )
| ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X3: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X9 @ X8 )
!= X3 )
| ( ( sK0 @ ( cP @ X5 @ X4 ) @ X3 @ ( cP @ X6 @ X7 ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f19]) ).
thf(f19,plain,
! [X3: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 )
| ( ( sK0 @ ( cP @ X5 @ X4 ) @ X3 @ X1 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: a,X3: a,X1: a,X8: a,X6: a,X9: a,X7: a,X4: a,X5: a] :
( ( ( sK0 @ X5 @ X9 @ X6 )
!= $true )
| ( ( sK0 @ X4 @ X8 @ X7 )
!= $true )
| ( ( cP @ X5 @ X4 )
!= X2 )
| ( ( cP @ X6 @ X7 )
!= X1 )
| ( ( cP @ X9 @ X8 )
!= X3 )
| ( ( sK0 @ X2 @ X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f14,plain,
( ( sK0 @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV196^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:41:57 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV196^5 : 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_1058 [Bro09]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.29/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.29/0.46 % Number of atoms : 8 ( 7 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 8 ( 8 avg)
% 0.29/0.46 % Number of connectives : 35 ( 0 ~; 2 |; 7 &; 24 @)
% 0.29/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 23 ( 23 avg)
% 0.29/0.46 % Number of types : 2 ( 1 usr)
% 0.29/0.46 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 10 ( 0 ^; 4 !; 6 ?; 10 :)
% 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(a_type,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(y,type,
% 0.29/0.46 y: a ).
% 0.29/0.46
% 0.29/0.46 thf(x,type,
% 0.29/0.46 x: a ).
% 0.29/0.46
% 0.29/0.46 thf(cP,type,
% 0.29/0.46 cP: a > a > a ).
% 0.29/0.46
% 0.29/0.46 thf(c0,type,
% 0.29/0.46 c0: a ).
% 0.29/0.46
% 0.29/0.46 thf(cS_JOIN_LEM2_pme,conjecture,
% 0.29/0.46 ! [R: a > a > a > $o] :
% 0.29/0.46 ( ( $true
% 0.29/0.46 & ! [Xa: a,Xb: a,Xc: a] :
% 0.29/0.46 ( ( ( ( Xa = c0 )
% 0.29/0.46 & ( Xb = Xc ) )
% 0.29/0.46 | ( ( Xb = c0 )
% 0.29/0.46 & ( Xa = Xc ) )
% 0.29/0.46 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 0.29/0.46 ( ( Xa
% 0.29/0.46 = ( cP @ Xx1 @ Xx2 ) )
% 0.29/0.46 & ( Xb
% 0.29/0.46 = ( cP @ Xy1 @ Xy2 ) )
% 0.29/0.46 & ( Xc
% 0.29/0.46 = ( cP @ Xz1 @ Xz2 ) )
% 0.29/0.46 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.29/0.46 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.29/0.46 => ( R @ Xa @ Xb @ Xc ) ) )
% 0.29/0.46 => ( R @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.48/1.27 ---- Embedded in THF ---
% 1.48/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.27 %%% Generated on Tue Feb 24 12:41:58 EST 2026
% 1.48/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.27 %%% Logic specification used:
% 1.48/1.27 %%% thf(spec, logic, $$dhol).
% 1.48/1.27
% 1.48/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dxINkJ9hSk/DTF2DTF31230.p
% See solution above
% 1.48/1.27 ------------------------
% 1.48/1.28 ---- Cleaned THF ---
% 1.48/1.29 thf(a_type,type,
% 1.48/1.29 a: $tType ).
% 1.48/1.29
% 1.48/1.29 thf(y,type,
% 1.48/1.29 y: a ).
% 1.48/1.29
% 1.48/1.29 thf(x,type,
% 1.48/1.29 x: a ).
% 1.48/1.29
% 1.48/1.29 thf(cP,type,
% 1.48/1.29 cP: a > a > a ).
% 1.48/1.29
% 1.48/1.29 thf(c0,type,
% 1.48/1.29 c0: a ).
% 1.48/1.29
% 1.48/1.29 thf(cS_JOIN_LEM2_pme,conjecture,
% 1.48/1.29 ! [R: a > a > a > $o] :
% 1.48/1.29 ( ( $true
% 1.48/1.29 & ! [Xa: a,Xb: a,Xc: a] :
% 1.48/1.29 ( ( ( ( Xa = c0 )
% 1.48/1.29 & ( Xb = Xc ) )
% 1.48/1.29 | ( ( Xb = c0 )
% 1.48/1.29 & ( Xa = Xc ) )
% 1.48/1.29 | ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
% 1.48/1.29 ( ( Xa
% 1.48/1.29 = ( cP @ Xx1 @ Xx2 ) )
% 1.48/1.29 & ( Xb
% 1.48/1.29 = ( cP @ Xy1 @ Xy2 ) )
% 1.48/1.29 & ( Xc
% 1.48/1.29 = ( cP @ Xz1 @ Xz2 ) )
% 1.48/1.29 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 1.48/1.29 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 1.48/1.29 => ( R @ Xa @ Xb @ Xc ) ) )
% 1.48/1.29 => ( R @ ( cP @ x @ c0 ) @ ( cP @ c0 @ y ) @ ( cP @ x @ y ) ) ) ).
% 1.48/1.29 ------------------------
% 1.64/1.30 % (31517)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_31230 for (2999ds/275Mi)
% 1.64/1.30 % (31517)First to succeed.
% 1.64/1.30 % (31517)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_31230
% 1.64/1.30 % SZS output start Proof for DTF2THF_31230
% 1.64/1.30 thf(type_def_5, type, a: $tType).
% 1.64/1.30 thf(func_def_0, type, a: $tType).
% 1.64/1.30 thf(func_def_1, type, y: a).
% 1.64/1.30 thf(func_def_2, type, x: a).
% 1.64/1.30 thf(func_def_3, type, cP: a > a > a).
% 1.64/1.30 thf(func_def_4, type, c0: a).
% 1.64/1.30 thf(func_def_8, type, sK0: a > a > a > $o).
% 1.64/1.30 thf(f25,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(subsumption_resolution,[status(thm)],[f24,f18])).
% 1.64/1.30 thf(f18,plain,(
% 1.64/1.30 ( ! [X2 : a] : (((sK0 @ X2 @ c0 @ X2) = $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f17])).
% 1.64/1.30 thf(f17,plain,(
% 1.64/1.30 ( ! [X2 : a,X1 : a] : ((X1 != X2) | ($true = (sK0 @ X2 @ c0 @ X1))) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 ( ! [X2 : a,X3 : a,X1 : a] : ((c0 != X3) | (X1 != X2) | ((sK0 @ X2 @ X3 @ X1) = $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ((sK0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((((c0 != X2) | (X1 != X3)) & ((c0 != X3) | (X1 != X2)) & ! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true) | ((cP @ X5 @ X4) != X2) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3))) | ((sK0 @ X2 @ X3 @ X1) = $true))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 ? [X0 : a > a > a > $o] : (((X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((((c0 != X2) | (X1 != X3)) & ((c0 != X3) | (X1 != X2)) & ! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((X0 @ X5 @ X9 @ X6) != $true) | ((X0 @ X4 @ X8 @ X7) != $true) | ((cP @ X5 @ X4) != X2) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3))) | ((X0 @ X2 @ X3 @ X1) = $true))) => (((sK0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true) & ! [X3 : a,X2 : a,X1 : a] : ((((c0 != X2) | (X1 != X3)) & ((c0 != X3) | (X1 != X2)) & ! [X9 : a,X8 : a,X7 : a,X6 : a,X5 : a,X4 : a] : (((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true) | ((cP @ X5 @ X4) != X2) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3))) | ((sK0 @ X2 @ X3 @ X1) = $true)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f8,plain,(
% 1.64/1.30 ? [X0 : a > a > a > $o] : (((X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true) & ! [X1 : a,X2 : a,X3 : a] : ((((c0 != X2) | (X1 != X3)) & ((c0 != X3) | (X1 != X2)) & ! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (((X0 @ X5 @ X9 @ X6) != $true) | ((X0 @ X4 @ X8 @ X7) != $true) | ((cP @ X5 @ X4) != X2) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3))) | ((X0 @ X2 @ X3 @ X1) = $true)))),
% 1.64/1.30 inference(rectify,[status(thm)],[f7])).
% 1.64/1.30 thf(f7,plain,(
% 1.64/1.30 ? [X0 : a > a > a > $o] : (((X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true) & ! [X3 : a,X1 : a,X2 : a] : ((((c0 != X1) | (X2 != X3)) & ((c0 != X2) | (X1 != X3)) & ! [X8 : a,X6 : a,X7 : a,X9 : a,X5 : a,X4 : a] : (((X0 @ X6 @ X4 @ X7) != $true) | ((X0 @ X8 @ X5 @ X9) != $true) | ((cP @ X6 @ X8) != X1) | ((cP @ X7 @ X9) != X3) | ((cP @ X4 @ X5) != X2))) | ((X0 @ X1 @ X2 @ X3) = $true)))),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f6])).
% 1.64/1.30 thf(f6,plain,(
% 1.64/1.30 ~! [X0 : a > a > a > $o] : (! [X2 : a,X1 : a,X3 : a] : ((((c0 = X1) & (X2 = X3)) | ((c0 = X2) & (X1 = X3)) | ? [X5 : a,X9 : a,X7 : a,X4 : a,X8 : a,X6 : a] : (((cP @ X7 @ X9) = X3) & ((X0 @ X8 @ X5 @ X9) = $true) & ((cP @ X6 @ X8) = X1) & ((cP @ X4 @ X5) = X2) & ((X0 @ X6 @ X4 @ X7) = $true))) => ((X0 @ X1 @ X2 @ X3) = $true)) => ((X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) = $true))),
% 1.64/1.30 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,plain,(
% 1.64/1.30 ~! [X0 : a > a > a > $o] : ((! [X2 : a,X1 : a,X3 : a] : ((((c0 = X1) & (X2 = X3)) | ((c0 = X2) & (X1 = X3)) | ? [X5 : a,X9 : a,X7 : a,X4 : a,X8 : a,X6 : a] : (((cP @ X7 @ X9) = X3) & ((X0 @ X8 @ X5 @ X9) = $true) & ((cP @ X6 @ X8) = X1) & ((cP @ X4 @ X5) = X2) & ((X0 @ X6 @ X4 @ X7) = $true))) => ((X0 @ X1 @ X2 @ X3) = $true)) & $true) => ((X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) = $true))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.30 thf(f4,plain,(
% 1.64/1.30 ~! [X0 : a > a > a > $o] : ((! [X1 : a,X2 : a,X3 : a] : ((? [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((X0 @ X6 @ X4 @ X7) & ((cP @ X4 @ X5) = X2) & (X0 @ X8 @ X5 @ X9) & ((cP @ X6 @ X8) = X1) & ((cP @ X7 @ X9) = X3)) | ((X2 = X3) & (c0 = X1)) | ((c0 = X2) & (X1 = X3))) => (X0 @ X1 @ X2 @ X3)) & $true) => (X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)))),
% 1.64/1.30 inference(rectify,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,negated_conjecture,(
% 1.64/1.30 ~! [X0 : a > a > a > $o] : ((! [X1 : a,X2 : a,X3 : a] : ((? [X6 : a,X7 : a,X4 : a,X8 : a,X5 : a,X9 : a] : ((X0 @ X4 @ X6 @ X8) & ((cP @ X6 @ X7) = X2) & (X0 @ X5 @ X7 @ X9) & ((cP @ X4 @ X5) = X1) & ((cP @ X8 @ X9) = X3)) | ((X2 = X3) & (c0 = X1)) | ((c0 = X2) & (X1 = X3))) => (X0 @ X1 @ X2 @ X3)) & $true) => (X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.30 thf(f1,conjecture,(
% 1.64/1.30 ! [X0 : a > a > a > $o] : ((! [X1 : a,X2 : a,X3 : a] : ((? [X6 : a,X7 : a,X4 : a,X8 : a,X5 : a,X9 : a] : ((X0 @ X4 @ X6 @ X8) & ((cP @ X6 @ X7) = X2) & (X0 @ X5 @ X7 @ X9) & ((cP @ X4 @ X5) = X1) & ((cP @ X8 @ X9) = X3)) | ((X2 = X3) & (c0 = X1)) | ((c0 = X2) & (X1 = X3))) => (X0 @ X1 @ X2 @ X3)) & $true) => (X0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.dxINkJ9hSk/DTF2THF_31230.p',cS_JOIN_LEM2_pme)).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 ((sK0 @ x @ c0 @ x) != $true)),
% 1.64/1.30 inference(subsumption_resolution,[status(thm)],[f23,f16])).
% 1.64/1.30 thf(f16,plain,(
% 1.64/1.30 ( ! [X3 : a] : (((sK0 @ c0 @ X3 @ X3) = $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f15])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 ( ! [X3 : a,X1 : a] : ((X1 != X3) | ((sK0 @ c0 @ X3 @ X1) = $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 ( ! [X2 : a,X3 : a,X1 : a] : ((c0 != X2) | (X1 != X3) | ((sK0 @ X2 @ X3 @ X1) = $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ((sK0 @ c0 @ y @ y) != $true) | ((sK0 @ x @ c0 @ x) != $true)),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f22])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 ((sK0 @ c0 @ y @ y) != $true) | ((sK0 @ x @ c0 @ x) != $true) | ($true != $true)),
% 1.64/1.30 inference(superposition,[status(thm)],[f14,f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 ( ! [X8 : a,X6 : a,X9 : a,X7 : a,X4 : a,X5 : a] : (((sK0 @ (cP @ X5 @ X4) @ (cP @ X9 @ X8) @ (cP @ X6 @ X7)) = $true) | ((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f20])).
% 1.64/1.30 thf(f20,plain,(
% 1.64/1.30 ( ! [X3 : a,X8 : a,X6 : a,X9 : a,X7 : a,X4 : a,X5 : a] : (((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true) | ((cP @ X9 @ X8) != X3) | ((sK0 @ (cP @ X5 @ X4) @ X3 @ (cP @ X6 @ X7)) = $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f19])).
% 1.64/1.30 thf(f19,plain,(
% 1.64/1.30 ( ! [X3 : a,X1 : a,X8 : a,X6 : a,X9 : a,X7 : a,X4 : a,X5 : a] : (((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3) | ((sK0 @ (cP @ X5 @ X4) @ X3 @ X1) = $true)) )),
% 1.64/1.30 inference(equality_resolution,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 ( ! [X2 : a,X3 : a,X1 : a,X8 : a,X6 : a,X9 : a,X7 : a,X4 : a,X5 : a] : (((sK0 @ X5 @ X9 @ X6) != $true) | ((sK0 @ X4 @ X8 @ X7) != $true) | ((cP @ X5 @ X4) != X2) | ((cP @ X6 @ X7) != X1) | ((cP @ X9 @ X8) != X3) | ((sK0 @ X2 @ X3 @ X1) = $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 ((sK0 @ (cP @ x @ c0) @ (cP @ c0 @ y) @ (cP @ x @ y)) != $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_31230
% 1.64/1.30 % (31517)------------------------------
% 1.64/1.30 % (31517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (31517)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (31517)Memory used [KB]: 5500
% 1.64/1.30 % (31517)Time elapsed: 0.003 s
% 1.64/1.30 % (31517)Instructions burned: 4 (million)
% 1.64/1.30 % (31517)------------------------------
% 1.64/1.30 % (31517)------------------------------
% 1.64/1.30 % (31511)Success in time 0.013 s
%------------------------------------------------------------------------------