%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG286^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n027.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 08:37:50 AM UTC 2026
% Result : Theorem 1.63s 1.34s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 84 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 242 ( 22 ~; 6 |; 38 &; 165 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cZ: a ).
thf(func_def_2,type,
u: a ).
thf(func_def_3,type,
y: a ).
thf(func_def_4,type,
x: a ).
thf(func_def_5,type,
cP: a > a > a ).
thf(func_def_6,type,
cR: a > a ).
thf(func_def_7,type,
cL: a > a ).
thf(f113,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f111,f29]) ).
thf(f29,plain,
( y
= ( cP @ x @ y ) ),
inference(superposition,[status(thm)],[f21,f13]) ).
thf(f13,plain,
! [X2: a,X1: a] :
( ( cR @ ( cP @ X2 @ X1 ) )
= X1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( u
= ( cP @ x @ y ) )
& ! [X0: a] :
( ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) )
& ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X2 @ X1 ) )
= X1 )
& ( cZ
= ( cL @ cZ ) )
& ( cZ = u )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ( cZ
= ( cR @ cZ ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( u
= ( cP @ x @ y ) )
& ! [X2: a] :
( ( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
| ( cZ = X2 ) )
& ( ( cZ != X2 )
| ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
!= X2 ) ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ( cZ = u )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ( cZ
= ( cR @ cZ ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( u
= ( cP @ x @ y ) )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ( cZ = u )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ( cZ
= ( cR @ cZ ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( cZ = u )
& ( u
= ( cP @ x @ y ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( cZ
= ( cR @ cZ ) )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cL @ cZ ) )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( cZ != u ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( cZ != u ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( cZ != u ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.j6YobgHyR4/DTF2THF_26845.p',cPU_PAIR_NOT_ZERO_pme) ).
thf(f21,plain,
( ( cP @ x @ y )
= ( cR @ ( cP @ x @ y ) ) ),
inference(definition_unfolding,[status(thm)],[f9,f17,f17]) ).
thf(f17,plain,
( cZ
= ( cP @ x @ y ) ),
inference(definition_unfolding,[status(thm)],[f11,f16]) ).
thf(f16,plain,
( u
= ( cP @ x @ y ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f11,plain,
cZ = u,
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f9,plain,
( cZ
= ( cR @ cZ ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f111,plain,
( y
!= ( cP @ x @ y ) ),
inference(superposition,[status(thm)],[f107,f37]) ).
thf(f37,plain,
( y
= ( cR @ y ) ),
inference(superposition,[status(thm)],[f26,f31]) ).
thf(f31,plain,
x = y,
inference(superposition,[status(thm)],[f28,f26]) ).
thf(f28,plain,
( x
= ( cR @ x ) ),
inference(superposition,[status(thm)],[f21,f24]) ).
thf(f24,plain,
( x
= ( cP @ x @ y ) ),
inference(superposition,[status(thm)],[f10,f20]) ).
thf(f20,plain,
( ( cP @ x @ y )
= ( cL @ ( cP @ x @ y ) ) ),
inference(definition_unfolding,[status(thm)],[f12,f17,f17]) ).
thf(f12,plain,
( cZ
= ( cL @ cZ ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f10,plain,
! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f26,plain,
( y
= ( cR @ x ) ),
inference(superposition,[status(thm)],[f13,f24]) ).
thf(f107,plain,
( y
!= ( cP @ x @ ( cR @ y ) ) ),
inference(superposition,[status(thm)],[f90,f54]) ).
thf(f54,plain,
( x
= ( cL @ y ) ),
inference(superposition,[status(thm)],[f10,f29]) ).
thf(f90,plain,
( y
!= ( cP @ ( cL @ y ) @ ( cR @ y ) ) ),
inference(superposition,[status(thm)],[f22,f29]) ).
thf(f22,plain,
( ( cP @ x @ y )
!= ( cP @ ( cL @ ( cP @ x @ y ) ) @ ( cR @ ( cP @ x @ y ) ) ) ),
inference(equality_resolution,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: a] :
( ( ( cP @ x @ y )
!= X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) ),
inference(definition_unfolding,[status(thm)],[f14,f17]) ).
thf(f14,plain,
! [X0: a] :
( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 03:43:37 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : ALG286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : General Algebra (Domain theory)
% 0.27/0.47 % Problem : TPS problem from PAIRING-UNPAIRING-ALG-THMS
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0979 [Bro09]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.27/0.47 % Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% 0.27/0.47 % Number of atoms : 8 ( 8 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 8 ( 8 avg)
% 0.27/0.47 % Number of connectives : 23 ( 2 ~; 0 |; 4 &; 14 @)
% 0.27/0.47 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 9 ( 9 avg)
% 0.27/0.47 % Number of types : 1 ( 1 usr)
% 0.27/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 8 ( 7 usr; 4 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(a_type,type,
% 0.27/0.47 a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(cZ,type,
% 0.27/0.47 cZ: a ).
% 0.27/0.47
% 0.27/0.47 thf(u,type,
% 0.27/0.47 u: a ).
% 0.27/0.47
% 0.27/0.47 thf(y,type,
% 0.27/0.47 y: a ).
% 0.27/0.47
% 0.27/0.47 thf(x,type,
% 0.27/0.47 x: a ).
% 0.27/0.47
% 0.27/0.47 thf(cP,type,
% 0.27/0.47 cP: a > a > a ).
% 0.27/0.47
% 0.27/0.47 thf(cR,type,
% 0.27/0.47 cR: a > a ).
% 0.27/0.47
% 0.27/0.47 thf(cL,type,
% 0.27/0.47 cL: a > a ).
% 0.27/0.47
% 0.27/0.47 thf(cPU_PAIR_NOT_ZERO_pme,conjecture,
% 0.27/0.47 ( ( ( ( cL @ cZ )
% 0.27/0.47 = cZ )
% 0.27/0.47 & ( ( cR @ cZ )
% 0.27/0.47 = cZ )
% 0.27/0.47 & ! [Xx0: a,Xy0: a] :
% 0.27/0.47 ( ( cL @ ( cP @ Xx0 @ Xy0 ) )
% 0.27/0.47 = Xx0 )
% 0.27/0.47 & ! [Xx0: a,Xy0: a] :
% 0.27/0.47 ( ( cR @ ( cP @ Xx0 @ Xy0 ) )
% 0.27/0.47 = Xy0 )
% 0.27/0.47 & ! [Xt: a] :
% 0.27/0.47 ( ( Xt != cZ )
% 0.27/0.47 <=> ( Xt
% 0.27/0.47 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
% 0.27/0.47 => ( ( u
% 0.27/0.47 = ( cP @ x @ y ) )
% 0.27/0.47 => ( u != cZ ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.63/1.31 ---- Embedded in THF ---
% 1.63/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.31 %%% Generated on Tue Feb 24 03:43:38 EST 2026
% 1.63/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.31 %%% Logic specification used:
% 1.63/1.31 %%% thf(spec, logic, $$dhol).
% 1.63/1.31
% 1.63/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.j6YobgHyR4/DTF2DTF26845.p
% See solution above
% 1.63/1.31 ------------------------
% 1.63/1.32 ---- Cleaned THF ---
% 1.63/1.32 thf(a_type,type,
% 1.63/1.32 a: $tType ).
% 1.63/1.32
% 1.63/1.32 thf(cZ,type,
% 1.63/1.32 cZ: a ).
% 1.63/1.32
% 1.63/1.32 thf(u,type,
% 1.63/1.32 u: a ).
% 1.63/1.32
% 1.63/1.32 thf(y,type,
% 1.63/1.32 y: a ).
% 1.63/1.32
% 1.63/1.32 thf(x,type,
% 1.63/1.32 x: a ).
% 1.63/1.32
% 1.63/1.32 thf(cP,type,
% 1.63/1.32 cP: a > a > a ).
% 1.63/1.32
% 1.63/1.32 thf(cR,type,
% 1.63/1.32 cR: a > a ).
% 1.63/1.32
% 1.63/1.32 thf(cL,type,
% 1.63/1.32 cL: a > a ).
% 1.63/1.32
% 1.63/1.32 thf(cPU_PAIR_NOT_ZERO_pme,conjecture,
% 1.63/1.32 ( ( ( ( cL @ cZ )
% 1.63/1.32 = cZ )
% 1.63/1.32 & ( ( cR @ cZ )
% 1.63/1.32 = cZ )
% 1.63/1.32 & ! [Xx0: a,Xy0: a] :
% 1.63/1.32 ( ( cL @ ( cP @ Xx0 @ Xy0 ) )
% 1.63/1.32 = Xx0 )
% 1.63/1.32 & ! [Xx0: a,Xy0: a] :
% 1.63/1.32 ( ( cR @ ( cP @ Xx0 @ Xy0 ) )
% 1.63/1.32 = Xy0 )
% 1.63/1.32 & ! [Xt: a] :
% 1.63/1.32 ( ( Xt != cZ )
% 1.63/1.32 <=> ( Xt
% 1.63/1.32 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
% 1.63/1.32 => ( ( u
% 1.63/1.32 = ( cP @ x @ y ) )
% 1.63/1.32 => ( u != cZ ) ) ) ).
% 1.63/1.32 ------------------------
% 1.63/1.33 % (26960)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26845 for (2999ds/183Mi)
% 1.63/1.34 % (26963)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26845 for (2999ds/2Mi)
% 1.63/1.34 % (26963)Instruction limit reached!
% 1.63/1.34 % (26963)------------------------------
% 1.63/1.34 % (26963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (26963)Termination reason: Unknown
% 1.63/1.34 % (26963)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (26963)Memory used [KB]: 5500
% 1.63/1.34 % (26963)Time elapsed: 0.002 s
% 1.63/1.34 % (26963)Instructions burned: 2 (million)
% 1.63/1.34 % (26963)------------------------------
% 1.63/1.34 % (26963)------------------------------
% 1.63/1.34 % (26960)First to succeed.
% 1.63/1.34 % (26960)Refutation found. Thanks to Tanya!
% 1.63/1.34 % SZS status Theorem for DTF2THF_26845
% 1.63/1.34 % SZS output start Proof for DTF2THF_26845
% 1.63/1.34 thf(type_def_5, type, a: $tType).
% 1.63/1.34 thf(func_def_0, type, a: $tType).
% 1.63/1.34 thf(func_def_1, type, cZ: a).
% 1.63/1.34 thf(func_def_2, type, u: a).
% 1.63/1.34 thf(func_def_3, type, y: a).
% 1.63/1.34 thf(func_def_4, type, x: a).
% 1.63/1.34 thf(func_def_5, type, cP: a > a > a).
% 1.63/1.34 thf(func_def_6, type, cR: a > a).
% 1.63/1.34 thf(func_def_7, type, cL: a > a).
% 1.63/1.34 thf(f113,plain,(
% 1.63/1.34 $false),
% 1.63/1.34 inference(subsumption_resolution,[status(thm)],[f111,f29])).
% 1.63/1.34 thf(f29,plain,(
% 1.63/1.34 (y = (cP @ x @ y))),
% 1.63/1.34 inference(superposition,[status(thm)],[f21,f13])).
% 1.63/1.34 thf(f13,plain,(
% 1.63/1.34 ( ! [X2 : a,X1 : a] : (((cR @ (cP @ X2 @ X1)) = X1)) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f8,plain,(
% 1.63/1.34 (u = (cP @ x @ y)) & ! [X0 : a] : ((((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0)) & ((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0))) & ! [X1 : a,X2 : a] : ((cR @ (cP @ X2 @ X1)) = X1) & (cZ = (cL @ cZ)) & (cZ = u) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & (cZ = (cR @ cZ))),
% 1.63/1.34 inference(rectify,[status(thm)],[f7])).
% 1.63/1.34 thf(f7,plain,(
% 1.63/1.34 (u = (cP @ x @ y)) & ! [X2 : a] : ((((cP @ (cL @ X2) @ (cR @ X2)) = X2) | (cZ = X2)) & ((cZ != X2) | ((cP @ (cL @ X2) @ (cR @ X2)) != X2))) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cL @ cZ)) & (cZ = u) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & (cZ = (cR @ cZ))),
% 1.63/1.34 inference(nnf_transformation,[status(thm)],[f6])).
% 1.63/1.34 thf(f6,plain,(
% 1.63/1.34 (u = (cP @ x @ y)) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cL @ cZ)) & (cZ = u) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & (cZ = (cR @ cZ))),
% 1.63/1.34 inference(flattening,[status(thm)],[f5])).
% 1.63/1.34 thf(f5,plain,(
% 1.63/1.34 ((cZ = u) & (u = (cP @ x @ y))) & ((cZ = (cR @ cZ)) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cL @ cZ)) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)))),
% 1.63/1.34 inference(ennf_transformation,[status(thm)],[f4])).
% 1.63/1.34 thf(f4,plain,(
% 1.63/1.34 ~(((cZ = (cR @ cZ)) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & ! [X0 : a,X1 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cL @ cZ)) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2))) => ((u = (cP @ x @ y)) => (cZ != u)))),
% 1.63/1.34 inference(rectify,[status(thm)],[f2])).
% 1.63/1.34 thf(f2,negated_conjecture,(
% 1.63/1.34 ~((! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & ! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ))) => ((u = (cP @ x @ y)) => (cZ != u)))),
% 1.63/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.34 thf(f1,conjecture,(
% 1.63/1.34 (! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & ! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ))) => ((u = (cP @ x @ y)) => (cZ != u))),
% 1.63/1.34 file('/export/starexec/sandbox2/tmp/tmp.j6YobgHyR4/DTF2THF_26845.p',cPU_PAIR_NOT_ZERO_pme)).
% 1.63/1.34 thf(f21,plain,(
% 1.63/1.34 ((cP @ x @ y) = (cR @ (cP @ x @ y)))),
% 1.63/1.34 inference(definition_unfolding,[status(thm)],[f9,f17,f17])).
% 1.63/1.34 thf(f17,plain,(
% 1.63/1.34 (cZ = (cP @ x @ y))),
% 1.63/1.34 inference(definition_unfolding,[status(thm)],[f11,f16])).
% 1.63/1.34 thf(f16,plain,(
% 1.63/1.34 (u = (cP @ x @ y))),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f11,plain,(
% 1.63/1.34 (cZ = u)),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f9,plain,(
% 1.63/1.34 (cZ = (cR @ cZ))),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f111,plain,(
% 1.63/1.34 (y != (cP @ x @ y))),
% 1.63/1.34 inference(superposition,[status(thm)],[f107,f37])).
% 1.63/1.34 thf(f37,plain,(
% 1.63/1.34 (y = (cR @ y))),
% 1.63/1.34 inference(superposition,[status(thm)],[f26,f31])).
% 1.63/1.34 thf(f31,plain,(
% 1.63/1.34 (x = y)),
% 1.63/1.34 inference(superposition,[status(thm)],[f28,f26])).
% 1.63/1.34 thf(f28,plain,(
% 1.63/1.34 (x = (cR @ x))),
% 1.63/1.34 inference(superposition,[status(thm)],[f21,f24])).
% 1.63/1.34 thf(f24,plain,(
% 1.63/1.34 (x = (cP @ x @ y))),
% 1.63/1.34 inference(superposition,[status(thm)],[f10,f20])).
% 1.63/1.34 thf(f20,plain,(
% 1.63/1.34 ((cP @ x @ y) = (cL @ (cP @ x @ y)))),
% 1.63/1.34 inference(definition_unfolding,[status(thm)],[f12,f17,f17])).
% 1.63/1.34 thf(f12,plain,(
% 1.63/1.34 (cZ = (cL @ cZ))),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f10,plain,(
% 1.63/1.34 ( ! [X3 : a,X4 : a] : (((cL @ (cP @ X4 @ X3)) = X4)) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 thf(f26,plain,(
% 1.63/1.34 (y = (cR @ x))),
% 1.63/1.34 inference(superposition,[status(thm)],[f13,f24])).
% 1.63/1.34 thf(f107,plain,(
% 1.63/1.34 (y != (cP @ x @ (cR @ y)))),
% 1.63/1.34 inference(superposition,[status(thm)],[f90,f54])).
% 1.63/1.34 thf(f54,plain,(
% 1.63/1.34 (x = (cL @ y))),
% 1.63/1.34 inference(superposition,[status(thm)],[f10,f29])).
% 1.63/1.34 thf(f90,plain,(
% 1.63/1.34 (y != (cP @ (cL @ y) @ (cR @ y)))),
% 1.63/1.34 inference(superposition,[status(thm)],[f22,f29])).
% 1.63/1.34 thf(f22,plain,(
% 1.63/1.34 ((cP @ x @ y) != (cP @ (cL @ (cP @ x @ y)) @ (cR @ (cP @ x @ y))))),
% 1.63/1.34 inference(equality_resolution,[status(thm)],[f19])).
% 1.63/1.34 thf(f19,plain,(
% 1.63/1.34 ( ! [X0 : a] : (((cP @ x @ y) != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0)) )),
% 1.63/1.34 inference(definition_unfolding,[status(thm)],[f14,f17])).
% 1.63/1.34 thf(f14,plain,(
% 1.63/1.34 ( ! [X0 : a] : ((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0)) )),
% 1.63/1.34 inference(cnf_transformation,[status(thm)],[f8])).
% 1.63/1.34 % SZS output end Proof for DTF2THF_26845
% 1.63/1.34 % (26960)------------------------------
% 1.63/1.34 % (26960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (26960)Termination reason: Refutation
% 1.63/1.34
% 1.63/1.34 % (26960)Memory used [KB]: 5500
% 1.63/1.34 % (26960)Time elapsed: 0.006 s
% 1.63/1.34 % (26960)Instructions burned: 9 (million)
% 1.63/1.34 % (26960)------------------------------
% 1.63/1.34 % (26960)------------------------------
% 1.63/1.34 % (26959)Success in time 0.01 s
%------------------------------------------------------------------------------