%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ALG287^5 : 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 : n013.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 1.62s 1.75s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 89 ( 79 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 226 ( 24 ~; 12 |; 41 &; 136 @)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
v: 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(func_def_8,type,
cZ: a ).
thf(f38,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f34,f37]) ).
thf(f37,plain,
spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f36]) ).
thf(f36,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[status(thm)],[f35,f21]) ).
thf(f21,plain,
( ( x != y )
| spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl0_1
<=> ( x = y ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f35,plain,
x = y,
inference(forward_demodulation,[status(thm)],[f32,f10]) ).
thf(f10,plain,
! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: a] :
( ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) )
& ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X4 @ X3 ) )
= X4 )
& ( ( x != y )
| ( u != v ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X4: a] :
( ( ( cZ != X4 )
| ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
!= X4 ) )
& ( ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 )
| ( cZ = X4 ) ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ( ( x != y )
| ( u != v ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ( ( x != y )
| ( u != v ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ( x != y )
| ( u != v ) )
& ( ( cP @ x @ u )
= ( cP @ y @ v ) )
& ! [X2: a,X3: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X2: a,X3: a] :
( ( cL @ ( cP @ X3 @ X2 ) )
= X3 )
& ! [X1: a,X0: a] :
( ( cR @ ( cP @ X1 @ X0 ) )
= X0 )
& ( cZ
= ( cR @ cZ ) )
& ( cZ
= ( cL @ cZ ) )
& ! [X4: a] :
( ( cZ != X4 )
<=> ( ( cP @ ( cL @ X4 ) @ ( cR @ X4 ) )
= X4 ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X1: a,X0: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X1: a,X0: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ! [X2: a] :
( ( ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) )
= X2 )
<=> ( cZ != X2 ) )
& ( cZ
= ( cL @ cZ ) )
& ( cZ
= ( cR @ cZ ) ) )
=> ( ( ( cP @ x @ u )
= ( cP @ y @ v ) )
=> ( ( u = v )
& ( x = y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.QBVyYO8HID/DTF2THF_2083.p',cPU_P_INJ_pme) ).
thf(f32,plain,
( x
= ( cL @ ( cP @ y @ v ) ) ),
inference(superposition,[status(thm)],[f10,f14]) ).
thf(f14,plain,
( ( cP @ x @ u )
= ( cP @ y @ v ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f34,plain,
spl0_2,
inference(avatar_split_clause,[status(thm)],[f33,f23]) ).
thf(f23,definition,
( spl0_2
<=> ( u = v ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f33,plain,
u = v,
inference(forward_demodulation,[status(thm)],[f31,f11]) ).
thf(f11,plain,
! [X2: a,X1: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f31,plain,
( u
= ( cR @ ( cP @ y @ v ) ) ),
inference(superposition,[status(thm)],[f11,f14]) ).
thf(f26,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f9,f23,f19]) ).
thf(f9,plain,
( ( x != y )
| ( u != v ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG287^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n013.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 03:43:08 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ALG287^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.46 % Domain : General Algebra (Domain theory)
% 0.31/0.46 % Problem : TPS problem from PAIRING-UNPAIRING-ALG-THMS
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Bro09]
% 0.31/0.46 % Names : tps_1000 [Bro09]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 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
% 0.31/0.46 % Syntax : Number of formulae : 10 ( 0 unt; 9 typ; 0 def)
% 0.31/0.46 % Number of atoms : 9 ( 9 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 9 ( 9 avg)
% 0.31/0.46 % Number of connectives : 25 ( 1 ~; 0 |; 5 &; 16 @)
% 0.31/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.31/0.46 % Number of types : 1 ( 1 usr)
% 0.31/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 9 ( 8 usr; 5 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(a_type,type,
% 0.31/0.46 a: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(v,type,
% 0.31/0.46 v: a ).
% 0.31/0.46
% 0.31/0.46 thf(u,type,
% 0.31/0.46 u: a ).
% 0.31/0.46
% 0.31/0.46 thf(y,type,
% 0.31/0.46 y: a ).
% 0.31/0.46
% 0.31/0.46 thf(x,type,
% 0.31/0.46 x: a ).
% 0.31/0.46
% 0.31/0.46 thf(cP,type,
% 0.31/0.46 cP: a > a > a ).
% 0.31/0.46
% 0.31/0.46 thf(cR,type,
% 0.31/0.46 cR: a > a ).
% 0.31/0.46
% 0.31/0.46 thf(cL,type,
% 0.31/0.46 cL: a > a ).
% 0.31/0.46
% 0.31/0.46 thf(cZ,type,
% 0.31/0.46 cZ: a ).
% 0.31/0.46
% 0.31/0.46 thf(cPU_P_INJ_pme,conjecture,
% 0.31/0.46 ( ( ( ( cL @ cZ )
% 0.31/0.46 = cZ )
% 0.31/0.46 & ( ( cR @ cZ )
% 0.31/0.46 = cZ )
% 0.31/0.46 & ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( cL @ ( cP @ Xx0 @ Xy0 ) )
% 0.31/0.46 = Xx0 )
% 0.31/0.46 & ! [Xx0: a,Xy0: a] :
% 0.31/0.46 ( ( cR @ ( cP @ Xx0 @ Xy0 ) )
% 0.31/0.46 = Xy0 )
% 0.31/0.46 & ! [Xt: a] :
% 0.31/0.46 ( ( Xt != cZ )
% 0.31/0.46 <=> ( Xt
% 0.31/0.46 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
% 0.31/0.46 => ( ( ( cP @ x @ u )
% 0.31/0.46 = ( cP @ y @ v ) )
% 0.31/0.46 => ( ( x = y )
% 0.31/0.46 & ( u = v ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.62/1.72 ---- Embedded in THF ---
% 1.62/1.72 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.72 %%% Generated on Tue Feb 24 03:43:09 EST 2026
% 1.62/1.72 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.72 %%% Logic specification used:
% 1.62/1.72 %%% thf(spec, logic, $$dhol).
% 1.62/1.72
% 1.62/1.72 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.QBVyYO8HID/DTF2DTF2083.p
% See solution above
% 1.62/1.72 ------------------------
% 1.62/1.73 ---- Cleaned THF ---
% 1.62/1.73 thf(a_type,type,
% 1.62/1.73 a: $tType ).
% 1.62/1.73
% 1.62/1.73 thf(v,type,
% 1.62/1.73 v: a ).
% 1.62/1.73
% 1.62/1.73 thf(u,type,
% 1.62/1.73 u: a ).
% 1.62/1.73
% 1.62/1.73 thf(y,type,
% 1.62/1.73 y: a ).
% 1.62/1.73
% 1.62/1.73 thf(x,type,
% 1.62/1.73 x: a ).
% 1.62/1.73
% 1.62/1.73 thf(cP,type,
% 1.62/1.73 cP: a > a > a ).
% 1.62/1.73
% 1.62/1.73 thf(cR,type,
% 1.62/1.73 cR: a > a ).
% 1.62/1.73
% 1.62/1.73 thf(cL,type,
% 1.62/1.73 cL: a > a ).
% 1.62/1.73
% 1.62/1.73 thf(cZ,type,
% 1.62/1.73 cZ: a ).
% 1.62/1.73
% 1.62/1.73 thf(cPU_P_INJ_pme,conjecture,
% 1.62/1.73 ( ( ( ( cL @ cZ )
% 1.62/1.73 = cZ )
% 1.62/1.73 & ( ( cR @ cZ )
% 1.62/1.73 = cZ )
% 1.62/1.73 & ! [Xx0: a,Xy0: a] :
% 1.62/1.73 ( ( cL @ ( cP @ Xx0 @ Xy0 ) )
% 1.62/1.73 = Xx0 )
% 1.62/1.73 & ! [Xx0: a,Xy0: a] :
% 1.62/1.73 ( ( cR @ ( cP @ Xx0 @ Xy0 ) )
% 1.62/1.73 = Xy0 )
% 1.62/1.73 & ! [Xt: a] :
% 1.62/1.73 ( ( Xt != cZ )
% 1.62/1.73 <=> ( Xt
% 1.62/1.73 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) ) )
% 1.62/1.73 => ( ( ( cP @ x @ u )
% 1.62/1.73 = ( cP @ y @ v ) )
% 1.62/1.73 => ( ( x = y )
% 1.62/1.73 & ( u = v ) ) ) ) ).
% 1.62/1.73 ------------------------
% 1.62/1.75 % (2414)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_2083 for (2999ds/275Mi)
% 1.62/1.75 % (2414)First to succeed.
% 1.62/1.75 % (2414)Refutation found. Thanks to Tanya!
% 1.62/1.75 % SZS status Theorem for DTF2THF_2083
% 1.62/1.75 % SZS output start Proof for DTF2THF_2083
% 1.62/1.75 thf(type_def_5, type, a: $tType).
% 1.62/1.75 thf(func_def_0, type, a: $tType).
% 1.62/1.75 thf(func_def_1, type, v: a).
% 1.62/1.75 thf(func_def_2, type, u: a).
% 1.62/1.75 thf(func_def_3, type, y: a).
% 1.62/1.75 thf(func_def_4, type, x: a).
% 1.62/1.75 thf(func_def_5, type, cP: a > a > a).
% 1.62/1.75 thf(func_def_6, type, cR: a > a).
% 1.62/1.75 thf(func_def_7, type, cL: a > a).
% 1.62/1.75 thf(func_def_8, type, cZ: a).
% 1.62/1.75 thf(f38,plain,(
% 1.62/1.75 $false),
% 1.62/1.75 inference(avatar_sat_refutation,[status(thm)],[f26,f34,f37])).
% 1.62/1.75 thf(f37,plain,(
% 1.62/1.75 spl0_1),
% 1.62/1.75 inference(avatar_contradiction_clause,[status(thm)],[f36])).
% 1.62/1.75 thf(f36,plain,(
% 1.62/1.75 $false | spl0_1),
% 1.62/1.75 inference(subsumption_resolution,[status(thm)],[f35,f21])).
% 1.62/1.75 thf(f21,plain,(
% 1.62/1.75 (x != y) | spl0_1),
% 1.62/1.75 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.62/1.75 thf(f19,definition,(
% 1.62/1.75 spl0_1 <=> (x = y)),
% 1.62/1.75 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.62/1.75 thf(f35,plain,(
% 1.62/1.75 (x = y)),
% 1.62/1.75 inference(forward_demodulation,[status(thm)],[f32,f10])).
% 1.62/1.75 thf(f10,plain,(
% 1.62/1.75 ( ! [X3 : a,X4 : a] : (((cL @ (cP @ X4 @ X3)) = X4)) )),
% 1.62/1.75 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.75 thf(f8,plain,(
% 1.62/1.75 ! [X0 : a] : (((cZ != X0) | ((cP @ (cL @ X0) @ (cR @ X0)) != X0)) & (((cP @ (cL @ X0) @ (cR @ X0)) = X0) | (cZ = X0))) & ((cP @ x @ u) = (cP @ y @ v)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X1 : a,X2 : a] : ((cR @ (cP @ X1 @ X2)) = X2) & ! [X3 : a,X4 : a] : ((cL @ (cP @ X4 @ X3)) = X4) & ((x != y) | (u != v))),
% 1.62/1.75 inference(rectify,[status(thm)],[f7])).
% 1.62/1.75 thf(f7,plain,(
% 1.62/1.75 ! [X4 : a] : (((cZ != X4) | ((cP @ (cL @ X4) @ (cR @ X4)) != X4)) & (((cP @ (cL @ X4) @ (cR @ X4)) = X4) | (cZ = X4))) & ((cP @ x @ u) = (cP @ y @ v)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & ! [X2 : a,X3 : a] : ((cL @ (cP @ X3 @ X2)) = X3) & ((x != y) | (u != v))),
% 1.62/1.75 inference(nnf_transformation,[status(thm)],[f6])).
% 1.62/1.75 thf(f6,plain,(
% 1.62/1.75 ! [X4 : a] : ((cZ != X4) <=> ((cP @ (cL @ X4) @ (cR @ X4)) = X4)) & ((cP @ x @ u) = (cP @ y @ v)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ)) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & ! [X2 : a,X3 : a] : ((cL @ (cP @ X3 @ X2)) = X3) & ((x != y) | (u != v))),
% 1.62/1.75 inference(flattening,[status(thm)],[f5])).
% 1.62/1.75 thf(f5,plain,(
% 1.62/1.75 (((x != y) | (u != v)) & ((cP @ x @ u) = (cP @ y @ v))) & (! [X2 : a,X3 : a] : ((cL @ (cP @ X3 @ X2)) = X3) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X4 : a] : ((cZ != X4) <=> ((cP @ (cL @ X4) @ (cR @ X4)) = X4)))),
% 1.62/1.75 inference(ennf_transformation,[status(thm)],[f4])).
% 1.62/1.75 thf(f4,plain,(
% 1.62/1.75 ~((! [X2 : a,X3 : a] : ((cL @ (cP @ X3 @ X2)) = X3) & ! [X1 : a,X0 : a] : ((cR @ (cP @ X1 @ X0)) = X0) & (cZ = (cR @ cZ)) & (cZ = (cL @ cZ)) & ! [X4 : a] : ((cZ != X4) <=> ((cP @ (cL @ X4) @ (cR @ X4)) = X4))) => (((cP @ x @ u) = (cP @ y @ v)) => ((u = v) & (x = y))))),
% 1.62/1.75 inference(rectify,[status(thm)],[f2])).
% 1.62/1.75 thf(f2,negated_conjecture,(
% 1.62/1.75 ~((! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ))) => (((cP @ x @ u) = (cP @ y @ v)) => ((u = v) & (x = y))))),
% 1.62/1.75 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.75 thf(f1,conjecture,(
% 1.62/1.75 (! [X1 : a,X0 : a] : ((cR @ (cP @ X0 @ X1)) = X1) & ! [X1 : a,X0 : a] : ((cL @ (cP @ X0 @ X1)) = X0) & ! [X2 : a] : (((cP @ (cL @ X2) @ (cR @ X2)) = X2) <=> (cZ != X2)) & (cZ = (cL @ cZ)) & (cZ = (cR @ cZ))) => (((cP @ x @ u) = (cP @ y @ v)) => ((u = v) & (x = y)))),
% 1.62/1.75 file('/export/starexec/sandbox/tmp/tmp.QBVyYO8HID/DTF2THF_2083.p',cPU_P_INJ_pme)).
% 1.62/1.75 thf(f32,plain,(
% 1.62/1.75 (x = (cL @ (cP @ y @ v)))),
% 1.62/1.75 inference(superposition,[status(thm)],[f10,f14])).
% 1.62/1.75 thf(f14,plain,(
% 1.62/1.75 ((cP @ x @ u) = (cP @ y @ v))),
% 1.62/1.75 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.75 thf(f34,plain,(
% 1.62/1.75 spl0_2),
% 1.62/1.75 inference(avatar_split_clause,[status(thm)],[f33,f23])).
% 1.62/1.75 thf(f23,definition,(
% 1.62/1.75 spl0_2 <=> (u = v)),
% 1.62/1.75 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.62/1.75 thf(f33,plain,(
% 1.62/1.75 (u = v)),
% 1.62/1.75 inference(forward_demodulation,[status(thm)],[f31,f11])).
% 1.62/1.75 thf(f11,plain,(
% 1.62/1.75 ( ! [X2 : a,X1 : a] : (((cR @ (cP @ X1 @ X2)) = X2)) )),
% 1.62/1.75 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.75 thf(f31,plain,(
% 1.62/1.75 (u = (cR @ (cP @ y @ v)))),
% 1.62/1.75 inference(superposition,[status(thm)],[f11,f14])).
% 1.62/1.75 thf(f26,plain,(
% 1.62/1.75 ~spl0_1 | ~spl0_2),
% 1.62/1.75 inference(avatar_split_clause,[status(thm)],[f9,f23,f19])).
% 1.62/1.75 thf(f9,plain,(
% 1.62/1.75 (x != y) | (u != v)),
% 1.62/1.75 inference(cnf_transformation,[status(thm)],[f8])).
% 1.62/1.75 % SZS output end Proof for DTF2THF_2083
% 1.62/1.75 % (2414)------------------------------
% 1.62/1.75 % (2414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.75 % (2414)Termination reason: Refutation
% 1.62/1.75
% 1.62/1.75 % (2414)Memory used [KB]: 5500
% 1.62/1.75 % (2414)Time elapsed: 0.004 s
% 1.62/1.75 % (2414)Instructions burned: 2 (million)
% 1.62/1.75 % (2414)------------------------------
% 1.62/1.75 % (2414)------------------------------
% 1.62/1.75 % (2408)Success in time 0.015 s
%------------------------------------------------------------------------------