%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM752^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 09:24:33 AM UTC 2026
% Result : Theorem 1.66s 1.46s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 168 ( 19 ~; 11 |; 0 &; 132 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(func_def_0,type,
frac: $tType ).
thf(func_def_1,type,
x: frac ).
thf(func_def_2,type,
y: frac ).
thf(func_def_3,type,
z: frac ).
thf(func_def_4,type,
eq: frac > frac > $o ).
thf(func_def_6,type,
pf: frac > frac > frac ).
thf(f26,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f25,f21]) ).
thf(f21,plain,
( ( eq @ x @ y )
= $true ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( eq @ x @ y )
= $true ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
eq @ x @ y,
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
eq @ x @ y,
file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',e) ).
thf(f25,plain,
( ( eq @ x @ y )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f24,f22]) ).
thf(f22,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: frac] :
( ( eq @ X0 @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: frac] : ( eq @ X0 @ X0 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: frac] : ( eq @ X0 @ X0 ),
file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz37) ).
thf(f24,plain,
( ( $true
!= ( eq @ z @ z ) )
| ( ( eq @ x @ y )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( eq @ x @ y )
!= $true )
| ( $true
!= ( eq @ z @ z ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f19,f20]) ).
thf(f20,plain,
! [X2: frac,X3: frac,X0: frac,X1: frac] :
( ( $true
= ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X3 ) ) )
| ( $true
!= ( eq @ X1 @ X0 ) )
| ( ( eq @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( ( eq @ X2 @ X3 )
!= $true )
| ( $true
!= ( eq @ X1 @ X0 ) )
| ( $true
= ( eq @ ( pf @ X1 @ X2 ) @ ( pf @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
! [X2: frac,X1: frac,X3: frac,X0: frac] :
( ( ( eq @ X3 @ X0 )
!= $true )
| ( $true
!= ( eq @ X1 @ X2 ) )
| ( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true ) ),
inference(flattening,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: frac,X1: frac,X3: frac,X2: frac] :
( ( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true )
| ( ( eq @ X3 @ X0 )
!= $true )
| ( $true
!= ( eq @ X1 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: frac,X1: frac,X3: frac,X2: frac] :
( ( $true
= ( eq @ X1 @ X2 ) )
=> ( ( ( eq @ X3 @ X0 )
= $true )
=> ( ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: frac,X1: frac,X2: frac,X3: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X0 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: frac,X0: frac,X1: frac,X2: frac] :
( ( eq @ X0 @ X1 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ ( pf @ X0 @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz56) ).
thf(f19,plain,
( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz62e) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM752^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.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 11:12:55 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
% 0.33/0.50 ---- Original DTF file ---
% 0.33/0.50 thf(spec,logic,$$dhol).
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 % File : NUM752^1 : TPTP v9.2.1. Released v3.7.0.
% 0.33/0.50 % Domain : Number Theory
% 0.33/0.50 % Problem : Landau theorem 62e
% 0.33/0.50 % Version : Especial.
% 0.33/0.50 % English : eq (pf z x) (pf z y)
% 0.33/0.50
% 0.33/0.50 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.33/0.50 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.33/0.50 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.50 % Source : [Bro09]
% 0.33/0.50 % Names : satz62e [Lan30]
% 0.33/0.50 % : satz72e [Lan30]
% 0.33/0.50
% 0.33/0.50 % Status : Theorem
% 0.33/0.50 % : Without extensionality : Theorem
% 0.33/0.50 % Rating : 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v3.7.0
% 0.33/0.50 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 0 def)
% 0.33/0.50 % Number of atoms : 6 ( 0 equ; 0 cnn)
% 0.33/0.50 % Maximal formula atoms : 3 ( 1 avg)
% 0.33/0.50 % Number of connectives : 22 ( 0 ~; 0 |; 0 &; 20 @)
% 0.33/0.50 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.33/0.50 % Maximal formula depth : 11 ( 6 avg)
% 0.33/0.50 % Number of types : 2 ( 1 usr)
% 0.33/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.33/0.50 % Number of symbols : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.33/0.50 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.33/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.33/0.50
% 0.33/0.50 % Comments :
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 thf(frac_type,type,
% 0.33/0.50 frac: $tType ).
% 0.33/0.50
% 0.33/0.50 thf(x,type,
% 0.33/0.50 x: frac ).
% 0.33/0.50
% 0.33/0.50 thf(y,type,
% 0.33/0.50 y: frac ).
% 0.33/0.50
% 0.33/0.50 thf(z,type,
% 0.33/0.50 z: frac ).
% 0.33/0.50
% 0.33/0.50 thf(eq,type,
% 0.33/0.50 eq: frac > frac > $o ).
% 0.33/0.50
% 0.33/0.50 thf(e,axiom,
% 0.33/0.50 eq @ x @ y ).
% 0.33/0.50
% 0.33/0.50 thf(pf,type,
% 0.33/0.50 pf: frac > frac > frac ).
% 0.33/0.50
% 0.33/0.50 thf(satz56,axiom,
% 0.33/0.50 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 0.33/0.50 ( ( eq @ Xx @ Xy )
% 0.33/0.50 => ( ( eq @ Xz @ Xu )
% 0.33/0.50 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 0.33/0.50
% 0.33/0.50 thf(satz37,axiom,
% 0.33/0.50 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 0.33/0.50
% 0.33/0.50 thf(satz62e,conjecture,
% 0.33/0.50 eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 0.33/0.50
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 ------------------------
% 1.66/1.43 ---- Embedded in THF ---
% 1.66/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.43 %%% Generated on Tue Feb 24 11:12:56 EST 2026
% 1.66/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.43 %%% Logic specification used:
% 1.66/1.43 %%% thf(spec, logic, $$dhol).
% 1.66/1.43
% 1.66/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2DTF7535.p
% See solution above
% 1.66/1.43 ------------------------
% 1.66/1.44 ---- Cleaned THF ---
% 1.66/1.44 thf(frac_type,type,
% 1.66/1.44 frac: $tType ).
% 1.66/1.44
% 1.66/1.44 thf(x,type,
% 1.66/1.44 x: frac ).
% 1.66/1.44
% 1.66/1.44 thf(y,type,
% 1.66/1.44 y: frac ).
% 1.66/1.44
% 1.66/1.44 thf(z,type,
% 1.66/1.44 z: frac ).
% 1.66/1.44
% 1.66/1.44 thf(eq,type,
% 1.66/1.44 eq: frac > frac > $o ).
% 1.66/1.44
% 1.66/1.44 thf(e,axiom,
% 1.66/1.44 eq @ x @ y ).
% 1.66/1.44
% 1.66/1.44 thf(pf,type,
% 1.66/1.44 pf: frac > frac > frac ).
% 1.66/1.44
% 1.66/1.44 thf(satz56,axiom,
% 1.66/1.44 ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
% 1.66/1.44 ( ( eq @ Xx @ Xy )
% 1.66/1.44 => ( ( eq @ Xz @ Xu )
% 1.66/1.44 => ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) ).
% 1.66/1.44
% 1.66/1.44 thf(satz37,axiom,
% 1.66/1.44 ! [Xx: frac] : ( eq @ Xx @ Xx ) ).
% 1.66/1.44
% 1.66/1.44 thf(satz62e,conjecture,
% 1.66/1.44 eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) ).
% 1.66/1.44 ------------------------
% 1.66/1.46 % (7647)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7535 for (3000ds/183Mi)
% 1.66/1.46 % (7648)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_7535 for (3000ds/4Mi)
% 1.66/1.46 % (7650)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7535 for (3000ds/2Mi)
% 1.66/1.46 % (7649)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_7535 for (3000ds/27Mi)
% 1.66/1.46 % (7651)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_7535 for (3000ds/2Mi)
% 1.66/1.46 % (7652)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_7535 for (3000ds/275Mi)
% 1.66/1.46 % (7653)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7535 for (3000ds/18Mi)
% 1.66/1.46 % (7650)Instruction limit reached!
% 1.66/1.46 % (7650)------------------------------
% 1.66/1.46 % (7650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7650)Termination reason: Unknown
% 1.66/1.46 % (7651)Instruction limit reached!
% 1.66/1.46 % (7651)------------------------------
% 1.66/1.46 % (7651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7650)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (7650)Memory used [KB]: 5500
% 1.66/1.46 % (7650)Time elapsed: 0.003 s
% 1.66/1.46 % (7650)Instructions burned: 2 (million)
% 1.66/1.46 % (7650)------------------------------
% 1.66/1.46 % (7650)------------------------------
% 1.66/1.46 % (7651)Termination reason: Unknown
% 1.66/1.46 % (7651)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (7651)Memory used [KB]: 5500
% 1.66/1.46 % (7651)Time elapsed: 0.003 s
% 1.66/1.46 % (7651)Instructions burned: 2 (million)
% 1.66/1.46 % (7651)------------------------------
% 1.66/1.46 % (7651)------------------------------
% 1.66/1.46 % (7652)First to succeed.
% 1.66/1.46 % (7648)Instruction limit reached!
% 1.66/1.46 % (7648)------------------------------
% 1.66/1.46 % (7648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7648)Termination reason: Unknown
% 1.66/1.46 % (7648)Termination phase: Saturation
% 1.66/1.46
% 1.66/1.46 % (7648)Memory used [KB]: 5500
% 1.66/1.46 % (7648)Time elapsed: 0.004 s
% 1.66/1.46 % (7648)Instructions burned: 4 (million)
% 1.66/1.46 % (7648)------------------------------
% 1.66/1.46 % (7648)------------------------------
% 1.66/1.46 % (7647)Also succeeded, but the first one will report.
% 1.66/1.46 % (7649)Also succeeded, but the first one will report.
% 1.66/1.46 % (7652)Refutation found. Thanks to Tanya!
% 1.66/1.46 % SZS status Theorem for DTF2THF_7535
% 1.66/1.46 % SZS output start Proof for DTF2THF_7535
% 1.66/1.46 thf(type_def_5, type, frac: $tType).
% 1.66/1.46 thf(func_def_0, type, frac: $tType).
% 1.66/1.46 thf(func_def_1, type, x: frac).
% 1.66/1.46 thf(func_def_2, type, y: frac).
% 1.66/1.46 thf(func_def_3, type, z: frac).
% 1.66/1.46 thf(func_def_4, type, eq: frac > frac > $o).
% 1.66/1.46 thf(func_def_6, type, pf: frac > frac > frac).
% 1.66/1.46 thf(f26,plain,(
% 1.66/1.46 $false),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f25,f21])).
% 1.66/1.46 thf(f21,plain,(
% 1.66/1.46 ((eq @ x @ y) = $true)),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.46 thf(f14,plain,(
% 1.66/1.46 ((eq @ x @ y) = $true)),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.46 thf(f13,plain,(
% 1.66/1.46 (eq @ x @ y)),
% 1.66/1.46 inference(rectify,[status(thm)],[f1])).
% 1.66/1.46 thf(f1,axiom,(
% 1.66/1.46 (eq @ x @ y)),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',e)).
% 1.66/1.46 thf(f25,plain,(
% 1.66/1.46 ((eq @ x @ y) != $true)),
% 1.66/1.46 inference(subsumption_resolution,[status(thm)],[f24,f22])).
% 1.66/1.46 thf(f22,plain,(
% 1.66/1.46 ( ! [X0 : frac] : (((eq @ X0 @ X0) = $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f8])).
% 1.66/1.46 thf(f8,plain,(
% 1.66/1.46 ! [X0 : frac] : ((eq @ X0 @ X0) = $true)),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.46 thf(f7,plain,(
% 1.66/1.46 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.66/1.46 inference(rectify,[status(thm)],[f3])).
% 1.66/1.46 thf(f3,axiom,(
% 1.66/1.46 ! [X0 : frac] : (eq @ X0 @ X0)),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz37)).
% 1.66/1.46 thf(f24,plain,(
% 1.66/1.46 ($true != (eq @ z @ z)) | ((eq @ x @ y) != $true)),
% 1.66/1.46 inference(trivial_inequality_removal,[status(thm)],[f23])).
% 1.66/1.46 thf(f23,plain,(
% 1.66/1.46 ((eq @ x @ y) != $true) | ($true != (eq @ z @ z)) | ($true != $true)),
% 1.66/1.46 inference(superposition,[status(thm)],[f19,f20])).
% 1.66/1.46 thf(f20,plain,(
% 1.66/1.46 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : (($true = (eq @ (pf @ X1 @ X2) @ (pf @ X0 @ X3))) | ($true != (eq @ X1 @ X0)) | ((eq @ X2 @ X3) != $true)) )),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f18])).
% 1.66/1.46 thf(f18,plain,(
% 1.66/1.46 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((eq @ X2 @ X3) != $true) | ($true != (eq @ X1 @ X0)) | ($true = (eq @ (pf @ X1 @ X2) @ (pf @ X0 @ X3))))),
% 1.66/1.46 inference(rectify,[status(thm)],[f17])).
% 1.66/1.46 thf(f17,plain,(
% 1.66/1.46 ! [X2 : frac,X1 : frac,X3 : frac,X0 : frac] : (((eq @ X3 @ X0) != $true) | ($true != (eq @ X1 @ X2)) | ((eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true))),
% 1.66/1.46 inference(flattening,[status(thm)],[f16])).
% 1.66/1.46 thf(f16,plain,(
% 1.66/1.46 ! [X0 : frac,X1 : frac,X3 : frac,X2 : frac] : ((((eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true) | ((eq @ X3 @ X0) != $true)) | ($true != (eq @ X1 @ X2)))),
% 1.66/1.46 inference(ennf_transformation,[status(thm)],[f10])).
% 1.66/1.46 thf(f10,plain,(
% 1.66/1.46 ! [X0 : frac,X1 : frac,X3 : frac,X2 : frac] : (($true = (eq @ X1 @ X2)) => (((eq @ X3 @ X0) = $true) => ((eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X0)) = $true)))),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.46 thf(f9,plain,(
% 1.66/1.46 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X1 @ X2) => ((eq @ X3 @ X0) => (eq @ (pf @ X1 @ X3) @ (pf @ X2 @ X0))))),
% 1.66/1.46 inference(rectify,[status(thm)],[f2])).
% 1.66/1.46 thf(f2,axiom,(
% 1.66/1.46 ! [X3 : frac,X0 : frac,X1 : frac,X2 : frac] : ((eq @ X0 @ X1) => ((eq @ X2 @ X3) => (eq @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz56)).
% 1.66/1.46 thf(f19,plain,(
% 1.66/1.46 ((eq @ (pf @ z @ x) @ (pf @ z @ y)) != $true)),
% 1.66/1.46 inference(cnf_transformation,[status(thm)],[f15])).
% 1.66/1.46 thf(f15,plain,(
% 1.66/1.46 ((eq @ (pf @ z @ x) @ (pf @ z @ y)) != $true)),
% 1.66/1.46 inference(flattening,[status(thm)],[f12])).
% 1.66/1.46 thf(f12,plain,(
% 1.66/1.46 ~((eq @ (pf @ z @ x) @ (pf @ z @ y)) = $true)),
% 1.66/1.46 inference(fool_elimination,[status(thm)],[f11])).
% 1.66/1.46 thf(f11,plain,(
% 1.66/1.46 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.66/1.46 inference(rectify,[status(thm)],[f5])).
% 1.66/1.46 thf(f5,negated_conjecture,(
% 1.66/1.46 ~(eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.66/1.46 inference(negated_conjecture,[status(cth)],[f4])).
% 1.66/1.46 thf(f4,conjecture,(
% 1.66/1.46 (eq @ (pf @ z @ x) @ (pf @ z @ y))),
% 1.66/1.46 file('/export/starexec/sandbox/tmp/tmp.7CWYr191Kh/DTF2THF_7535.p',satz62e)).
% 1.66/1.46 % SZS output end Proof for DTF2THF_7535
% 1.66/1.46 % (7652)------------------------------
% 1.66/1.46 % (7652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.46 % (7652)Termination reason: Refutation
% 1.66/1.46
% 1.66/1.46 % (7652)Memory used [KB]: 5500
% 1.66/1.46 % (7652)Time elapsed: 0.003 s
% 1.66/1.46 % (7652)Instructions burned: 2 (million)
% 1.66/1.46 % (7652)------------------------------
% 1.66/1.46 % (7652)------------------------------
% 1.66/1.46 % (7646)Success in time 0.017 s
%------------------------------------------------------------------------------