%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU919^5 : 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 : n015.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 09:37:45 AM UTC 2026
% Result : Theorem 1.49s 1.25s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 19 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 103 ( 8 ~; 0 |; 4 &; 83 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 16 ^; 2 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
g: $i > $i ).
thf(func_def_3,type,
cP: $i > $o ).
thf(func_def_5,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f15,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
$true != $true,
inference(superposition,[status(thm)],[f13,f10]) ).
thf(f10,plain,
( ( cP @ ( f @ ( g @ a ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
& ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
& ( ( cP @ ( g @ ( f @ a ) ) )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP @ ( g @ ( f @ a ) ) )
!= $true )
& ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
& ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
=> ( ( ( cP @ ( f @ ( g @ a ) ) )
= $true )
=> ( ( cP @ ( g @ ( f @ a ) ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) )
= ( ^ [X1: $i] : ( g @ ( f @ X1 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) )
= ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) )
= ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) ) )
=> ( ( cP @ ( f @ ( g @ a ) ) )
=> ( cP @ ( g @ ( f @ a ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ILAfEcZ5Qh/DTF2THF_807.p',cTHM127_pme) ).
thf(f13,plain,
( ( cP @ ( f @ ( g @ a ) ) )
!= $true ),
inference(backward_demodulation,[status(thm)],[f8,f12]) ).
thf(f12,plain,
! [X1: $i] :
( ( f @ ( g @ X1 ) )
= ( g @ ( f @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f8,plain,
( ( cP @ ( g @ ( f @ a ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU919^5 : 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 : n015.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 12:37:16 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU919^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory (Functions)
% 0.28/0.46 % Problem : TPS problem THM127
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0111 [Bro09]
% 0.28/0.46 % : THM127 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.28/0.46 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.28/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.28/0.46 % Number of connectives : 12 ( 0 ~; 0 |; 0 &; 10 @)
% 0.28/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 6 ( 6 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(a,type,
% 0.28/0.46 a: $i ).
% 0.28/0.46
% 0.28/0.46 thf(f,type,
% 0.28/0.46 f: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(g,type,
% 0.28/0.46 g: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(cP,type,
% 0.28/0.46 cP: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(cTHM127_pme,conjecture,
% 0.28/0.46 ( ( ( ^ [Xx: $i] : ( f @ ( g @ Xx ) ) )
% 0.28/0.46 = ( ^ [Xx: $i] : ( g @ ( f @ Xx ) ) ) )
% 0.28/0.46 => ( ( cP @ ( f @ ( g @ a ) ) )
% 0.28/0.46 => ( cP @ ( g @ ( f @ a ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.49/1.22 ---- Embedded in THF ---
% 1.49/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.22 %%% Generated on Tue Feb 24 12:37:17 EST 2026
% 1.49/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.22 %%% Logic specification used:
% 1.49/1.22 %%% thf(spec, logic, $$dhol).
% 1.49/1.22
% 1.49/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ILAfEcZ5Qh/DTF2DTF807.p
% See solution above
% 1.49/1.22 ------------------------
% 1.49/1.23 ---- Cleaned THF ---
% 1.49/1.23 thf(a,type,
% 1.49/1.23 a: $i ).
% 1.49/1.23
% 1.49/1.23 thf(f,type,
% 1.49/1.23 f: $i > $i ).
% 1.49/1.23
% 1.49/1.23 thf(g,type,
% 1.49/1.23 g: $i > $i ).
% 1.49/1.23
% 1.49/1.23 thf(cP,type,
% 1.49/1.23 cP: $i > $o ).
% 1.49/1.23
% 1.49/1.23 thf(cTHM127_pme,conjecture,
% 1.49/1.23 ( ( ( ^ [Xx: $i] : ( f @ ( g @ Xx ) ) )
% 1.49/1.23 = ( ^ [Xx: $i] : ( g @ ( f @ Xx ) ) ) )
% 1.49/1.23 => ( ( cP @ ( f @ ( g @ a ) ) )
% 1.49/1.23 => ( cP @ ( g @ ( f @ a ) ) ) ) ) ).
% 1.49/1.23 ------------------------
% 1.49/1.25 % (910)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_807 for (2999ds/27Mi)
% 1.49/1.25 % (909)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_807 for (2999ds/4Mi)
% 1.49/1.25 % (910)First to succeed.
% 1.49/1.25 % (909)Also succeeded, but the first one will report.
% 1.49/1.25 % (910)Refutation found. Thanks to Tanya!
% 1.49/1.25 % SZS status Theorem for DTF2THF_807
% 1.49/1.25 % SZS output start Proof for DTF2THF_807
% 1.49/1.25 thf(func_def_1, type, f: $i > $i).
% 1.49/1.25 thf(func_def_2, type, g: $i > $i).
% 1.49/1.25 thf(func_def_3, type, cP: $i > $o).
% 1.49/1.25 thf(func_def_5, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.49/1.25 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.49/1.25 thf(f15,plain,(
% 1.49/1.25 $false),
% 1.49/1.25 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.49/1.25 thf(f14,plain,(
% 1.49/1.25 ($true != $true)),
% 1.49/1.25 inference(superposition,[status(thm)],[f13,f10])).
% 1.49/1.25 thf(f10,plain,(
% 1.49/1.25 ((cP @ (f @ (g @ a))) = $true)),
% 1.49/1.25 inference(cnf_transformation,[status(thm)],[f7])).
% 1.49/1.25 thf(f7,plain,(
% 1.49/1.25 ((cP @ (f @ (g @ a))) = $true) & ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) & ((cP @ (g @ (f @ a))) != $true)),
% 1.49/1.25 inference(flattening,[status(thm)],[f6])).
% 1.49/1.25 thf(f6,plain,(
% 1.49/1.25 (((cP @ (g @ (f @ a))) != $true) & ((cP @ (f @ (g @ a))) = $true)) & ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0))))),
% 1.49/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.25 thf(f5,plain,(
% 1.49/1.25 ~(((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) => (((cP @ (f @ (g @ a))) = $true) => ((cP @ (g @ (f @ a))) = $true)))),
% 1.49/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.25 thf(f4,plain,(
% 1.49/1.25 ~(((^[X0 : $i] : (f @ (g @ X0))) = (^[X1 : $i] : (g @ (f @ X1)))) => ((cP @ (f @ (g @ a))) => (cP @ (g @ (f @ a)))))),
% 1.49/1.25 inference(rectify,[status(thm)],[f2])).
% 1.49/1.25 thf(f2,negated_conjecture,(
% 1.49/1.25 ~(((^[X0 : $i] : (f @ (g @ X0))) = (^[X0 : $i] : (g @ (f @ X0)))) => ((cP @ (f @ (g @ a))) => (cP @ (g @ (f @ a)))))),
% 1.49/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.25 thf(f1,conjecture,(
% 1.49/1.25 ((^[X0 : $i] : (f @ (g @ X0))) = (^[X0 : $i] : (g @ (f @ X0)))) => ((cP @ (f @ (g @ a))) => (cP @ (g @ (f @ a))))),
% 1.49/1.25 file('/export/starexec/sandbox/tmp/tmp.ILAfEcZ5Qh/DTF2THF_807.p',cTHM127_pme)).
% 1.49/1.25 thf(f13,plain,(
% 1.49/1.25 ((cP @ (f @ (g @ a))) != $true)),
% 1.49/1.25 inference(backward_demodulation,[status(thm)],[f8,f12])).
% 1.49/1.25 thf(f12,plain,(
% 1.49/1.25 ( ! [X1 : $i] : (((f @ (g @ X1)) = (g @ (f @ X1)))) )),
% 1.49/1.25 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.49/1.25 thf(f11,plain,(
% 1.49/1.25 ( ! [X1 : $i] : ((((^[Y0 : $i]: (f @ (g @ Y0))) @ X1) = ((^[Y0 : $i]: (g @ (f @ Y0))) @ X1))) )),
% 1.49/1.25 inference(argument_congruence,[status(thm)],[f9])).
% 1.49/1.25 thf(f9,plain,(
% 1.49/1.25 ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0))))),
% 1.49/1.25 inference(cnf_transformation,[status(thm)],[f7])).
% 1.49/1.25 thf(f8,plain,(
% 1.49/1.25 ((cP @ (g @ (f @ a))) != $true)),
% 1.49/1.25 inference(cnf_transformation,[status(thm)],[f7])).
% 1.49/1.25 % SZS output end Proof for DTF2THF_807
% 1.49/1.25 % (910)------------------------------
% 1.49/1.25 % (910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.25 % (910)Termination reason: Refutation
% 1.49/1.25
% 1.49/1.25 % (910)Memory used [KB]: 5500
% 1.49/1.25 % (910)Time elapsed: 0.002 s
% 1.49/1.25 % (910)Instructions burned: 1 (million)
% 1.49/1.25 % (910)------------------------------
% 1.49/1.25 % (910)------------------------------
% 1.49/1.25 % (906)Success in time 0.012 s
%------------------------------------------------------------------------------