%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO237^5 : 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 : n023.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 09:53:44 AM UTC 2026
% Result : Theorem 1.52s 1.28s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 24 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 82 ( 11 ~; 1 |; 6 &; 52 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 14 ^; 7 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
g: $i > $i ).
thf(func_def_1,type,
p: ( $i > $i ) > $o ).
thf(func_def_3,type,
q: $i > $o ).
thf(func_def_4,type,
f: $i > $i ).
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f17,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f16,f10]) ).
thf(f10,plain,
! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( q @ x )
= $true )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
& ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true )
& ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true )
& ( ( q @ x )
= $true )
& ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true )
& ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true )
=> ( ( ( q @ x )
= $true )
=> ( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X1: $i] : ( f @ X1 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X2: $i] : ( g @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X0: $i] : ( g @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( f @ X0 )
= ( g @ X0 ) )
=> ( ( p
@ ^ [X0: $i] : ( f @ X0 ) )
=> ( ( q @ x )
=> ( p
@ ^ [X0: $i] : ( g @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.oAD3K8k3IF/DTF2THF_7666.p',cTHM508) ).
thf(f16,plain,
( ( g @ sK2 )
!= ( f @ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
f != g,
inference(trivial_inequality_removal,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true != $true )
| ( f != g ) ),
inference(constrained_superposition,[status(thm)],[f12,f13]) ).
thf(f13,plain,
( ( p @ f )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( p
@ ^ [Y0: $i] : ( f @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f12,plain,
( $true
!= ( p @ g ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( p
@ ^ [Y0: $i] : ( g @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO237^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 14:27:19 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.22/0.45 ---- Original DTF file ---
% 0.22/0.45 thf(spec,logic,$$dhol).
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 % File : SYO237^5 : TPTP v9.2.1. Released v4.0.0.
% 0.22/0.45 % Domain : Syntactic
% 0.22/0.45 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.22/0.45 % Version : Especial.
% 0.22/0.45 % English :
% 0.22/0.45
% 0.22/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.45 % Source : [Bro09]
% 0.22/0.45 % Names : tps_0793 [Bro09]
% 0.22/0.45
% 0.22/0.45 % Status : Theorem
% 0.22/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.22/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.22/0.45 % Number of atoms : 4 ( 1 equ; 0 cnn)
% 0.22/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.22/0.45 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 7 @)
% 0.22/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.22/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.22/0.45 % Number of types : 2 ( 0 usr)
% 0.22/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.22/0.45 % Number of symbols : 6 ( 5 usr; 1 con; 0-2 aty)
% 0.22/0.45 % Number of variables : 3 ( 2 ^; 1 !; 0 ?; 3 :)
% 0.22/0.45 % SPC : TH0_THM_EQU_NAR
% 0.22/0.45
% 0.22/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 thf(g,type,
% 0.22/0.45 g: $i > $i ).
% 0.22/0.45
% 0.22/0.45 thf(p,type,
% 0.22/0.45 p: ( $i > $i ) > $o ).
% 0.22/0.45
% 0.22/0.45 thf(x,type,
% 0.22/0.45 x: $i ).
% 0.22/0.45
% 0.22/0.45 thf(q,type,
% 0.22/0.45 q: $i > $o ).
% 0.22/0.45
% 0.22/0.45 thf(f,type,
% 0.22/0.45 f: $i > $i ).
% 0.22/0.45
% 0.22/0.45 thf(cTHM508,conjecture,
% 0.22/0.45 ( ! [Xx0: $i] :
% 0.22/0.45 ( ( f @ Xx0 )
% 0.22/0.45 = ( g @ Xx0 ) )
% 0.22/0.45 => ( ( p
% 0.22/0.45 @ ^ [Xx0: $i] : ( f @ Xx0 ) )
% 0.22/0.45 => ( ( q @ x )
% 0.22/0.45 => ( p
% 0.22/0.45 @ ^ [Xx0: $i] : ( g @ Xx0 ) ) ) ) ) ).
% 0.22/0.45
% 0.22/0.45 %------------------------------------------------------------------------------
% 0.22/0.45 ------------------------
% 1.52/1.25 ---- Embedded in THF ---
% 1.52/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.25 %%% Generated on Tue Feb 24 14:27:20 EST 2026
% 1.52/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.25 %%% Logic specification used:
% 1.52/1.25 %%% thf(spec, logic, $$dhol).
% 1.52/1.25
% 1.52/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.oAD3K8k3IF/DTF2DTF7666.p
% See solution above
% 1.52/1.25 ------------------------
% 1.52/1.26 ---- Cleaned THF ---
% 1.52/1.26 thf(g,type,
% 1.52/1.26 g: $i > $i ).
% 1.52/1.26
% 1.52/1.26 thf(p,type,
% 1.52/1.26 p: ( $i > $i ) > $o ).
% 1.52/1.26
% 1.52/1.26 thf(x,type,
% 1.52/1.26 x: $i ).
% 1.52/1.26
% 1.52/1.26 thf(q,type,
% 1.52/1.26 q: $i > $o ).
% 1.52/1.26
% 1.52/1.26 thf(f,type,
% 1.52/1.26 f: $i > $i ).
% 1.52/1.26
% 1.52/1.26 thf(cTHM508,conjecture,
% 1.52/1.26 ( ! [Xx0: $i] :
% 1.52/1.26 ( ( f @ Xx0 )
% 1.52/1.26 = ( g @ Xx0 ) )
% 1.52/1.26 => ( ( p
% 1.52/1.26 @ ^ [Xx0: $i] : ( f @ Xx0 ) )
% 1.52/1.26 => ( ( q @ x )
% 1.52/1.26 => ( p
% 1.52/1.26 @ ^ [Xx0: $i] : ( g @ Xx0 ) ) ) ) ) ).
% 1.52/1.26 ------------------------
% 1.52/1.28 % (7798)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7666 for (3000ds/183Mi)
% 1.52/1.28 % (7803)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_7666 for (3000ds/275Mi)
% 1.52/1.28 % (7804)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7666 for (3000ds/18Mi)
% 1.52/1.28 % (7798)First to succeed.
% 1.52/1.28 % (7803)Refutation not found, incomplete strategy
% 1.52/1.28 % (7803)------------------------------
% 1.52/1.28 % (7803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (7803)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.28
% 1.52/1.28
% 1.52/1.28 % (7803)Memory used [KB]: 5500
% 1.52/1.28 % (7803)Time elapsed: 0.003 s
% 1.52/1.28 % (7803)Instructions burned: 2 (million)
% 1.52/1.28 % (7803)------------------------------
% 1.52/1.28 % (7803)------------------------------
% 1.52/1.28 % (7799)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_7666 for (3000ds/4Mi)
% 1.52/1.28 % (7804)Also succeeded, but the first one will report.
% 1.52/1.28 % (7798)Refutation found. Thanks to Tanya!
% 1.52/1.28 % SZS status Theorem for DTF2THF_7666
% 1.52/1.28 % SZS output start Proof for DTF2THF_7666
% 1.52/1.28 thf(func_def_0, type, g: $i > $i).
% 1.52/1.28 thf(func_def_1, type, p: ($i > $i) > $o).
% 1.52/1.28 thf(func_def_3, type, q: $i > $o).
% 1.52/1.28 thf(func_def_4, type, f: $i > $i).
% 1.52/1.28 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.52/1.28 thf(f17,plain,(
% 1.52/1.28 $false),
% 1.52/1.28 inference(subsumption_resolution,[status(thm)],[f16,f10])).
% 1.52/1.28 thf(f10,plain,(
% 1.52/1.28 ( ! [X0 : $i] : (((f @ X0) = (g @ X0))) )),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.28 thf(f7,plain,(
% 1.52/1.28 ((q @ x) = $true) & ! [X0 : $i] : ((f @ X0) = (g @ X0)) & ((p @ (^[Y0 : $i]: (f @ Y0))) = $true) & ((p @ (^[Y0 : $i]: (g @ Y0))) != $true)),
% 1.52/1.28 inference(flattening,[status(thm)],[f6])).
% 1.52/1.28 thf(f6,plain,(
% 1.52/1.28 ((((p @ (^[Y0 : $i]: (g @ Y0))) != $true) & ((q @ x) = $true)) & ((p @ (^[Y0 : $i]: (f @ Y0))) = $true)) & ! [X0 : $i] : ((f @ X0) = (g @ X0))),
% 1.52/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.28 thf(f5,plain,(
% 1.52/1.28 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => (((p @ (^[Y0 : $i]: (f @ Y0))) = $true) => (((q @ x) = $true) => ((p @ (^[Y0 : $i]: (g @ Y0))) = $true))))),
% 1.52/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.28 thf(f4,plain,(
% 1.52/1.28 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ (^[X1 : $i] : (f @ X1))) => ((q @ x) => (p @ (^[X2 : $i] : (g @ X2))))))),
% 1.52/1.28 inference(rectify,[status(thm)],[f2])).
% 1.52/1.28 thf(f2,negated_conjecture,(
% 1.52/1.28 ~(! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ (^[X0 : $i] : (f @ X0))) => ((q @ x) => (p @ (^[X0 : $i] : (g @ X0))))))),
% 1.52/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.28 thf(f1,conjecture,(
% 1.52/1.28 ! [X0 : $i] : ((f @ X0) = (g @ X0)) => ((p @ (^[X0 : $i] : (f @ X0))) => ((q @ x) => (p @ (^[X0 : $i] : (g @ X0)))))),
% 1.52/1.28 file('/export/starexec/sandbox2/tmp/tmp.oAD3K8k3IF/DTF2THF_7666.p',cTHM508)).
% 1.52/1.28 thf(f16,plain,(
% 1.52/1.28 ((g @ sK2) != (f @ sK2))),
% 1.52/1.28 inference(negative_extensionality,[status(thm)],[f15])).
% 1.52/1.28 thf(f15,plain,(
% 1.52/1.28 (f != g)),
% 1.52/1.28 inference(trivial_inequality_removal,[status(thm)],[f14])).
% 1.52/1.28 thf(f14,plain,(
% 1.52/1.28 ($true != $true) | (f != g)),
% 1.52/1.28 inference(constrained_superposition,[status(thm)],[f12,f13])).
% 1.52/1.28 thf(f13,plain,(
% 1.52/1.28 ((p @ f) = $true)),
% 1.52/1.28 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.52/1.28 thf(f9,plain,(
% 1.52/1.28 ((p @ (^[Y0 : $i]: (f @ Y0))) = $true)),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.28 thf(f12,plain,(
% 1.52/1.28 ($true != (p @ g))),
% 1.52/1.28 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.52/1.28 thf(f8,plain,(
% 1.52/1.28 ((p @ (^[Y0 : $i]: (g @ Y0))) != $true)),
% 1.52/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.52/1.28 % SZS output end Proof for DTF2THF_7666
% 1.52/1.28 % (7798)------------------------------
% 1.52/1.28 % (7798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (7798)Termination reason: Refutation
% 1.52/1.28
% 1.52/1.28 % (7798)Memory used [KB]: 5500
% 1.52/1.28 % (7798)Time elapsed: 0.002 s
% 1.52/1.28 % (7798)Instructions burned: 1 (million)
% 1.52/1.28 % (7798)------------------------------
% 1.52/1.28 % (7798)------------------------------
% 1.52/1.28 % (7797)Success in time 0.004 s
%------------------------------------------------------------------------------