%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU930^5 : 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 : n021.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 09:37:46 AM UTC 2026
% Result : Theorem 1.32s 1.20s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 60 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 147 ( 18 ~; 8 |; 18 &; 87 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 20 ^; 19 !; 3 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_9,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f22,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f21,f13]) ).
thf(f13,plain,
( ( f @ sK0 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
& ( ( f @ sK0 )
!= sK0 )
& ( sK0
= ( g @ sK0 ) )
& ! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( sK0 = X1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( ( f @ X0 )
!= X0 )
& ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( X0 = X1 ) ) )
=> ( ( ( f @ sK0 )
!= sK0 )
& ( sK0
= ( g @ sK0 ) )
& ! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( sK0 = X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
& ? [X0: $i] :
( ( ( f @ X0 )
!= X0 )
& ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( X0 = X1 ) ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( ( f @ X0 )
!= X0 )
& ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( X0 = X1 ) ) )
& ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X0 = X1 ) ) )
=> ( ( f @ X0 )
= X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) )
=> ! [X2: $i] :
( ( ( ( g @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( g @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
=> ( ( f @ X2 )
= X2 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X1: $i] : ( f @ ( g @ X1 ) ) ) )
=> ! [X2: $i] :
( ( ( ( g @ X2 )
= X2 )
& ! [X3: $i] :
( ( ( g @ X3 )
= X3 )
=> ( X2 = X3 ) ) )
=> ( ( f @ X2 )
= X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X0 = X1 ) ) )
=> ( ( f @ X0 )
= X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ^ [X0: $i] : ( g @ ( f @ X0 ) ) )
= ( ^ [X0: $i] : ( f @ ( g @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ( ( g @ X0 )
= X0 )
& ! [X1: $i] :
( ( ( g @ X1 )
= X1 )
=> ( X0 = X1 ) ) )
=> ( ( f @ X0 )
= X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eRFf7rXyyG/DTF2THF_15614.p',cTHM171A_pme) ).
thf(f21,plain,
( ( f @ sK0 )
= sK0 ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( f @ sK0 )
= sK0 )
| ( ( f @ sK0 )
!= ( f @ sK0 ) ) ),
inference(superposition,[status(thm)],[f18,f12]) ).
thf(f12,plain,
( sK0
= ( g @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f18,plain,
! [X0: $i] :
( ( ( f @ ( g @ X0 ) )
!= ( f @ X0 ) )
| ( ( f @ X0 )
= sK0 ) ),
inference(superposition,[status(thm)],[f11,f17]) ).
thf(f17,plain,
! [X1: $i] :
( ( f @ ( g @ X1 ) )
= ( g @ ( f @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: $i] : ( g @ ( f @ Y0 ) ) )
= ( ^ [Y0: $i] : ( f @ ( g @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f11,plain,
! [X1: $i] :
( ( ( g @ X1 )
!= X1 )
| ( sK0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU930^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n021.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 12:37:23 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.40 ---- Original DTF file ---
% 0.17/0.40 thf(spec,logic,$$dhol).
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 % File : SEU930^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.40 % Domain : Set Theory (Functions)
% 0.17/0.40 % Problem : TPS problem THM171A
% 0.17/0.40 % Version : Especial.
% 0.17/0.40 % English : If g commutes with f, any unique fixed point of gi is a fixed
% 0.17/0.40 % point of f.
% 0.17/0.40
% 0.17/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.40 % Source : [Bro09]
% 0.17/0.40 % Names : tps_0250 [Bro09]
% 0.17/0.40 % : THM171A [TPS]
% 0.17/0.40
% 0.17/0.40 % Status : Theorem
% 0.17/0.40 % 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, 0.12 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 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.40 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.17/0.40 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.17/0.40 % Maximal formula atoms : 5 ( 5 avg)
% 0.17/0.40 % Number of connectives : 11 ( 0 ~; 0 |; 1 &; 7 @)
% 0.17/0.40 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.17/0.40 % Maximal formula depth : 7 ( 7 avg)
% 0.17/0.40 % Number of types : 1 ( 0 usr)
% 0.17/0.40 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.17/0.40 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.40 % Number of variables : 4 ( 2 ^; 2 !; 0 ?; 4 :)
% 0.17/0.40 % SPC : TH0_THM_EQU_NAR
% 0.17/0.40
% 0.17/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.40 % : Polymorphic definitions expanded.
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 thf(f,type,
% 0.17/0.40 f: $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(g,type,
% 0.17/0.40 g: $i > $i ).
% 0.17/0.40
% 0.17/0.40 thf(cTHM171A_pme,conjecture,
% 0.17/0.40 ( ( ( ^ [Xx: $i] : ( f @ ( g @ Xx ) ) )
% 0.17/0.40 = ( ^ [Xx: $i] : ( g @ ( f @ Xx ) ) ) )
% 0.17/0.40 => ! [Xx: $i] :
% 0.17/0.40 ( ( ( ( g @ Xx )
% 0.17/0.40 = Xx )
% 0.17/0.40 & ! [Xz: $i] :
% 0.17/0.40 ( ( ( g @ Xz )
% 0.17/0.40 = Xz )
% 0.17/0.40 => ( Xz = Xx ) ) )
% 0.17/0.40 => ( ( f @ Xx )
% 0.17/0.40 = Xx ) ) ) ).
% 0.17/0.40
% 0.17/0.40 %------------------------------------------------------------------------------
% 0.17/0.40 ------------------------
% 1.20/1.17 ---- Embedded in THF ---
% 1.20/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.20/1.17 %%% Generated on Tue Feb 24 12:37:24 EST 2026
% 1.20/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.20/1.17 %%% Logic specification used:
% 1.20/1.17 %%% thf(spec, logic, $$dhol).
% 1.20/1.17
% 1.20/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eRFf7rXyyG/DTF2DTF15614.p
% See solution above
% 1.20/1.17 ------------------------
% 1.20/1.18 ---- Cleaned THF ---
% 1.20/1.18 thf(f,type,
% 1.20/1.18 f: $i > $i ).
% 1.20/1.18
% 1.20/1.18 thf(g,type,
% 1.20/1.18 g: $i > $i ).
% 1.20/1.18
% 1.20/1.18 thf(cTHM171A_pme,conjecture,
% 1.20/1.18 ( ( ( ^ [Xx: $i] : ( f @ ( g @ Xx ) ) )
% 1.20/1.18 = ( ^ [Xx: $i] : ( g @ ( f @ Xx ) ) ) )
% 1.20/1.18 => ! [Xx: $i] :
% 1.20/1.18 ( ( ( ( g @ Xx )
% 1.20/1.18 = Xx )
% 1.20/1.18 & ! [Xz: $i] :
% 1.20/1.18 ( ( ( g @ Xz )
% 1.20/1.18 = Xz )
% 1.20/1.18 => ( Xz = Xx ) ) )
% 1.20/1.18 => ( ( f @ Xx )
% 1.20/1.18 = Xx ) ) ) ).
% 1.20/1.18 ------------------------
% 1.20/1.19 % (15712)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15614 for (3000ds/183Mi)
% 1.20/1.19 % (15712)First to succeed.
% 1.32/1.20 % (15712)Refutation found. Thanks to Tanya!
% 1.32/1.20 % SZS status Theorem for DTF2THF_15614
% 1.32/1.20 % SZS output start Proof for DTF2THF_15614
% 1.32/1.20 thf(func_def_0, type, f: $i > $i).
% 1.32/1.20 thf(func_def_1, type, g: $i > $i).
% 1.32/1.20 thf(func_def_9, type, ph2: !>[X0: $tType]:(X0)).
% 1.32/1.20 thf(f22,plain,(
% 1.32/1.20 $false),
% 1.32/1.20 inference(subsumption_resolution,[status(thm)],[f21,f13])).
% 1.32/1.20 thf(f13,plain,(
% 1.32/1.20 ((f @ sK0) != sK0)),
% 1.32/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.20 thf(f10,plain,(
% 1.32/1.20 ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) & (((f @ sK0) != sK0) & (sK0 = (g @ sK0)) & ! [X1 : $i] : (((g @ X1) != X1) | (sK0 = X1)))),
% 1.32/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.32/1.20 thf(f9,plain,(
% 1.32/1.20 ? [X0 : $i] : (((f @ X0) != X0) & ((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) != X1) | (X0 = X1))) => (((f @ sK0) != sK0) & (sK0 = (g @ sK0)) & ! [X1 : $i] : (((g @ X1) != X1) | (sK0 = X1)))),
% 1.32/1.20 introduced(definition,[],[choice_axiom])).
% 1.32/1.20 thf(f8,plain,(
% 1.32/1.20 ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) & ? [X0 : $i] : (((f @ X0) != X0) & ((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) != X1) | (X0 = X1)))),
% 1.32/1.20 inference(flattening,[status(thm)],[f7])).
% 1.32/1.20 thf(f7,plain,(
% 1.32/1.20 ? [X0 : $i] : (((f @ X0) != X0) & (((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) != X1) | (X0 = X1)))) & ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0))))),
% 1.32/1.20 inference(ennf_transformation,[status(thm)],[f6])).
% 1.32/1.20 thf(f6,plain,(
% 1.32/1.20 ~(((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) => ! [X0 : $i] : ((((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) = X1) => (X0 = X1))) => ((f @ X0) = X0)))),
% 1.32/1.20 inference(rectify,[status(thm)],[f5])).
% 1.32/1.20 thf(f5,plain,(
% 1.32/1.20 ~(((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0)))) => ! [X2 : $i] : ((((g @ X2) = X2) & ! [X3 : $i] : (((g @ X3) = X3) => (X2 = X3))) => ((f @ X2) = X2)))),
% 1.32/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.32/1.20 thf(f4,plain,(
% 1.32/1.20 ~(((^[X0 : $i] : (g @ (f @ X0))) = (^[X1 : $i] : (f @ (g @ X1)))) => ! [X2 : $i] : ((((g @ X2) = X2) & ! [X3 : $i] : (((g @ X3) = X3) => (X2 = X3))) => ((f @ X2) = X2)))),
% 1.32/1.20 inference(rectify,[status(thm)],[f2])).
% 1.32/1.20 thf(f2,negated_conjecture,(
% 1.32/1.20 ~(((^[X0 : $i] : (g @ (f @ X0))) = (^[X0 : $i] : (f @ (g @ X0)))) => ! [X0 : $i] : ((((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) = X1) => (X0 = X1))) => ((f @ X0) = X0)))),
% 1.32/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.32/1.20 thf(f1,conjecture,(
% 1.32/1.20 ((^[X0 : $i] : (g @ (f @ X0))) = (^[X0 : $i] : (f @ (g @ X0)))) => ! [X0 : $i] : ((((g @ X0) = X0) & ! [X1 : $i] : (((g @ X1) = X1) => (X0 = X1))) => ((f @ X0) = X0))),
% 1.32/1.20 file('/export/starexec/sandbox/tmp/tmp.eRFf7rXyyG/DTF2THF_15614.p',cTHM171A_pme)).
% 1.32/1.20 thf(f21,plain,(
% 1.32/1.20 ((f @ sK0) = sK0)),
% 1.32/1.20 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.32/1.20 thf(f19,plain,(
% 1.32/1.20 ((f @ sK0) = sK0) | ((f @ sK0) != (f @ sK0))),
% 1.32/1.20 inference(superposition,[status(thm)],[f18,f12])).
% 1.32/1.20 thf(f12,plain,(
% 1.32/1.20 (sK0 = (g @ sK0))),
% 1.32/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.20 thf(f18,plain,(
% 1.32/1.20 ( ! [X0 : $i] : (((f @ (g @ X0)) != (f @ X0)) | ((f @ X0) = sK0)) )),
% 1.32/1.20 inference(superposition,[status(thm)],[f11,f17])).
% 1.32/1.20 thf(f17,plain,(
% 1.32/1.20 ( ! [X1 : $i] : (((f @ (g @ X1)) = (g @ (f @ X1)))) )),
% 1.32/1.20 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.32/1.20 thf(f16,plain,(
% 1.32/1.20 ( ! [X1 : $i] : ((((^[Y0 : $i]: (f @ (g @ Y0))) @ X1) = ((^[Y0 : $i]: (g @ (f @ Y0))) @ X1))) )),
% 1.32/1.20 inference(argument_congruence,[status(thm)],[f14])).
% 1.32/1.20 thf(f14,plain,(
% 1.32/1.20 ((^[Y0 : $i]: (g @ (f @ Y0))) = (^[Y0 : $i]: (f @ (g @ Y0))))),
% 1.32/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.20 thf(f11,plain,(
% 1.32/1.20 ( ! [X1 : $i] : (((g @ X1) != X1) | (sK0 = X1)) )),
% 1.32/1.20 inference(cnf_transformation,[status(thm)],[f10])).
% 1.32/1.20 % SZS output end Proof for DTF2THF_15614
% 1.32/1.20 % (15712)------------------------------
% 1.32/1.20 % (15712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.32/1.20 % (15712)Termination reason: Refutation
% 1.32/1.20
% 1.32/1.20 % (15712)Memory used [KB]: 5500
% 1.32/1.20 % (15712)Time elapsed: 0.003 s
% 1.32/1.20 % (15712)Instructions burned: 1 (million)
% 1.32/1.20 % (15712)------------------------------
% 1.32/1.20 % (15712)------------------------------
% 1.32/1.20 % (15711)Success in time 0.012 s
%------------------------------------------------------------------------------