TSTP Solution File: SEU823^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU823^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.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 : Tue May 21 03:51:50 EDT 2024
% Result : Theorem 0.17s 0.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU823^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.16 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.17/0.38 % Computer : n004.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun May 19 16:56:08 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.17/0.38 This is a TH0_THM_EQU_NAR problem
% 0.17/0.38 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.40 % (31802)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.17/0.40 % (31796)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.17/0.40 % (31797)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 theBenchmark for (2999ds/4Mi)
% 0.17/0.40 % (31798)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 theBenchmark for (2999ds/27Mi)
% 0.17/0.40 % (31799)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.40 % (31800)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.40 % (31801)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.17/0.40 % (31803)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.40 % (31799)Instruction limit reached!
% 0.17/0.40 % (31799)------------------------------
% 0.17/0.40 % (31799)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (31799)Termination reason: Unknown
% 0.17/0.40 % (31799)Termination phase: Property scanning
% 0.17/0.40
% 0.17/0.40 % (31800)Instruction limit reached!
% 0.17/0.40 % (31800)------------------------------
% 0.17/0.40 % (31800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (31800)Termination reason: Unknown
% 0.17/0.40 % (31800)Termination phase: shuffling
% 0.17/0.40
% 0.17/0.40 % (31800)Memory used [KB]: 1023
% 0.17/0.40 % (31800)Time elapsed: 0.003 s
% 0.17/0.40 % (31800)Instructions burned: 2 (million)
% 0.17/0.40 % (31800)------------------------------
% 0.17/0.40 % (31800)------------------------------
% 0.17/0.40 % (31799)Memory used [KB]: 1023
% 0.17/0.40 % (31799)Time elapsed: 0.003 s
% 0.17/0.40 % (31799)Instructions burned: 2 (million)
% 0.17/0.40 % (31799)------------------------------
% 0.17/0.40 % (31799)------------------------------
% 0.17/0.40 % (31797)Instruction limit reached!
% 0.17/0.40 % (31797)------------------------------
% 0.17/0.40 % (31797)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (31797)Termination reason: Unknown
% 0.17/0.40 % (31797)Termination phase: Function definition elimination
% 0.17/0.40
% 0.17/0.40 % (31797)Memory used [KB]: 1023
% 0.17/0.40 % (31797)Time elapsed: 0.004 s
% 0.17/0.40 % (31797)Instructions burned: 4 (million)
% 0.17/0.40 % (31797)------------------------------
% 0.17/0.40 % (31797)------------------------------
% 0.17/0.40 % (31803)Instruction limit reached!
% 0.17/0.40 % (31803)------------------------------
% 0.17/0.40 % (31803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.40 % (31803)Termination reason: Unknown
% 0.17/0.40 % (31803)Termination phase: Property scanning
% 0.17/0.40
% 0.17/0.40 % (31803)Memory used [KB]: 1023
% 0.17/0.40 % (31803)Time elapsed: 0.004 s
% 0.17/0.40 % (31803)Instructions burned: 4 (million)
% 0.17/0.40 % (31803)------------------------------
% 0.17/0.40 % (31803)------------------------------
% 0.17/0.40 % (31801)First to succeed.
% 0.17/0.41 % (31802)Instruction limit reached!
% 0.17/0.41 % (31802)------------------------------
% 0.17/0.41 % (31802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (31802)Termination reason: Unknown
% 0.17/0.41 % (31802)Termination phase: Saturation
% 0.17/0.41
% 0.17/0.41 % (31802)Memory used [KB]: 5500
% 0.17/0.41 % (31802)Time elapsed: 0.010 s
% 0.17/0.41 % (31802)Instructions burned: 18 (million)
% 0.17/0.41 % (31802)------------------------------
% 0.17/0.41 % (31802)------------------------------
% 0.17/0.41 % (31801)Refutation found. Thanks to Tanya!
% 0.17/0.41 % SZS status Theorem for theBenchmark
% 0.17/0.41 % SZS output start Proof for theBenchmark
% 0.17/0.41 thf(func_def_0, type, in: $i > $i > $o).
% 0.17/0.41 thf(func_def_1, type, powerset: $i > $i).
% 0.17/0.41 thf(func_def_2, type, nonempty: $i > $o).
% 0.17/0.41 thf(func_def_3, type, transitiveset: $i > $o).
% 0.17/0.41 thf(func_def_4, type, stricttotalorderedByIn: $i > $o).
% 0.17/0.41 thf(func_def_6, type, wellorderedByIn: $i > $o).
% 0.17/0.41 thf(func_def_7, type, ordinal: $i > $o).
% 0.17/0.41 thf(f103,plain,(
% 0.17/0.41 $false),
% 0.17/0.41 inference(avatar_sat_refutation,[],[f95,f102])).
% 0.17/0.41 thf(f102,plain,(
% 0.17/0.41 ~spl7_2),
% 0.17/0.41 inference(avatar_contradiction_clause,[],[f101])).
% 0.17/0.41 thf(f101,plain,(
% 0.17/0.41 $false | ~spl7_2),
% 0.17/0.41 inference(subsumption_resolution,[],[f100,f53])).
% 0.17/0.41 thf(f53,plain,(
% 0.17/0.41 ((ordinal @ sK5) = $true)),
% 0.17/0.41 inference(cnf_transformation,[],[f40])).
% 0.17/0.41 thf(f40,plain,(
% 0.17/0.41 (ordinalTransSet = $true) & (((ordinal @ sK5) = $true) & (((in @ sK6 @ sK5) = $true) & ((in @ sK5 @ sK6) = $true))) & (ordinalIrrefl = $true)),
% 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f24,f39,f38])).
% 0.17/0.41 thf(f38,plain,(
% 0.17/0.41 ? [X0] : (((ordinal @ X0) = $true) & ? [X1] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true))) => (((ordinal @ sK5) = $true) & ? [X1] : (((in @ X1 @ sK5) = $true) & ((in @ sK5 @ X1) = $true)))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f39,plain,(
% 0.17/0.41 ? [X1] : (((in @ X1 @ sK5) = $true) & ((in @ sK5 @ X1) = $true)) => (((in @ sK6 @ sK5) = $true) & ((in @ sK5 @ sK6) = $true))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f24,plain,(
% 0.17/0.41 (ordinalTransSet = $true) & ? [X0] : (((ordinal @ X0) = $true) & ? [X1] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true))) & (ordinalIrrefl = $true)),
% 0.17/0.41 inference(flattening,[],[f23])).
% 0.17/0.41 thf(f23,plain,(
% 0.17/0.41 (? [X0] : (((ordinal @ X0) = $true) & ? [X1] : (((in @ X1 @ X0) = $true) & ((in @ X0 @ X1) = $true))) & (ordinalIrrefl = $true)) & (ordinalTransSet = $true)),
% 0.17/0.41 inference(ennf_transformation,[],[f21])).
% 0.17/0.41 thf(f21,plain,(
% 0.17/0.41 ~((ordinalTransSet = $true) => ((ordinalIrrefl = $true) => ! [X0] : (((ordinal @ X0) = $true) => ! [X1] : (((in @ X0 @ X1) = $true) => ((in @ X1 @ X0) != $true)))))),
% 0.17/0.41 inference(flattening,[],[f18])).
% 0.17/0.41 thf(f18,plain,(
% 0.17/0.41 ~((ordinalTransSet = $true) => ((ordinalIrrefl = $true) => ! [X0] : (((ordinal @ X0) = $true) => ! [X1] : (((in @ X0 @ X1) = $true) => ~((in @ X1 @ X0) = $true)))))),
% 0.17/0.41 inference(fool_elimination,[],[f17])).
% 0.17/0.41 thf(f17,plain,(
% 0.17/0.41 ~(ordinalTransSet => (ordinalIrrefl => ! [X0] : ((ordinal @ X0) => ! [X1] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)))))),
% 0.17/0.41 inference(rectify,[],[f7])).
% 0.17/0.41 thf(f7,negated_conjecture,(
% 0.17/0.41 ~(ordinalTransSet => (ordinalIrrefl => ! [X2] : ((ordinal @ X2) => ! [X0] : ((in @ X2 @ X0) => ~(in @ X0 @ X2)))))),
% 0.17/0.41 inference(negated_conjecture,[],[f6])).
% 0.17/0.41 thf(f6,conjecture,(
% 0.17/0.41 ordinalTransSet => (ordinalIrrefl => ! [X2] : ((ordinal @ X2) => ! [X0] : ((in @ X2 @ X0) => ~(in @ X0 @ X2))))),
% 0.17/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalNoCycle)).
% 0.17/0.41 thf(f100,plain,(
% 0.17/0.41 ((ordinal @ sK5) != $true) | ~spl7_2),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f96])).
% 0.17/0.41 thf(f96,plain,(
% 0.17/0.41 ($true != $true) | ((ordinal @ sK5) != $true) | ~spl7_2),
% 0.17/0.41 inference(superposition,[],[f84,f52])).
% 0.17/0.41 thf(f52,plain,(
% 0.17/0.41 ((in @ sK6 @ sK5) = $true)),
% 0.17/0.41 inference(cnf_transformation,[],[f40])).
% 0.17/0.41 thf(f84,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((in @ sK6 @ X0) != $true) | ((ordinal @ X0) != $true)) ) | ~spl7_2),
% 0.17/0.41 inference(avatar_component_clause,[],[f83])).
% 0.17/0.41 thf(f83,plain,(
% 0.17/0.41 spl7_2 <=> ! [X0] : (((ordinal @ X0) != $true) | ((in @ sK6 @ X0) != $true))),
% 0.17/0.41 introduced(avatar_definition,[new_symbols(naming,[spl7_2])])).
% 0.17/0.41 thf(f95,plain,(
% 0.17/0.41 spl7_2),
% 0.17/0.41 inference(avatar_split_clause,[],[f93,f83])).
% 0.17/0.41 thf(f93,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK6 @ X0) != $true)) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f91])).
% 0.17/0.41 thf(f91,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((in @ sK6 @ X0) != $true) | ($true != $true) | ((ordinal @ X0) != $true)) )),
% 0.17/0.41 inference(superposition,[],[f89,f51])).
% 0.17/0.41 thf(f51,plain,(
% 0.17/0.41 ((in @ sK5 @ sK6) = $true)),
% 0.17/0.41 inference(cnf_transformation,[],[f40])).
% 0.17/0.41 thf(f89,plain,(
% 0.17/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ sK5 @ X1) != $true) | ((in @ X1 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f88])).
% 0.17/0.41 thf(f88,plain,(
% 0.17/0.41 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ sK5 @ X1) != $true) | ((in @ X1 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.17/0.41 inference(duplicate_literal_removal,[],[f87])).
% 0.17/0.41 thf(f87,plain,(
% 0.17/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((ordinal @ X0) != $true) | ((in @ sK5 @ X1) != $true) | ((ordinal @ X0) != $true) | ($true != $true)) )),
% 0.17/0.41 inference(superposition,[],[f76,f64])).
% 0.17/0.41 thf(f64,plain,(
% 0.17/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) = $true) | ((in @ X4 @ X5) != $true) | ($true != (ordinal @ X3)) | ($true != (in @ X5 @ X3))) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f63])).
% 0.17/0.41 thf(f63,plain,(
% 0.17/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X5 @ X3)) | ($true != (ordinal @ X3)) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) )),
% 0.17/0.41 inference(definition_unfolding,[],[f45,f54])).
% 0.17/0.41 thf(f54,plain,(
% 0.17/0.41 (ordinalTransSet = $true)),
% 0.17/0.41 inference(cnf_transformation,[],[f40])).
% 0.17/0.41 thf(f45,plain,(
% 0.17/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true) | ($true != (ordinal @ X3)) | (ordinalTransSet != $true)) )),
% 0.17/0.41 inference(cnf_transformation,[],[f37])).
% 0.17/0.41 thf(f37,plain,(
% 0.17/0.41 ((ordinalTransSet = $true) | ((($true = (in @ sK4 @ sK2)) & ((in @ sK3 @ sK4) = $true) & ($true != (in @ sK3 @ sK2))) & ((ordinal @ sK2) = $true))) & (! [X3] : (! [X4,X5] : (($true != (in @ X5 @ X3)) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) | ($true != (ordinal @ X3))) | (ordinalTransSet != $true))),
% 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f34,f36,f35])).
% 0.17/0.41 thf(f35,plain,(
% 0.17/0.41 ? [X0] : (? [X1,X2] : (((in @ X2 @ X0) = $true) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true)) & ((ordinal @ X0) = $true)) => (? [X2,X1] : (($true = (in @ X2 @ sK2)) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ sK2) != $true)) & ((ordinal @ sK2) = $true))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f36,plain,(
% 0.17/0.41 ? [X2,X1] : (($true = (in @ X2 @ sK2)) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ sK2) != $true)) => (($true = (in @ sK4 @ sK2)) & ((in @ sK3 @ sK4) = $true) & ($true != (in @ sK3 @ sK2)))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f34,plain,(
% 0.17/0.41 ((ordinalTransSet = $true) | ? [X0] : (? [X1,X2] : (((in @ X2 @ X0) = $true) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true)) & ((ordinal @ X0) = $true))) & (! [X3] : (! [X4,X5] : (($true != (in @ X5 @ X3)) | ((in @ X4 @ X5) != $true) | ((in @ X4 @ X3) = $true)) | ($true != (ordinal @ X3))) | (ordinalTransSet != $true))),
% 0.17/0.41 inference(rectify,[],[f33])).
% 0.17/0.41 thf(f33,plain,(
% 0.17/0.41 ((ordinalTransSet = $true) | ? [X0] : (? [X1,X2] : (((in @ X2 @ X0) = $true) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) != $true)) & ((ordinal @ X0) = $true))) & (! [X0] : (! [X1,X2] : (((in @ X2 @ X0) != $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true)) | ((ordinal @ X0) != $true)) | (ordinalTransSet != $true))),
% 0.17/0.41 inference(nnf_transformation,[],[f26])).
% 0.17/0.41 thf(f26,plain,(
% 0.17/0.41 (ordinalTransSet = $true) <=> ! [X0] : (! [X1,X2] : (((in @ X2 @ X0) != $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) = $true)) | ((ordinal @ X0) != $true))),
% 0.17/0.41 inference(flattening,[],[f25])).
% 0.17/0.41 thf(f25,plain,(
% 0.17/0.41 ! [X0] : (! [X1,X2] : ((((in @ X1 @ X0) = $true) | ((in @ X1 @ X2) != $true)) | ((in @ X2 @ X0) != $true)) | ((ordinal @ X0) != $true)) <=> (ordinalTransSet = $true)),
% 0.17/0.41 inference(ennf_transformation,[],[f10])).
% 0.17/0.41 thf(f10,plain,(
% 0.17/0.41 ! [X0] : (((ordinal @ X0) = $true) => ! [X1,X2] : (((in @ X2 @ X0) = $true) => (((in @ X1 @ X2) = $true) => ((in @ X1 @ X0) = $true)))) <=> (ordinalTransSet = $true)),
% 0.17/0.41 inference(fool_elimination,[],[f9])).
% 0.17/0.41 thf(f9,plain,(
% 0.17/0.41 (ordinalTransSet = ! [X0] : ((ordinal @ X0) => ! [X1,X2] : ((in @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0)))))),
% 0.17/0.41 inference(rectify,[],[f4])).
% 0.17/0.41 thf(f4,axiom,(
% 0.17/0.41 (ordinalTransSet = ! [X2] : ((ordinal @ X2) => ! [X1,X0] : ((in @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2)))))),
% 0.17/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet)).
% 0.17/0.41 thf(f76,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((in @ sK5 @ X0) != $true) | ((ordinal @ X0) != $true)) )),
% 0.17/0.41 inference(subsumption_resolution,[],[f75,f53])).
% 0.17/0.41 thf(f75,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK5 @ X0) != $true) | ((ordinal @ sK5) != $true)) )),
% 0.17/0.41 inference(subsumption_resolution,[],[f74,f51])).
% 0.17/0.41 thf(f74,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((ordinal @ X0) != $true) | ((in @ sK5 @ sK6) != $true) | ((in @ sK5 @ X0) != $true) | ((ordinal @ sK5) != $true)) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f69])).
% 0.17/0.41 thf(f69,plain,(
% 0.17/0.41 ( ! [X0 : $i] : (((in @ sK5 @ sK6) != $true) | ($true != $true) | ((ordinal @ sK5) != $true) | ((ordinal @ X0) != $true) | ((in @ sK5 @ X0) != $true)) )),
% 0.17/0.41 inference(superposition,[],[f67,f52])).
% 0.17/0.41 thf(f67,plain,(
% 0.17/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X0) != $true) | ((ordinal @ X0) != $true) | ((ordinal @ X1) != $true) | ((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) != $true)) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f66])).
% 0.17/0.41 thf(f66,plain,(
% 0.17/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((ordinal @ X1) != $true) | ((in @ X0 @ X2) != $true) | ($true != $true) | ((in @ X2 @ X0) != $true) | ((in @ X0 @ X1) != $true) | ((ordinal @ X0) != $true)) )),
% 0.17/0.41 inference(superposition,[],[f65,f64])).
% 0.17/0.41 thf(f65,plain,(
% 0.17/0.41 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X3 @ X3)) | ((ordinal @ X2) != $true) | ((in @ X3 @ X2) != $true)) )),
% 0.17/0.41 inference(trivial_inequality_removal,[],[f58])).
% 0.17/0.41 thf(f58,plain,(
% 0.17/0.41 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X3 @ X3)) | ((in @ X3 @ X2) != $true) | ((ordinal @ X2) != $true) | ($true != $true)) )),
% 0.17/0.41 inference(definition_unfolding,[],[f41,f50])).
% 0.17/0.41 thf(f50,plain,(
% 0.17/0.41 (ordinalIrrefl = $true)),
% 0.17/0.41 inference(cnf_transformation,[],[f40])).
% 0.17/0.41 thf(f41,plain,(
% 0.17/0.41 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X3 @ X3)) | ((in @ X3 @ X2) != $true) | ((ordinal @ X2) != $true) | (ordinalIrrefl != $true)) )),
% 0.17/0.41 inference(cnf_transformation,[],[f32])).
% 0.17/0.41 thf(f32,plain,(
% 0.17/0.41 ((ordinalIrrefl = $true) | ((((in @ sK1 @ sK1) = $true) & ((in @ sK1 @ sK0) = $true)) & ((ordinal @ sK0) = $true))) & (! [X2] : (! [X3] : (($true != (in @ X3 @ X3)) | ((in @ X3 @ X2) != $true)) | ((ordinal @ X2) != $true)) | (ordinalIrrefl != $true))),
% 0.17/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f29,f31,f30])).
% 0.17/0.41 thf(f30,plain,(
% 0.17/0.41 ? [X0] : (? [X1] : (($true = (in @ X1 @ X1)) & ((in @ X1 @ X0) = $true)) & ((ordinal @ X0) = $true)) => (? [X1] : (($true = (in @ X1 @ X1)) & ((in @ X1 @ sK0) = $true)) & ((ordinal @ sK0) = $true))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f31,plain,(
% 0.17/0.41 ? [X1] : (($true = (in @ X1 @ X1)) & ((in @ X1 @ sK0) = $true)) => (((in @ sK1 @ sK1) = $true) & ((in @ sK1 @ sK0) = $true))),
% 0.17/0.41 introduced(choice_axiom,[])).
% 0.17/0.41 thf(f29,plain,(
% 0.17/0.41 ((ordinalIrrefl = $true) | ? [X0] : (? [X1] : (($true = (in @ X1 @ X1)) & ((in @ X1 @ X0) = $true)) & ((ordinal @ X0) = $true))) & (! [X2] : (! [X3] : (($true != (in @ X3 @ X3)) | ((in @ X3 @ X2) != $true)) | ((ordinal @ X2) != $true)) | (ordinalIrrefl != $true))),
% 0.17/0.41 inference(rectify,[],[f28])).
% 0.17/0.41 thf(f28,plain,(
% 0.17/0.41 ((ordinalIrrefl = $true) | ? [X0] : (? [X1] : (($true = (in @ X1 @ X1)) & ((in @ X1 @ X0) = $true)) & ((ordinal @ X0) = $true))) & (! [X0] : (! [X1] : (($true != (in @ X1 @ X1)) | ((in @ X1 @ X0) != $true)) | ((ordinal @ X0) != $true)) | (ordinalIrrefl != $true))),
% 0.17/0.41 inference(nnf_transformation,[],[f27])).
% 0.17/0.41 thf(f27,plain,(
% 0.17/0.41 (ordinalIrrefl = $true) <=> ! [X0] : (! [X1] : (($true != (in @ X1 @ X1)) | ((in @ X1 @ X0) != $true)) | ((ordinal @ X0) != $true))),
% 0.17/0.41 inference(ennf_transformation,[],[f22])).
% 0.17/0.41 thf(f22,plain,(
% 0.17/0.41 ! [X0] : (((ordinal @ X0) = $true) => ! [X1] : (((in @ X1 @ X0) = $true) => ($true != (in @ X1 @ X1)))) <=> (ordinalIrrefl = $true)),
% 0.17/0.41 inference(flattening,[],[f12])).
% 0.17/0.41 thf(f12,plain,(
% 0.17/0.41 (ordinalIrrefl = $true) <=> ! [X0] : (((ordinal @ X0) = $true) => ! [X1] : (((in @ X1 @ X0) = $true) => ~($true = (in @ X1 @ X1))))),
% 0.17/0.41 inference(fool_elimination,[],[f11])).
% 0.17/0.41 thf(f11,plain,(
% 0.17/0.41 (ordinalIrrefl = ! [X0] : ((ordinal @ X0) => ! [X1] : ((in @ X1 @ X0) => ~(in @ X1 @ X1))))),
% 0.17/0.41 inference(rectify,[],[f5])).
% 0.17/0.41 thf(f5,axiom,(
% 0.17/0.41 (ordinalIrrefl = ! [X2] : ((ordinal @ X2) => ! [X0] : ((in @ X0 @ X2) => ~(in @ X0 @ X0))))),
% 0.17/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalIrrefl)).
% 0.17/0.41 % SZS output end Proof for theBenchmark
% 0.17/0.41 % (31801)------------------------------
% 0.17/0.41 % (31801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.41 % (31801)Termination reason: Refutation
% 0.17/0.41
% 0.17/0.41 % (31801)Memory used [KB]: 5500
% 0.17/0.41 % (31801)Time elapsed: 0.010 s
% 0.17/0.41 % (31801)Instructions burned: 7 (million)
% 0.17/0.41 % (31801)------------------------------
% 0.17/0.41 % (31801)------------------------------
% 0.17/0.41 % (31795)Success in time 0.021 s
% 0.17/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------