%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM637^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:20 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM637^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:08:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.28 % (968648)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (968660)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (968660)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (968660)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1983384796:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.22/0.28 % (968660)Refutation not found, incomplete strategy
% 0.22/0.28 % (968660)------------------------------
% 0.22/0.28 % (968660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968660)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968660)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.28 % (968660)Time elapsed: 0.003 s
% 0.22/0.28 % (968660)Peak memory usage: 12 MB
% 0.22/0.28 % (968660)Instructions burned: 8 (million)
% 0.22/0.28 % (968660)------------------------------
% 0.22/0.28 % (968660)------------------------------
% 0.22/0.28 % (968656)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1655735452:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.22/0.28 % (968654)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1627184643:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.22/0.28 % (968655)lrs+10_16_si=on:nwc=1.5:random_seed=3544041686:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.22/0.28 % (968659)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2237539947:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_3000 on theBenchmark for (3000ds/75Mi)
% 0.22/0.28 % (968658)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2420236148:i=24:av=off:rtra=on_3000 on theBenchmark for (3000ds/24Mi)
% 0.22/0.28 % (968657)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2798377476:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_3000 on theBenchmark for (3000ds/634Mi)
% 0.22/0.28 % (968656)Refutation not found, incomplete strategy
% 0.22/0.28 % (968656)------------------------------
% 0.22/0.28 % (968656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968656)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968656)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.28 % (968656)Time elapsed: 0.002 s
% 0.22/0.28 % (968656)Peak memory usage: 12 MB
% 0.22/0.28 % (968656)Instructions burned: 2 (million)
% 0.22/0.28 % (968656)------------------------------
% 0.22/0.28 % (968656)------------------------------
% 0.22/0.28 % (968654)Refutation not found, incomplete strategy
% 0.22/0.28 % (968654)------------------------------
% 0.22/0.28 % (968654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968654)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968654)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.28 % (968654)Time elapsed: 0.006 s
% 0.22/0.28 % (968654)Peak memory usage: 12 MB
% 0.22/0.28 % (968654)Instructions burned: 10 (million)
% 0.22/0.28 % (968669)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3826163669:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.28 % (968654)------------------------------
% 0.22/0.28 % (968654)------------------------------
% 0.22/0.28 % (968669)Instruction limit reached!
% 0.22/0.28 % (968669)------------------------------
% 0.22/0.28 % (968669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968669)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968669)Termination reason: Instruction limit
% 0.22/0.28 % (968669)Termination phase: Saturation
% 0.22/0.28 % (968669)Time elapsed: 0.001 s
% 0.22/0.28 % (968669)Peak memory usage: 12 MB
% 0.22/0.28 % (968669)Instructions burned: 2 (million)
% 0.22/0.28 % (968657)Refutation not found, incomplete strategy
% 0.22/0.28 % (968657)------------------------------
% 0.22/0.28 % (968657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968657)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968657)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.28 % (968657)Time elapsed: 0.008 s
% 0.22/0.28 % (968657)Peak memory usage: 12 MB
% 0.22/0.28 % (968657)Instructions burned: 12 (million)
% 0.22/0.28 % (968657)------------------------------
% 0.22/0.28 % (968657)------------------------------
% 0.22/0.28 % (968655)Instruction limit reached!
% 0.22/0.28 % (968655)------------------------------
% 0.22/0.28 % (968655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968655)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968655)Termination reason: Instruction limit
% 0.22/0.28 % (968655)Termination phase: Saturation
% 0.22/0.28 % (968655)Time elapsed: 0.011 s
% 0.22/0.28 % (968655)Peak memory usage: 12 MB
% 0.22/0.28 % (968655)Instructions burned: 19 (million)
% 0.22/0.28 % (968658) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-968648-968658"...
% 0.22/0.28 % (968658)...printing done.
% 0.22/0.28 % (968658)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, nat: $tType).
% 0.22/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(type_def_7, type, set: $tType).
% 0.22/0.28 thf(func_def_0, type, x: nat).
% 0.22/0.28 thf(func_def_1, type, n_1: nat).
% 0.22/0.28 thf(func_def_2, type, suc: (nat > nat)).
% 0.22/0.28 thf(func_def_3, type, esti: (nat > set > $o)).
% 0.22/0.28 thf(func_def_4, type, setof: ((nat > $o) > set)).
% 0.22/0.28 thf(func_def_8, type, sK0: (set > nat)).
% 0.22/0.28 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.28 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 (x != n_1)),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 ! [X1 : nat,X0 : (nat > $o)] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estie)).
% 0.22/0.28 thf(f3,axiom,(
% 0.22/0.28 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X1 : nat] : (esti @ X1 @ X0)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 0.22/0.28 thf(f4,axiom,(
% 0.22/0.28 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estii)).
% 0.22/0.28 thf(f6,conjecture,(
% 0.22/0.28 ~ ! [X0 : nat] : (x != ((suc @ X0)))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz3)).
% 0.22/0.28 thf(f7,negated_conjecture,(
% 0.22/0.28 ~ ~ ! [X0 : nat] : (x != ((suc @ X0)))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 0.22/0.28 inference(rectify,[],[f3])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ! [X0 : set] : ((((esti @ n_1 @ X0)) = $true) => (! [X1 : nat] : ((((esti @ X1 @ X0)) = $true) => (((esti @ (suc @ X1) @ X0)) = $true)) => ! [X2 : nat] : (((esti @ X2 @ X0)) = $true)))),
% 0.22/0.28 inference(fool_elimination,[],[f8])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.22/0.28 inference(rectify,[],[f4])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ! [X1 : nat,X0 : (nat > $o)] : ((((X0 @ X1)) = $true) => (((esti @ X1 @ (setof @ X0))) = $true))),
% 0.22/0.28 inference(fool_elimination,[],[f10])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ! [X0 : nat,X1 : (nat > $o)] : ((esti @ X0 @ (setof @ X1)) => (X1 @ X0))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ! [X1 : (nat > $o),X0 : nat] : (($true = ((esti @ X0 @ (setof @ X1)))) => ($true = ((X1 @ X0))))),
% 0.22/0.28 inference(fool_elimination,[],[f12])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 ! [X0 : nat] : (x != ((suc @ X0)))),
% 0.22/0.28 inference(flattening,[],[f7])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ! [X0 : nat,X1 : (nat > $o)] : (($true != ((esti @ X0 @ (setof @ X1)))) | ($true = ((X1 @ X0))))),
% 0.22/0.28 inference(ennf_transformation,[],[f13])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) != $true) | (((esti @ X1 @ (setof @ X0))) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f11])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ! [X0 : set] : ((! [X2 : nat] : (((esti @ X2 @ X0)) = $true) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true))) | (((esti @ n_1 @ X0)) != $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f9])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ! [X0 : set] : (! [X2 : nat] : (((esti @ X2 @ X0)) = $true) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.22/0.28 inference(flattening,[],[f21])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | ? [X2 : nat] : ((((esti @ (suc @ X2) @ X0)) != $true) & (((esti @ X2 @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.22/0.28 inference(rectify,[],[f22])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) & (((esti @ (sK0 @ X0) @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f23])).
% 0.22/0.28 thf(f26,plain,(
% 0.22/0.28 ( ! [X0 : set,X1 : nat] : (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) | (((esti @ X1 @ X0)) = $true) | (((esti @ n_1 @ X0)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f24])).
% 0.22/0.28 thf(f27,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f20])).
% 0.22/0.28 thf(f28,plain,(
% 0.22/0.28 (x != n_1)),
% 0.22/0.28 inference(cnf_transformation,[],[f1])).
% 0.22/0.28 thf(f29,plain,(
% 0.22/0.28 ( ! [X0 : nat,X1 : (nat > $o)] : (($true != ((esti @ X0 @ (setof @ X1)))) | ($true = ((X1 @ X0)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f18])).
% 0.22/0.28 thf(f31,plain,(
% 0.22/0.28 ( ! [X0 : nat] : ((x != ((suc @ X0)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f16])).
% 0.22/0.28 thf(f37,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | ($true != ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | (((esti @ X1 @ (setof @ X0))) = $true) | (((esti @ n_1 @ (setof @ X0))) != $true)) )),
% 0.22/0.28 inference(superposition,[],[f26,f27])).
% 0.22/0.28 thf(f38,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | (((esti @ n_1 @ (setof @ X0))) != $true) | (((esti @ X1 @ (setof @ X0))) = $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f37])).
% 0.22/0.28 thf(f67,plain,(
% 0.22/0.28 ( ! [X2 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))) = $true) | ($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true != (((^[Y0 : nat]: (~ (X2 @ Y0))) @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))))) )),
% 0.22/0.28 inference(primitive_instantiation,[],[f38])).
% 0.22/0.28 thf(f69,plain,(
% 0.22/0.28 ( ! [X2 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | (((~ (X2 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))))) != $true) | (((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))) = $true)) )),
% 0.22/0.28 inference(beta-eta_normalization,[],[f67])).
% 0.22/0.28 thf(f70,plain,(
% 0.22/0.28 ( ! [X2 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | (((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))) = $true) | ($true = ((X2 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))))) )),
% 0.22/0.28 inference(not_proxy_clausification,[],[f69])).
% 0.22/0.28 thf(f135,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (((((^[Y0 : nat]: (~ (X0 @ Y0))) @ n_1)) != $true) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true != $true) | ($true = ((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))))) )),
% 0.22/0.28 inference(superposition,[],[f70,f27])).
% 0.22/0.28 thf(f136,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (((((^[Y0 : nat]: (~ (X0 @ Y0))) @ n_1)) != $true) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))))) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f135])).
% 0.22/0.28 thf(f137,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (($true = ((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))))) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | (((~ (X0 @ n_1))) != $true)) )),
% 0.22/0.28 inference(beta-eta_normalization,[],[f136])).
% 0.22/0.28 thf(f138,plain,(
% 0.22/0.28 ( ! [X0 : (nat > $o),X1 : nat] : (($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))))) | ($true = ((X0 @ n_1)))) )),
% 0.22/0.28 inference(not_proxy_clausification,[],[f137])).
% 0.22/0.28 thf(f163,plain,(
% 0.22/0.28 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = ((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0))))))))) | (((X1 @ n_1)) = $true) | ($true != $true) | ($true = (((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0)))) )),
% 0.22/0.28 inference(superposition,[],[f29,f138])).
% 0.22/0.28 thf(f168,plain,(
% 0.22/0.28 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = (((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0))) | ($true = ((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0))))))))) | (((X1 @ n_1)) = $true)) )),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f163])).
% 0.22/0.28 thf(f169,plain,(
% 0.22/0.28 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = ((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0))))))))) | ($true = ((~ (X1 @ X0)))) | (((X1 @ n_1)) = $true)) )),
% 0.22/0.28 inference(beta-eta_normalization,[],[f168])).
% 0.22/0.28 thf(f170,plain,(
% 0.22/0.28 ( ! [X0 : nat,X1 : (nat > $o)] : (($false = ((X1 @ X0))) | ($true = ((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0))))))))) | (((X1 @ n_1)) = $true)) )),
% 0.22/0.28 inference(not_proxy_clausification,[],[f169])).
% 0.22/0.28 thf(f182,plain,(
% 0.22/0.28 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0))))))) = X0) | (((X0 = n_1)) = $true)) )),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f170])).
% 0.22/0.28 thf(f210,plain,(
% 0.22/0.28 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0))))))) = X0) | (n_1 = X0)) )),
% 0.22/0.28 inference(equality_proxy_clausification,[],[f182])).
% 0.22/0.28 thf(f295,plain,(
% 0.22/0.28 ( ! [X0 : nat] : ((x != X0) | (n_1 = X0)) )),
% 0.22/0.28 inference(superposition,[],[f31,f210])).
% 0.22/0.28 thf(f313,plain,(
% 0.22/0.28 (x != x) | (x = n_1)),
% 0.22/0.28 inference(imitation,[],[f295])).
% 0.22/0.28 thf(f315,plain,(
% 0.22/0.28 (x = n_1)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f313])).
% 0.22/0.28 thf(f316,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f315,f28])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (968658)------------------------------
% 0.22/0.28 % (968658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (968658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (968658)CaDiCaL version: 2.1.3
% 0.22/0.28 % (968658)Termination reason: Refutation
% 0.22/0.28 % (968658)Time elapsed: 0.012 s
% 0.22/0.28 % (968658)Peak memory usage: 12 MB
% 0.22/0.28 % (968658)Instructions burned: 21 (million)
% 0.22/0.28 % (968648)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------