%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM636^1 : 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 : n019.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 08:18:19 AM UTC 2026
% Result : Theorem 0.51s 0.38s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n019.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 12:01:48 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.31 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
% 0.51/0.38 % (665839)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.38 % (665845)lrs+10_16_si=on:nwc=1.5:random_seed=4187362527:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.38 % (665844)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3017058606:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.38 % (665850)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.38 % (665850)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
% 0.51/0.38 % (665845)Instruction limit reached!
% 0.51/0.38 % (665845)------------------------------
% 0.51/0.38 % (665845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665845)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665845)Termination reason: Instruction limit
% 0.51/0.38 % (665845)Termination phase: Saturation
% 0.51/0.38 % (665845)Time elapsed: 0.010 s
% 0.51/0.38 % (665845)Peak memory usage: 12 MB
% 0.51/0.38 % (665845)Instructions burned: 20 (million)
% 0.51/0.38 % (665849)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2044708329:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.38 % (665846)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3372918078:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.38 % (665848)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2972860403:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.38 % (665847)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=610587915: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_2999 on theBenchmark for (2999ds/634Mi)
% 0.51/0.38 % (665850)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=1450052800:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.38 % (665846)Refutation not found, incomplete strategy
% 0.51/0.38 % (665846)------------------------------
% 0.51/0.38 % (665846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665846)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665846)Termination reason: Refutation not found, incomplete strategy
% 0.51/0.38 % (665846)Time elapsed: 0.004 s
% 0.51/0.38 % (665846)Peak memory usage: 12 MB
% 0.51/0.38 % (665846)Instructions burned: 2 (million)
% 0.51/0.38 % (665844)Refutation not found, incomplete strategy
% 0.51/0.38 % (665844)------------------------------
% 0.51/0.38 % (665844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665844)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665844)Termination reason: Refutation not found, incomplete strategy
% 0.51/0.38 % (665844)Time elapsed: 0.013 s
% 0.51/0.38 % (665844)Peak memory usage: 12 MB
% 0.51/0.38 % (665844)Instructions burned: 12 (million)
% 0.51/0.38 % (665846)------------------------------
% 0.51/0.38 % (665846)------------------------------
% 0.51/0.38 % (665844)------------------------------
% 0.51/0.38 % (665844)------------------------------
% 0.51/0.38 % (665850)Refutation not found, incomplete strategy
% 0.51/0.38 % (665850)------------------------------
% 0.51/0.38 % (665850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665850)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665850)Termination reason: Refutation not found, incomplete strategy
% 0.51/0.38 % (665850)Time elapsed: 0.010 s
% 0.51/0.38 % (665850)Peak memory usage: 12 MB
% 0.51/0.38 % (665850)Instructions burned: 9 (million)
% 0.51/0.38 % (665850)------------------------------
% 0.51/0.38 % (665850)------------------------------
% 0.51/0.38 % (665847)Refutation not found, incomplete strategy
% 0.51/0.38 % (665847)------------------------------
% 0.51/0.38 % (665847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665847)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665847)Termination reason: Refutation not found, incomplete strategy
% 0.51/0.38 % (665847)Time elapsed: 0.014 s
% 0.51/0.38 % (665847)Peak memory usage: 12 MB
% 0.51/0.38 % (665847)Instructions burned: 12 (million)
% 0.51/0.38 % (665853)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4051664504:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.38 % (665847)------------------------------
% 0.51/0.38 % (665847)------------------------------
% 0.51/0.38 % (665853)Instruction limit reached!
% 0.51/0.38 % (665853)------------------------------
% 0.51/0.38 % (665853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.38 % (665853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.38 % (665853)CaDiCaL version: 2.1.3
% 0.51/0.38 % (665853)Termination reason: Instruction limit
% 0.51/0.38 % (665853)Termination phase: Saturation
% 0.51/0.38 % (665853)Time elapsed: 0.002 s
% 0.51/0.38 % (665853)Peak memory usage: 12 MB
% 0.51/0.38 % (665853)Instructions burned: 3 (million)
% 0.51/0.38 % (665848) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-665839-665848"...
% 0.51/0.38 % (665848)...printing done.
% 0.51/0.38 % (665848)Refutation found. Thanks to Tanya!
% 0.51/0.38 % SZS status Theorem for theBenchmark
% 0.51/0.38 % SZS output start Proof for theBenchmark
% 0.51/0.38 thf(type_def_5, type, nat: $tType).
% 0.51/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.51/0.38 thf(type_def_7, type, set: $tType).
% 0.51/0.38 thf(func_def_0, type, x: nat).
% 0.51/0.38 thf(func_def_1, type, suc: (nat > nat)).
% 0.51/0.38 thf(func_def_2, type, esti: (nat > set > $o)).
% 0.51/0.38 thf(func_def_3, type, setof: ((nat > $o) > set)).
% 0.51/0.38 thf(func_def_5, type, n_1: nat).
% 0.51/0.38 thf(func_def_8, type, sK0: (set > nat)).
% 0.51/0.38 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.51/0.38 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.51/0.38 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.51/0.38 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.51/0.38 thf(f1,axiom,(
% 0.51/0.38 ! [X1 : nat,X0 : (nat > $o)] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estie)).
% 0.51/0.38 thf(f2,axiom,(
% 0.51/0.38 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X1 : nat] : (esti @ X1 @ X0)))),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 0.51/0.38 thf(f3,axiom,(
% 0.51/0.38 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estii)).
% 0.51/0.38 thf(f4,axiom,(
% 0.51/0.38 ! [X0 : nat] : (((suc @ X0)) != n_1)),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 0.51/0.38 thf(f5,axiom,(
% 0.51/0.38 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (((suc @ X0)) != ((suc @ X1))))),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz1)).
% 0.51/0.38 thf(f6,conjecture,(
% 0.51/0.38 (((suc @ x)) != x)),
% 0.51/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz2)).
% 0.51/0.38 thf(f7,negated_conjecture,(
% 0.51/0.38 ~ (((suc @ x)) != x)),
% 0.51/0.38 inference(negated_conjecture,[status(cth)],[f6])).
% 0.51/0.38 thf(f8,plain,(
% 0.51/0.38 ! [X0 : nat,X1 : (nat > $o)] : ((esti @ X0 @ (setof @ X1)) => (X1 @ X0))),
% 0.51/0.38 inference(rectify,[],[f1])).
% 0.51/0.38 thf(f9,plain,(
% 0.51/0.38 ! [X1 : (nat > $o),X0 : nat] : (($true = ((esti @ X0 @ (setof @ X1)))) => ($true = ((X1 @ X0))))),
% 0.51/0.38 inference(fool_elimination,[],[f8])).
% 0.51/0.38 thf(f10,plain,(
% 0.51/0.38 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 0.51/0.38 inference(rectify,[],[f2])).
% 0.51/0.38 thf(f11,plain,(
% 0.51/0.38 ! [X0 : set] : ((((esti @ n_1 @ X0)) = $true) => (! [X1 : nat] : ((((esti @ X1 @ X0)) = $true) => (((esti @ (suc @ X1) @ X0)) = $true)) => ! [X2 : nat] : ($true = ((esti @ X2 @ X0)))))),
% 0.51/0.38 inference(fool_elimination,[],[f10])).
% 0.51/0.38 thf(f12,plain,(
% 0.51/0.38 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.51/0.38 inference(rectify,[],[f3])).
% 0.51/0.38 thf(f13,plain,(
% 0.51/0.38 ! [X1 : nat,X0 : (nat > $o)] : ((((X0 @ X1)) = $true) => (((esti @ X1 @ (setof @ X0))) = $true))),
% 0.51/0.38 inference(fool_elimination,[],[f12])).
% 0.51/0.38 thf(f14,plain,(
% 0.51/0.38 (x = ((suc @ x)))),
% 0.51/0.38 inference(flattening,[],[f7])).
% 0.51/0.38 thf(f15,plain,(
% 0.51/0.38 ! [X1 : (nat > $o),X0 : nat] : (($true = ((X1 @ X0))) | ($true != ((esti @ X0 @ (setof @ X1)))))),
% 0.51/0.38 inference(ennf_transformation,[],[f9])).
% 0.51/0.38 thf(f16,plain,(
% 0.51/0.38 ! [X0 : set] : ((! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true))) | (((esti @ n_1 @ X0)) != $true))),
% 0.51/0.38 inference(ennf_transformation,[],[f11])).
% 0.51/0.38 thf(f17,plain,(
% 0.51/0.38 ! [X0 : set] : (! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.51/0.38 inference(flattening,[],[f16])).
% 0.51/0.38 thf(f18,plain,(
% 0.51/0.38 ! [X1 : nat,X0 : (nat > $o)] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) != $true))),
% 0.51/0.38 inference(ennf_transformation,[],[f13])).
% 0.51/0.38 thf(f19,plain,(
% 0.51/0.38 ! [X1 : nat,X0 : nat] : ((((suc @ X0)) != ((suc @ X1))) | (X0 = X1))),
% 0.51/0.38 inference(ennf_transformation,[],[f5])).
% 0.51/0.38 thf(f20,plain,(
% 0.51/0.38 ! [X0 : nat,X1 : (nat > $o)] : (($true = ((esti @ X0 @ (setof @ X1)))) | ($true != ((X1 @ X0))))),
% 0.51/0.38 inference(rectify,[],[f18])).
% 0.51/0.38 thf(f21,plain,(
% 0.51/0.38 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) = $true) | (((esti @ X1 @ (setof @ X0))) != $true))),
% 0.51/0.38 inference(rectify,[],[f15])).
% 0.51/0.38 thf(f22,plain,(
% 0.51/0.38 ! [X0 : nat,X1 : nat] : ((((suc @ X0)) != ((suc @ X1))) | (X0 = X1))),
% 0.51/0.38 inference(rectify,[],[f19])).
% 0.51/0.38 thf(f23,plain,(
% 0.51/0.38 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | ? [X2 : nat] : ((((esti @ (suc @ X2) @ X0)) != $true) & ($true = ((esti @ X2 @ X0)))) | (((esti @ n_1 @ X0)) != $true))),
% 0.51/0.38 inference(rectify,[],[f17])).
% 0.51/0.38 thf(f24,plain,(
% 0.51/0.38 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | ((((esti @ (suc @ (sK0 @ X0)) @ X0)) != $true) & (((esti @ (sK0 @ X0) @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.51/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f23])).
% 0.51/0.38 thf(f25,plain,(
% 0.51/0.38 (x = ((suc @ x)))),
% 0.51/0.38 inference(cnf_transformation,[],[f14])).
% 0.51/0.38 thf(f26,plain,(
% 0.51/0.38 ( ! [X0 : nat] : ((n_1 != ((suc @ X0)))) )),
% 0.51/0.38 inference(cnf_transformation,[],[f4])).
% 0.51/0.38 thf(f27,plain,(
% 0.51/0.38 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = ((esti @ X0 @ (setof @ X1)))) | ($true != ((X1 @ X0)))) )),
% 0.51/0.38 inference(cnf_transformation,[],[f20])).
% 0.51/0.38 thf(f28,plain,(
% 0.51/0.38 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) != $true) | (((X0 @ X1)) = $true)) )),
% 0.51/0.38 inference(cnf_transformation,[],[f21])).
% 0.51/0.38 thf(f29,plain,(
% 0.51/0.38 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != ((suc @ X0))) | (X0 = X1)) )),
% 0.51/0.38 inference(cnf_transformation,[],[f22])).
% 0.51/0.38 thf(f30,plain,(
% 0.51/0.38 ( ! [X0 : set,X1 : nat] : ((((esti @ n_1 @ X0)) != $true) | (((esti @ X1 @ X0)) = $true) | (((esti @ (sK0 @ X0) @ X0)) = $true)) )),
% 0.51/0.38 inference(cnf_transformation,[],[f24])).
% 0.51/0.38 thf(f31,plain,(
% 0.51/0.38 ( ! [X0 : set,X1 : nat] : ((((esti @ (suc @ (sK0 @ X0)) @ X0)) != $true) | (((esti @ n_1 @ X0)) != $true) | (((esti @ X1 @ X0)) = $true)) )),
% 0.51/0.38 inference(cnf_transformation,[],[f24])).
% 0.51/0.38 thf(f33,plain,(
% 0.51/0.38 (n_1 != x)),
% 0.51/0.38 inference(superposition,[],[f26,f25])).
% 0.51/0.38 thf(f34,plain,(
% 0.51/0.38 ( ! [X0 : nat] : ((((suc @ X0)) != x) | (x = X0)) )),
% 0.51/0.38 inference(superposition,[],[f29,f25])).
% 0.51/0.38 thf(f38,plain,(
% 0.51/0.38 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | ($true != $true) | ($true != ((X0 @ n_1))) | ($true = ((esti @ (sK0 @ (setof @ X0)) @ (setof @ X0))))) )),
% 0.51/0.38 inference(superposition,[],[f30,f27])).
% 0.51/0.38 thf(f39,plain,(
% 0.51/0.38 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((X0 @ n_1))) | (((esti @ X1 @ (setof @ X0))) = $true) | ($true = ((esti @ (sK0 @ (setof @ X0)) @ (setof @ X0))))) )),
% 0.51/0.38 inference(trivial_inequality_removal,[],[f38])).
% 0.51/0.38 thf(f40,plain,(
% 0.51/0.38 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | ($true != ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | ($true != ((esti @ n_1 @ (setof @ X0)))) | (((esti @ X1 @ (setof @ X0))) = $true)) )),
% 0.51/0.38 inference(superposition,[],[f31,f27])).
% 0.51/0.38 thf(f41,plain,(
% 0.51/0.38 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | ($true != ((esti @ n_1 @ (setof @ X0)))) | (((esti @ X1 @ (setof @ X0))) = $true)) )),
% 0.51/0.38 inference(trivial_inequality_removal,[],[f40])).
% 0.51/0.39 thf(f44,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true != (((^[Y0 : nat]: (~ (X2 @ Y0))) @ n_1))) | ($true = ((esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))) )),
% 0.51/0.39 inference(primitive_instantiation,[],[f39])).
% 0.51/0.39 thf(f51,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true != ((~ (X2 @ n_1))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f44])).
% 0.51/0.39 thf(f52,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((X2 @ n_1)))) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f51])).
% 0.51/0.39 thf(f71,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true != (((^[Y0 : nat]: (~ (X2 @ Y0))) @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))))) | ($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))) )),
% 0.51/0.39 inference(primitive_instantiation,[],[f41])).
% 0.51/0.39 thf(f74,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | (((~ (X2 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))))) != $true) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f71])).
% 0.51/0.39 thf(f75,plain,(
% 0.51/0.39 ( ! [X2 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0))))))) | (((X2 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X2 @ Y0)))))))) = $true)) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f74])).
% 0.51/0.39 thf(f96,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : (($true = ((X0 @ n_1))) | ($true = ((esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true != $true)) )),
% 0.51/0.39 inference(equality_factoring,[],[f52])).
% 0.51/0.39 thf(f99,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : (($true = ((esti @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))) @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ n_1)))) )),
% 0.51/0.39 inference(trivial_inequality_removal,[],[f96])).
% 0.51/0.39 thf(f107,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o),X1 : nat] : (($true != (((^[Y0 : nat]: (~ (X0 @ Y0))) @ n_1))) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true != $true) | (((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) = $true)) )),
% 0.51/0.39 inference(superposition,[],[f75,f27])).
% 0.51/0.39 thf(f108,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o),X1 : nat] : (($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | (((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) = $true) | ($true != (((^[Y0 : nat]: (~ (X0 @ Y0))) @ n_1)))) )),
% 0.51/0.39 inference(trivial_inequality_removal,[],[f107])).
% 0.51/0.39 thf(f109,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((~ (X0 @ n_1)))) | (((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) = $true) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f108])).
% 0.51/0.39 thf(f110,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))) = $true) | ($true = ((esti @ X1 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) | ($true = ((X0 @ n_1)))) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f109])).
% 0.51/0.39 thf(f111,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : (($true != $true) | ($true = ((X0 @ n_1))) | ((((^[Y0 : nat]: (~ (X0 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) = $true)) )),
% 0.51/0.39 inference(superposition,[],[f28,f99])).
% 0.51/0.39 thf(f112,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : (((((^[Y0 : nat]: (~ (X0 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) = $true) | ($true = ((X0 @ n_1)))) )),
% 0.51/0.39 inference(trivial_inequality_removal,[],[f111])).
% 0.51/0.39 thf(f113,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : (($true = ((X0 @ n_1))) | ($true = ((~ (X0 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0)))))))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f112])).
% 0.51/0.39 thf(f114,plain,(
% 0.51/0.39 ( ! [X0 : (nat > $o)] : ((((X0 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 @ Y0))))))) = $false) | ($true = ((X0 @ n_1)))) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f113])).
% 0.51/0.39 thf(f118,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : (((((^[Y0 : nat]: (~ (X1 @ Y0))) @ n_1)) = $true) | ($false = (((^[Y0 : nat]: (~ (X1 @ Y0))) @ (sK0 @ (setof @ (^[Y0 : nat]: (~ ((^[Y1 : nat]: (~ (X1 @ Y1))) @ Y0))))))))) )),
% 0.51/0.39 inference(primitive_instantiation,[],[f114])).
% 0.51/0.39 thf(f123,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : (($true = ((~ (X1 @ n_1)))) | ($false = ((~ (X1 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (~ (X1 @ Y0))))))))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f118])).
% 0.51/0.39 thf(f124,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : (($false = ((~ (X1 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (~ (X1 @ Y0)))))))))) | ($false = ((X1 @ n_1)))) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f123])).
% 0.51/0.39 thf(f125,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : (($false = ((X1 @ n_1))) | (((X1 @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (~ (X1 @ Y0)))))))) = $true)) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f124])).
% 0.51/0.39 thf(f126,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : ((((X1 @ (sK0 @ (setof @ (^[Y0 : nat]: (X1 @ Y0)))))) = $true) | ($false = ((X1 @ n_1)))) )),
% 0.51/0.39 inference(boolean_simplification,[],[f125])).
% 0.51/0.39 thf(f127,plain,(
% 0.51/0.39 ( ! [X1 : (nat > $o)] : ((((X1 @ (sK0 @ (setof @ X1)))) = $true) | ($false = ((X1 @ n_1)))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f126])).
% 0.51/0.39 thf(f154,plain,(
% 0.51/0.39 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = (((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0))) | ($true != $true) | (((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0)))))))) = $true) | ($true = ((X1 @ n_1)))) )),
% 0.51/0.39 inference(superposition,[],[f28,f110])).
% 0.51/0.39 thf(f156,plain,(
% 0.51/0.39 ( ! [X0 : nat,X1 : (nat > $o)] : (($true = (((^[Y0 : nat]: (~ (X1 @ Y0))) @ X0))) | ($true = ((X1 @ n_1))) | (((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0)))))))) = $true)) )),
% 0.51/0.39 inference(trivial_inequality_removal,[],[f154])).
% 0.51/0.39 thf(f157,plain,(
% 0.51/0.39 ( ! [X0 : nat,X1 : (nat > $o)] : ((((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0)))))))) = $true) | ($true = ((X1 @ n_1))) | ($true = ((~ (X1 @ X0))))) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f156])).
% 0.51/0.39 thf(f158,plain,(
% 0.51/0.39 ( ! [X0 : nat,X1 : (nat > $o)] : (($false = ((X1 @ X0))) | (((X1 @ (suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X1 @ Y0)))))))) = $true) | ($true = ((X1 @ n_1)))) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f157])).
% 0.51/0.39 thf(f173,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0))))))) = X0) | ($true = ((X0 = n_1)))) )),
% 0.51/0.39 inference(leibniz_equality_elimination,[],[f158])).
% 0.51/0.39 thf(f181,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0))))))) = X0) | (n_1 = X0)) )),
% 0.51/0.39 inference(equality_proxy_clausification,[],[f173])).
% 0.51/0.39 thf(f257,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((x = ((sK0 @ (setof @ (^[Y0 : nat]: (~ (X0 = Y0))))))) | (x != X0) | (n_1 = X0)) )),
% 0.51/0.39 inference(superposition,[],[f34,f181])).
% 0.51/0.39 thf(f273,plain,(
% 0.51/0.39 ( ! [X0 : nat] : (($true = (((^[Y0 : nat]: (~ (X0 = Y0))) @ x))) | (x != X0) | (n_1 = X0) | ((((^[Y0 : nat]: (~ (X0 = Y0))) @ n_1)) = $false)) )),
% 0.51/0.39 inference(superposition,[],[f127,f257])).
% 0.51/0.39 thf(f279,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((x != X0) | (((~ (X0 = x))) = $true) | (((~ (X0 = n_1))) = $false) | (n_1 = X0)) )),
% 0.51/0.39 inference(beta-eta_normalization,[],[f273])).
% 0.51/0.39 thf(f280,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((((~ (X0 = n_1))) = $false) | (((X0 = x)) = $false) | (n_1 = X0) | (x != X0)) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f279])).
% 0.51/0.39 thf(f281,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((x != X0) | ($true = ((X0 = n_1))) | (((X0 = x)) = $false) | (n_1 = X0)) )),
% 0.51/0.39 inference(not_proxy_clausification,[],[f280])).
% 0.51/0.39 thf(f282,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((x != X0) | (n_1 = X0) | (((X0 = x)) = $false) | (n_1 = X0)) )),
% 0.51/0.39 inference(equality_proxy_clausification,[],[f281])).
% 0.51/0.39 thf(f283,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((n_1 = X0) | (x != X0) | (x != X0) | (n_1 = X0)) )),
% 0.51/0.39 inference(equality_proxy_clausification,[],[f282])).
% 0.51/0.39 thf(f284,plain,(
% 0.51/0.39 ( ! [X0 : nat] : ((x != X0) | (n_1 = X0)) )),
% 0.51/0.39 inference(duplicate_literal_removal,[],[f283])).
% 0.51/0.39 thf(f340,plain,(
% 0.51/0.39 (n_1 = x)),
% 0.51/0.39 inference(equality_resolution,[],[f284])).
% 0.51/0.39 thf(f342,plain,(
% 0.51/0.39 $false),
% 0.51/0.39 inference(forward_subsumption_resolution,[],[f340,f33])).
% 0.51/0.39 % SZS output end Proof for theBenchmark
% 0.51/0.39 % (665848)------------------------------
% 0.51/0.39 % (665848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.39 % (665848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.39 % (665848)CaDiCaL version: 2.1.3
% 0.51/0.39 % (665848)Termination reason: Refutation
% 0.51/0.39 % (665848)Time elapsed: 0.024 s
% 0.51/0.39 % (665848)Peak memory usage: 12 MB
% 0.51/0.39 % (665848)Instructions burned: 23 (million)
% 0.51/0.39 % (665839)Success in time 0.063 s
% 0.51/0.39 % Vampire exiting
%------------------------------------------------------------------------------