%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n009.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 08:19:10 AM UTC 2026
% Result : Theorem 1.72s 0.50s
% Output : Refutation 1.72s
% 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 SAT
% 0.11/0.22 % Computer : n009.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 12:07:45 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.27 Running first-order model finding
% 0.11/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/0.50 % (3906667)Will run a generic schedule for satisfiability detection.
% 0.93/0.50 % (3906678)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1660781234:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.93/0.50 % (3906673)% WARNING: option uhcvi not known.
% 0.93/0.50 % (3906672)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3382563118_2999 on theBenchmark for (2999ds/0Mi)
% 0.93/0.50 % Exception at run slice level
% 0.93/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.50 % (3906673)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1014171149:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.93/0.50 % (3906675)dis+10_1_sil=32000:sp=arity:random_seed=3591948961:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.93/0.50 % (3906674)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1656249477:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.93/0.50 % (3906677)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=989930930:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.93/0.50 % (3906676)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=759594286:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.93/0.50 % (3906673)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.50 % (3906673)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.93/0.50 % (3906676)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.50 % (3906682)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4046123521:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.93/0.50 % Exception at run slice level
% 0.93/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.50 % (3906689)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1135007613:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.93/0.50 % (3906678)Instruction limit reached!
% 0.93/0.50 % (3906678)------------------------------
% 0.93/0.50 % (3906678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.50 % (3906678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.50 % (3906678)CaDiCaL version: 2.1.3
% 0.93/0.50 % (3906678)Termination reason: Instruction limit
% 0.93/0.50 % (3906678)Termination phase: Saturation
% 0.93/0.50 % (3906678)Time elapsed: 0.074 s
% 0.93/0.50 % (3906678)Peak memory usage: 12 MB
% 0.93/0.50 % (3906678)Instructions burned: 159 (million)
% 0.93/0.50 % (3906692)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3995634983:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.93/0.50 % (3906692)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.50 % (3906692)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.93/0.50 % (3906675)Instruction limit reached!
% 0.93/0.50 % (3906675)------------------------------
% 0.93/0.50 % (3906675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.50 % (3906675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.50 % (3906675)CaDiCaL version: 2.1.3
% 0.93/0.50 % (3906675)Termination reason: Instruction limit
% 0.93/0.50 % (3906675)Termination phase: Saturation
% 0.93/0.50 % (3906675)Time elapsed: 0.093 s
% 0.93/0.50 % (3906675)Peak memory usage: 12 MB
% 0.93/0.50 % (3906675)Instructions burned: 103 (million)
% 0.93/0.50 % (3906676)Instruction limit reached!
% 0.93/0.50 % (3906676)------------------------------
% 0.93/0.50 % (3906676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.50 % (3906676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.50 % (3906676)CaDiCaL version: 2.1.3
% 0.93/0.50 % (3906676)Termination reason: Instruction limit
% 0.93/0.50 % (3906676)Termination phase: Saturation
% 0.93/0.50 % (3906676)Time elapsed: 0.101 s
% 0.93/0.50 % (3906676)Peak memory usage: 12 MB
% 0.93/0.50 % (3906676)Instructions burned: 117 (million)
% 0.93/0.50 % (3906677)Instruction limit reached!
% 0.93/0.50 % (3906677)------------------------------
% 0.93/0.50 % (3906677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.50 % (3906677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.50 % (3906677)CaDiCaL version: 2.1.3
% 1.72/0.50 % (3906677)Termination reason: Instruction limit
% 1.72/0.50 % (3906677)Termination phase: Saturation
% 1.72/0.50 % (3906677)Time elapsed: 0.115 s
% 1.72/0.50 % (3906677)Peak memory usage: 12 MB
% 1.72/0.50 % (3906677)Instructions burned: 132 (million)
% 1.72/0.50 % (3906696)ott-21_1_sil=16000:fs=off:random_seed=2186318829:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.72/0.50 % (3906697)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3809253078:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.72/0.50 % (3906699)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3789295076:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.72/0.50 % Exception at run slice level
% 1.72/0.50 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.72/0.50 % (3906689)Instruction limit reached!
% 1.72/0.50 % (3906689)------------------------------
% 1.72/0.50 % (3906689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.50 % (3906689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.50 % (3906689)CaDiCaL version: 2.1.3
% 1.72/0.50 % (3906689)Termination reason: Instruction limit
% 1.72/0.50 % (3906689)Termination phase: Saturation
% 1.72/0.50 % (3906689)Time elapsed: 0.123 s
% 1.72/0.50 % (3906689)Peak memory usage: 12 MB
% 1.72/0.50 % (3906689)Instructions burned: 131 (million)
% 1.72/0.50 % (3906692) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3906667-3906692"...
% 1.72/0.50 % (3906692)...printing done.
% 1.72/0.50 % (3906692)Refutation found. Thanks to Tanya!
% 1.72/0.50 % SZS status Theorem for theBenchmark
% 1.72/0.50 % SZS output start Proof for theBenchmark
% 1.72/0.50 thf(type_def_5, type, nat: $tType).
% 1.72/0.50 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.72/0.50 thf(type_def_7, type, set: $tType).
% 1.72/0.50 thf(func_def_0, type, x: nat).
% 1.72/0.50 thf(func_def_1, type, n_1: nat).
% 1.72/0.50 thf(func_def_2, type, suc: (nat > nat)).
% 1.72/0.50 thf(func_def_3, type, esti: (nat > set > $o)).
% 1.72/0.50 thf(func_def_4, type, setof: ((nat > $o) > set)).
% 1.72/0.50 thf(func_def_8, type, sK0: (set > nat)).
% 1.72/0.50 thf(func_def_9, type, vNOT: ($o > $o)).
% 1.72/0.50 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 1.72/0.50 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.72/0.50 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.72/0.50 thf(f1,axiom,(
% 1.72/0.50 (x != n_1)),
% 1.72/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 1.72/0.50 thf(f2,axiom,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.72/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estie)).
% 1.72/0.50 thf(f3,axiom,(
% 1.72/0.50 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X1 : nat] : (esti @ X1 @ X0)))),
% 1.72/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5)).
% 1.72/0.50 thf(f4,axiom,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.72/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',estii)).
% 1.72/0.50 thf(f6,conjecture,(
% 1.72/0.50 ~ ! [X0 : nat] : (x != ((suc @ X0)))),
% 1.72/0.50 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz3)).
% 1.72/0.50 thf(f7,negated_conjecture,(
% 1.72/0.50 ~ ~ ! [X0 : nat] : (x != ((suc @ X0)))),
% 1.72/0.50 inference(negated_conjecture,[status(cth)],[f6])).
% 1.72/0.50 thf(f8,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 1.72/0.50 inference(rectify,[],[f2])).
% 1.72/0.50 thf(f9,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) => (((X0 @ X1)) = $true))),
% 1.72/0.50 inference(fool_elimination,[],[f8])).
% 1.72/0.50 thf(f10,plain,(
% 1.72/0.50 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 1.72/0.50 inference(rectify,[],[f3])).
% 1.72/0.50 thf(f11,plain,(
% 1.72/0.50 ! [X0 : set] : ((((esti @ n_1 @ X0)) = $true) => (! [X1 : nat] : ((((esti @ X1 @ X0)) = $true) => (((esti @ (suc @ X1) @ X0)) = $true)) => ! [X2 : nat] : ($true = ((esti @ X2 @ X0)))))),
% 1.72/0.50 inference(fool_elimination,[],[f10])).
% 1.72/0.50 thf(f12,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 1.72/0.50 inference(rectify,[],[f4])).
% 1.72/0.50 thf(f13,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) = $true) => (((esti @ X1 @ (setof @ X0))) = $true))),
% 1.72/0.50 inference(fool_elimination,[],[f12])).
% 1.72/0.50 thf(f17,plain,(
% 1.72/0.50 ! [X0 : nat] : (x != ((suc @ X0)))),
% 1.72/0.50 inference(flattening,[],[f7])).
% 1.72/0.50 thf(f18,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) = $true) | (((esti @ X1 @ (setof @ X0))) != $true))),
% 1.72/0.50 inference(ennf_transformation,[],[f9])).
% 1.72/0.50 thf(f19,plain,(
% 1.72/0.50 ! [X0 : set] : ((! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true))) | (((esti @ n_1 @ X0)) != $true))),
% 1.72/0.50 inference(ennf_transformation,[],[f11])).
% 1.72/0.50 thf(f20,plain,(
% 1.72/0.50 ! [X0 : set] : (! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 1.72/0.50 inference(flattening,[],[f19])).
% 1.72/0.50 thf(f21,plain,(
% 1.72/0.50 ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) != $true))),
% 1.72/0.50 inference(ennf_transformation,[],[f13])).
% 1.72/0.50 thf(f23,plain,(
% 1.72/0.50 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | ? [X2 : nat] : (($true != ((esti @ (suc @ X2) @ X0))) & ($true = ((esti @ X2 @ X0)))) | (((esti @ n_1 @ X0)) != $true))),
% 1.72/0.50 inference(rectify,[],[f20])).
% 1.72/0.50 thf(f24,plain,(
% 1.72/0.50 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) & ($true = ((esti @ (sK0 @ X0) @ X0)))) | (((esti @ n_1 @ X0)) != $true))),
% 1.72/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f23])).
% 1.72/0.50 thf(f25,plain,(
% 1.72/0.50 (x != n_1)),
% 1.72/0.50 inference(cnf_transformation,[],[f1])).
% 1.72/0.50 thf(f26,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) != $true) | (((X0 @ X1)) = $true)) )),
% 1.72/0.50 inference(cnf_transformation,[],[f18])).
% 1.72/0.50 thf(f28,plain,(
% 1.72/0.50 ( ! [X0 : set,X1 : nat] : (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) | (((esti @ X1 @ X0)) = $true) | (((esti @ n_1 @ X0)) != $true)) )),
% 1.72/0.50 inference(cnf_transformation,[],[f24])).
% 1.72/0.50 thf(f29,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) != $true) | (((esti @ X1 @ (setof @ X0))) = $true)) )),
% 1.72/0.50 inference(cnf_transformation,[],[f21])).
% 1.72/0.50 thf(f31,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((x != ((suc @ X0)))) )),
% 1.72/0.50 inference(cnf_transformation,[],[f17])).
% 1.72/0.50 thf(f33,definition,(
% 1.72/0.50 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.72/0.50 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.72/0.50 thf(f48,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 1.72/0.50 inference(constrained_superposition,[],[f29,f33])).
% 1.72/0.50 thf(f50,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 1.72/0.50 inference(trivial_inequality_removal,[],[f48])).
% 1.72/0.50 thf(f157,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | ($true != ((esti @ n_1 @ (setof @ X0)))) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0))))))) )),
% 1.72/0.50 inference(constrained_superposition,[],[f28,f50])).
% 1.72/0.50 thf(f161,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ X0)))) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0))))))) )),
% 1.72/0.50 inference(trivial_inequality_removal,[],[f157])).
% 1.72/0.50 thf(f1517,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | ($false = ((X0 @ n_1)))) )),
% 1.72/0.50 inference(constrained_superposition,[],[f161,f50])).
% 1.72/0.50 thf(f1543,plain,(
% 1.72/0.50 ( ! [X0 : (nat > $o),X1 : nat] : (($false = ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ n_1)))) )),
% 1.72/0.50 inference(trivial_inequality_removal,[],[f1517])).
% 1.72/0.50 thf(f1617,plain,(
% 1.72/0.50 ( ! [X0 : nat,X1 : (nat > $o)] : (($true != $true) | ($true = ((X1 @ X0))) | ($false = ((X1 @ (suc @ (sK0 @ (setof @ X1)))))) | ($false = ((X1 @ n_1)))) )),
% 1.72/0.50 inference(constrained_superposition,[],[f26,f1543])).
% 1.72/0.50 thf(f1677,plain,(
% 1.72/0.50 ( ! [X0 : nat,X1 : (nat > $o)] : (($false = ((X1 @ (suc @ (sK0 @ (setof @ X1)))))) | ($true = ((X1 @ X0))) | ($false = ((X1 @ n_1)))) )),
% 1.72/0.50 inference(trivial_inequality_removal,[],[f1617])).
% 1.72/0.50 thf(f1825,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($false = (((^[Y0 : nat]: (~ (Y0 = X0))) @ n_1)))) )),
% 1.72/0.50 inference(leibniz_equality_elimination,[],[f1677])).
% 1.72/0.50 thf(f2144,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($false = ((~ (n_1 = X0))))) )),
% 1.72/0.50 inference(beta-eta_normalization,[],[f1825])).
% 1.72/0.50 thf(f2145,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($true = ((n_1 = X0)))) )),
% 1.72/0.50 inference(not_proxy_clausification,[],[f2144])).
% 1.72/0.50 thf(f2146,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | (n_1 = X0)) )),
% 1.72/0.50 inference(equality_proxy_clausification,[],[f2145])).
% 1.72/0.50 thf(f2368,plain,(
% 1.72/0.50 ( ! [X0 : nat] : ((x != X0) | (n_1 = X0)) )),
% 1.72/0.50 inference(constrained_superposition,[],[f31,f2146])).
% 1.72/0.50 thf(f2396,plain,(
% 1.72/0.50 (x = n_1)),
% 1.72/0.50 inference(equality_resolution,[],[f2368])).
% 1.72/0.50 thf(f2397,plain,(
% 1.72/0.50 $false),
% 1.72/0.50 inference(forward_subsumption_resolution,[],[f2396,f25])).
% 1.72/0.50 % SZS output end Proof for theBenchmark
% 1.72/0.50 % (3906692)------------------------------
% 1.72/0.50 % (3906692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.50 % (3906692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.50 % (3906692)CaDiCaL version: 2.1.3
% 1.72/0.50 % (3906692)Termination reason: Refutation
% 1.72/0.50 % (3906692)Time elapsed: 0.096 s
% 1.72/0.50 % (3906692)Peak memory usage: 14 MB
% 1.72/0.50 % (3906692)Instructions burned: 213 (million)
% 1.72/0.50 % (3906667)Success in time 0.213 s
% 1.72/0.50 % Vampire exiting
%------------------------------------------------------------------------------