%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM636^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 0.54s 0.35s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM636^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n010.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 12:02:18 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.35 % (2768482)Will run a generic schedule for satisfiability detection.
% 0.54/0.35 % (2768492)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1157616375:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.54/0.35 % (2768488)% WARNING: option uhcvi not known.
% 0.54/0.35 % (2768487)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2007853073_2999 on theBenchmark for (2999ds/0Mi)
% 0.54/0.35 % (2768491)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3291312427:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.54/0.35 % (2768488)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3077403897:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.54/0.35 % (2768489)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3778430937:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.54/0.35 % (2768491)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.54/0.35 % (2768488)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.54/0.35 % (2768493)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3373034743:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.54/0.35 % Exception at run slice level
% 0.54/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.54/0.35 % (2768488)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.54/0.35 % (2768490)dis+10_1_sil=32000:sp=arity:random_seed=1748554980:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.54/0.35 % (2768500)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3177174910:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.54/0.35 % Exception at run slice level
% 0.54/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.54/0.35 % (2768492)Instruction limit reached!
% 0.54/0.35 % (2768492)------------------------------
% 0.54/0.35 % (2768492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.35 % (2768492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.35 % (2768492)CaDiCaL version: 2.1.3
% 0.54/0.35 % (2768492)Termination reason: Instruction limit
% 0.54/0.35 % (2768492)Termination phase: Saturation
% 0.54/0.35 % (2768492)Time elapsed: 0.035 s
% 0.54/0.35 % (2768492)Peak memory usage: 12 MB
% 0.54/0.35 % (2768492)Instructions burned: 131 (million)
% 0.54/0.35 % (2768504)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=1655373193:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.54/0.35 % (2768503)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=712148300:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.54/0.35 % (2768504)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.54/0.35 % (2768504)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.54/0.35 % (2768491)Instruction limit reached!
% 0.54/0.35 % (2768491)------------------------------
% 0.54/0.35 % (2768491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.35 % (2768491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.35 % (2768491)CaDiCaL version: 2.1.3
% 0.54/0.35 % (2768491)Termination reason: Instruction limit
% 0.54/0.35 % (2768491)Termination phase: Saturation
% 0.54/0.35 % (2768491)Time elapsed: 0.057 s
% 0.54/0.35 % (2768491)Peak memory usage: 12 MB
% 0.54/0.35 % (2768491)Instructions burned: 116 (million)
% 0.54/0.35 % (2768507)ott-21_1_sil=16000:fs=off:random_seed=3631224232:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.54/0.35 % (2768493)Instruction limit reached!
% 0.54/0.35 % (2768493)------------------------------
% 0.54/0.35 % (2768493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.35 % (2768493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.35 % (2768493)CaDiCaL version: 2.1.3
% 0.54/0.35 % (2768493)Termination reason: Instruction limit
% 0.54/0.35 % (2768493)Termination phase: Saturation
% 0.54/0.35 % (2768493)Time elapsed: 0.081 s
% 0.54/0.35 % (2768493)Peak memory usage: 12 MB
% 0.54/0.35 % (2768493)Instructions burned: 159 (million)
% 0.54/0.35 % (2768490)Instruction limit reached!
% 0.54/0.35 % (2768490)------------------------------
% 0.54/0.35 % (2768490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.35 % (2768490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.35 % (2768490)CaDiCaL version: 2.1.3
% 0.54/0.35 % (2768490)Termination reason: Instruction limit
% 0.54/0.35 % (2768490)Termination phase: Saturation
% 0.54/0.35 % (2768490)Time elapsed: 0.075 s
% 0.54/0.35 % (2768490)Peak memory usage: 12 MB
% 0.54/0.35 % (2768490)Instructions burned: 103 (million)
% 0.54/0.35 % (2768509)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1805362372:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.54/0.35 % (2768504) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2768482-2768504"...
% 0.54/0.35 % (2768504)...printing done.
% 0.54/0.35 % (2768504)Refutation found. Thanks to Tanya!
% 0.54/0.35 % SZS status Theorem for theBenchmark
% 0.54/0.35 % SZS output start Proof for theBenchmark
% 0.54/0.35 thf(type_def_5, type, nat: $tType).
% 0.54/0.35 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.54/0.35 thf(type_def_7, type, set: $tType).
% 0.54/0.35 thf(func_def_0, type, x: nat).
% 0.54/0.35 thf(func_def_1, type, suc: (nat > nat)).
% 0.54/0.35 thf(func_def_2, type, esti: (nat > set > $o)).
% 0.54/0.35 thf(func_def_3, type, setof: ((nat > $o) > set)).
% 0.54/0.35 thf(func_def_5, type, n_1: nat).
% 0.54/0.35 thf(func_def_8, type, sK0: (set > nat)).
% 0.54/0.35 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.54/0.35 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.54/0.35 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.54/0.35 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.35 thf(f1,axiom,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',estie)).
% 0.54/0.35 thf(f2,axiom,(
% 0.54/0.35 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X1 : nat] : (esti @ X1 @ X0)))),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)).
% 0.54/0.35 thf(f3,axiom,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',estii)).
% 0.54/0.35 thf(f4,axiom,(
% 0.54/0.35 ! [X0 : nat] : (((suc @ X0)) != n_1)),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 0.54/0.35 thf(f5,axiom,(
% 0.54/0.35 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (((suc @ X0)) != ((suc @ X1))))),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1)).
% 0.54/0.35 thf(f6,conjecture,(
% 0.54/0.35 (((suc @ x)) != x)),
% 0.54/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz2)).
% 0.54/0.35 thf(f7,negated_conjecture,(
% 0.54/0.35 ~ (((suc @ x)) != x)),
% 0.54/0.35 inference(negated_conjecture,[status(cth)],[f6])).
% 0.54/0.35 thf(f8,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((esti @ X1 @ (setof @ X0)) => (X0 @ X1))),
% 0.54/0.35 inference(rectify,[],[f1])).
% 0.54/0.35 thf(f9,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) => (((X0 @ X1)) = $true))),
% 0.54/0.35 inference(fool_elimination,[],[f8])).
% 0.54/0.35 thf(f10,plain,(
% 0.54/0.35 ! [X0 : set] : ((esti @ n_1 @ X0) => (! [X1 : nat] : ((esti @ X1 @ X0) => (esti @ (suc @ X1) @ X0)) => ! [X2 : nat] : (esti @ X2 @ X0)))),
% 0.54/0.35 inference(rectify,[],[f2])).
% 0.54/0.35 thf(f11,plain,(
% 0.54/0.35 ! [X0 : set] : ((((esti @ n_1 @ X0)) = $true) => (! [X1 : nat] : ((((esti @ X1 @ X0)) = $true) => (((esti @ (suc @ X1) @ X0)) = $true)) => ! [X2 : nat] : ($true = ((esti @ X2 @ X0)))))),
% 0.54/0.35 inference(fool_elimination,[],[f10])).
% 0.54/0.35 thf(f12,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((X0 @ X1) => (esti @ X1 @ (setof @ X0)))),
% 0.54/0.35 inference(rectify,[],[f3])).
% 0.54/0.35 thf(f13,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) = $true) => (((esti @ X1 @ (setof @ X0))) = $true))),
% 0.54/0.35 inference(fool_elimination,[],[f12])).
% 0.54/0.35 thf(f14,plain,(
% 0.54/0.35 (x = ((suc @ x)))),
% 0.54/0.35 inference(flattening,[],[f7])).
% 0.54/0.35 thf(f15,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) = $true) | (((esti @ X1 @ (setof @ X0))) != $true))),
% 0.54/0.35 inference(ennf_transformation,[],[f9])).
% 0.54/0.35 thf(f16,plain,(
% 0.54/0.35 ! [X0 : set] : ((! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true))) | (((esti @ n_1 @ X0)) != $true))),
% 0.54/0.35 inference(ennf_transformation,[],[f11])).
% 0.54/0.35 thf(f17,plain,(
% 0.54/0.35 ! [X0 : set] : (! [X2 : nat] : ($true = ((esti @ X2 @ X0))) | ? [X1 : nat] : ((((esti @ (suc @ X1) @ X0)) != $true) & (((esti @ X1 @ X0)) = $true)) | (((esti @ n_1 @ X0)) != $true))),
% 0.54/0.35 inference(flattening,[],[f16])).
% 0.54/0.35 thf(f18,plain,(
% 0.54/0.35 ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) != $true))),
% 0.54/0.35 inference(ennf_transformation,[],[f13])).
% 0.54/0.35 thf(f19,plain,(
% 0.54/0.35 ! [X0 : nat,X1 : nat] : ((((suc @ X0)) != ((suc @ X1))) | (X0 = X1))),
% 0.54/0.35 inference(ennf_transformation,[],[f5])).
% 0.54/0.35 thf(f20,plain,(
% 0.54/0.35 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | ? [X2 : nat] : (($true != ((esti @ (suc @ X2) @ X0))) & ($true = ((esti @ X2 @ X0)))) | (((esti @ n_1 @ X0)) != $true))),
% 0.54/0.35 inference(rectify,[],[f17])).
% 0.54/0.35 thf(f21,plain,(
% 0.54/0.35 ! [X0 : set] : (! [X1 : nat] : (((esti @ X1 @ X0)) = $true) | (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) & ($true = ((esti @ (sK0 @ X0) @ X0)))) | (((esti @ n_1 @ X0)) != $true))),
% 0.54/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f20])).
% 0.54/0.35 thf(f22,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) != $true) | (((X0 @ X1)) = $true)) )),
% 0.54/0.35 inference(cnf_transformation,[],[f15])).
% 0.54/0.35 thf(f23,plain,(
% 0.54/0.35 ( ! [X0 : set,X1 : nat] : ((((esti @ n_1 @ X0)) != $true) | ($true = ((esti @ (sK0 @ X0) @ X0))) | (((esti @ X1 @ X0)) = $true)) )),
% 0.54/0.35 inference(cnf_transformation,[],[f21])).
% 0.54/0.35 thf(f24,plain,(
% 0.54/0.35 ( ! [X0 : set,X1 : nat] : (($true != ((esti @ (suc @ (sK0 @ X0)) @ X0))) | (((esti @ X1 @ X0)) = $true) | (((esti @ n_1 @ X0)) != $true)) )),
% 0.54/0.35 inference(cnf_transformation,[],[f21])).
% 0.54/0.35 thf(f25,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : ((((X0 @ X1)) != $true) | (((esti @ X1 @ (setof @ X0))) = $true)) )),
% 0.54/0.35 inference(cnf_transformation,[],[f18])).
% 0.54/0.35 thf(f26,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((n_1 != ((suc @ X0)))) )),
% 0.54/0.35 inference(cnf_transformation,[],[f4])).
% 0.54/0.35 thf(f27,plain,(
% 0.54/0.35 ( ! [X0 : nat,X1 : nat] : ((((suc @ X1)) != ((suc @ X0))) | (X0 = X1)) )),
% 0.54/0.35 inference(cnf_transformation,[],[f19])).
% 0.54/0.35 thf(f28,plain,(
% 0.54/0.35 (x = ((suc @ x)))),
% 0.54/0.35 inference(cnf_transformation,[],[f14])).
% 0.54/0.35 thf(f30,definition,(
% 0.54/0.35 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.54/0.35 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.54/0.35 thf(f31,plain,(
% 0.54/0.35 (n_1 != x)),
% 0.54/0.35 inference(constrained_superposition,[],[f26,f28])).
% 0.54/0.35 thf(f32,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((((suc @ X0)) != x) | (x = X0)) )),
% 0.54/0.35 inference(constrained_superposition,[],[f27,f28])).
% 0.54/0.35 thf(f54,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.54/0.35 inference(constrained_superposition,[],[f25,f30])).
% 0.54/0.35 thf(f56,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : ((((esti @ X1 @ (setof @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f54])).
% 0.54/0.35 thf(f116,plain,(
% 0.54/0.35 ( ! [X0 : set,X1 : nat] : (($true != $true) | ($true = ((esti @ (sK0 @ X0) @ X0))) | (((esti @ X1 @ X0)) = $true) | (((esti @ n_1 @ X0)) = $false)) )),
% 0.54/0.35 inference(constrained_superposition,[],[f23,f30])).
% 0.54/0.35 thf(f117,plain,(
% 0.54/0.35 ( ! [X0 : set,X1 : nat] : (($true = ((esti @ (sK0 @ X0) @ X0))) | (((esti @ X1 @ X0)) = $true) | (((esti @ n_1 @ X0)) = $false)) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f116])).
% 0.54/0.35 thf(f132,plain,(
% 0.54/0.35 ( ! [X0 : set] : (($true != $true) | ($true = ((esti @ (sK0 @ X0) @ X0))) | (((esti @ n_1 @ X0)) = $false)) )),
% 0.54/0.35 inference(equality_factoring,[],[f117])).
% 0.54/0.35 thf(f134,plain,(
% 0.54/0.35 ( ! [X0 : set] : (($true = ((esti @ (sK0 @ X0) @ X0))) | (((esti @ n_1 @ X0)) = $false)) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f132])).
% 0.54/0.35 thf(f151,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($true != $true) | ($true = ((X0 @ (sK0 @ (setof @ X0))))) | ($false = ((esti @ n_1 @ (setof @ X0))))) )),
% 0.54/0.35 inference(constrained_superposition,[],[f22,f134])).
% 0.54/0.35 thf(f158,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($true = ((X0 @ (sK0 @ (setof @ X0))))) | ($false = ((esti @ n_1 @ (setof @ X0))))) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f151])).
% 0.54/0.35 thf(f177,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($true = $false) | ($false = ((X0 @ n_1))) | ($true = ((X0 @ (sK0 @ (setof @ X0)))))) )),
% 0.54/0.35 inference(constrained_superposition,[],[f56,f158])).
% 0.54/0.35 thf(f198,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($true = ((X0 @ (sK0 @ (setof @ X0))))) | ($false = ((X0 @ n_1)))) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f177])).
% 0.54/0.35 thf(f264,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($true != ((X0 @ n_1))) | ($false = ((X0 @ n_1))) | ($false != ((X0 @ (sK0 @ (setof @ X0)))))) )),
% 0.54/0.35 inference(equality_factoring,[],[f198])).
% 0.54/0.35 thf(f296,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o)] : (($false != ((X0 @ (sK0 @ (setof @ X0))))) | ($false = ((X0 @ n_1)))) )),
% 0.54/0.35 inference(forward_subsumption_resolution,[],[f264,f30])).
% 0.54/0.35 thf(f597,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | ($true != ((esti @ n_1 @ (setof @ X0)))) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0))))))) )),
% 0.54/0.35 inference(constrained_superposition,[],[f24,f56])).
% 0.54/0.35 thf(f610,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : (($true != ((esti @ n_1 @ (setof @ X0)))) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0))))))) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f597])).
% 0.54/0.35 thf(f1705,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : (($true != $true) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | ($false = ((X0 @ n_1)))) )),
% 0.54/0.35 inference(constrained_superposition,[],[f610,f56])).
% 0.54/0.35 thf(f1728,plain,(
% 0.54/0.35 ( ! [X0 : (nat > $o),X1 : nat] : (($false = ((X0 @ (suc @ (sK0 @ (setof @ X0)))))) | (((esti @ X1 @ (setof @ X0))) = $true) | ($false = ((X0 @ n_1)))) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f1705])).
% 0.54/0.35 thf(f1796,plain,(
% 0.54/0.35 ( ! [X0 : nat,X1 : (nat > $o)] : (($true != $true) | ($true = ((X1 @ X0))) | ($false = ((X1 @ (suc @ (sK0 @ (setof @ X1)))))) | ($false = ((X1 @ n_1)))) )),
% 0.54/0.35 inference(constrained_superposition,[],[f22,f1728])).
% 0.54/0.35 thf(f1867,plain,(
% 0.54/0.35 ( ! [X0 : nat,X1 : (nat > $o)] : (($false = ((X1 @ (suc @ (sK0 @ (setof @ X1)))))) | ($true = ((X1 @ X0))) | ($false = ((X1 @ n_1)))) )),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f1796])).
% 0.54/0.35 thf(f2003,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($false = (((^[Y0 : nat]: (~ (Y0 = X0))) @ n_1)))) )),
% 0.54/0.35 inference(leibniz_equality_elimination,[],[f1867])).
% 0.54/0.35 thf(f2322,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($false = ((~ (n_1 = X0))))) )),
% 0.54/0.35 inference(beta-eta_normalization,[],[f2003])).
% 0.54/0.35 thf(f2323,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | ($true = ((n_1 = X0)))) )),
% 0.54/0.35 inference(not_proxy_clausification,[],[f2322])).
% 0.54/0.35 thf(f2324,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((((suc @ (sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) = X0) | (n_1 = X0)) )),
% 0.54/0.35 inference(equality_proxy_clausification,[],[f2323])).
% 0.54/0.35 thf(f2732,plain,(
% 0.54/0.35 ( ! [X0 : nat] : ((x != X0) | (x = ((sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = X0))))))) | (n_1 = X0)) )),
% 0.54/0.35 inference(constrained_superposition,[],[f32,f2324])).
% 0.54/0.35 thf(f2768,plain,(
% 0.54/0.35 (x = ((sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = x))))))) | (n_1 = x)),
% 0.54/0.35 inference(equality_resolution,[],[f2732])).
% 0.54/0.35 thf(f2769,plain,(
% 0.54/0.35 (x = ((sK0 @ (setof @ (^[Y0 : nat]: (~ (Y0 = x)))))))),
% 0.54/0.35 inference(forward_subsumption_resolution,[],[f2768,f31])).
% 0.54/0.35 thf(f2778,plain,(
% 0.54/0.35 ($false != (((^[Y0 : nat]: (~ (Y0 = x))) @ x))) | ($false = (((^[Y0 : nat]: (~ (Y0 = x))) @ n_1)))),
% 0.54/0.35 inference(constrained_superposition,[],[f296,f2769])).
% 0.54/0.35 thf(f2818,plain,(
% 0.54/0.35 ($false != ((~ (x = x)))) | ($false = ((~ (n_1 = x))))),
% 0.54/0.35 inference(beta-eta_normalization,[],[f2778])).
% 0.54/0.35 thf(f2819,plain,(
% 0.54/0.35 ($false = ((x = x))) | ($false = ((~ (n_1 = x))))),
% 0.54/0.35 inference(not_proxy_clausification,[],[f2818])).
% 0.54/0.35 thf(f2820,plain,(
% 0.54/0.35 (x != x) | ($false = ((~ (n_1 = x))))),
% 0.54/0.35 inference(equality_proxy_clausification,[],[f2819])).
% 0.54/0.35 thf(f2821,plain,(
% 0.54/0.35 (x != x) | ($true = ((n_1 = x)))),
% 0.54/0.35 inference(not_proxy_clausification,[],[f2820])).
% 0.54/0.35 thf(f2822,plain,(
% 0.54/0.35 (x != x) | (n_1 = x)),
% 0.54/0.35 inference(equality_proxy_clausification,[],[f2821])).
% 0.54/0.35 thf(f2823,plain,(
% 0.54/0.35 (n_1 = x)),
% 0.54/0.35 inference(trivial_inequality_removal,[],[f2822])).
% 0.54/0.35 thf(f2843,plain,(
% 0.54/0.35 $false),
% 0.54/0.35 inference(forward_subsumption_resolution,[],[f2823,f31])).
% 0.54/0.35 % SZS output end Proof for theBenchmark
% 0.54/0.35 % (2768504)------------------------------
% 0.54/0.35 % (2768504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.35 % (2768504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.35 % (2768504)CaDiCaL version: 2.1.3
% 0.54/0.35 % (2768504)Termination reason: Refutation
% 0.54/0.35 % (2768504)Time elapsed: 0.063 s
% 0.54/0.35 % (2768504)Peak memory usage: 13 MB
% 0.54/0.35 % (2768504)Instructions burned: 246 (million)
% 0.54/0.35 % (2768482)Success in time 0.138 s
% 0.54/0.35 % Vampire exiting
%------------------------------------------------------------------------------