%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.35s 0.42s
% Output : Refutation 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n003.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 12:04:59 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.34 Running higher-order theorem proving
% 0.29/0.36 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.42 % (2427385)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.42 % (2427390)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3902228094:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.42 % (2427390) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2427385-2427390"...
% 0.35/0.42 % (2427390)...printing done.
% 0.35/0.42 % (2427390)Refutation found. Thanks to Tanya!
% 0.35/0.42 % SZS status Theorem for theBenchmark
% 0.35/0.42 % SZS output start Proof for theBenchmark
% 0.35/0.42 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.35/0.42 thf(func_def_1, type, succ: ($i > $i)).
% 0.35/0.42 thf(func_def_6, type, sK1: (($i > $o) > $i)).
% 0.35/0.42 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.35/0.42 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.35/0.42 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.35/0.42 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.35/0.42 thf(f1,axiom,(
% 0.35/0.42 ! [X0 : $i] : (((succ @ X0)) != one)),
% 0.35/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_first)).
% 0.35/0.42 thf(f2,axiom,(
% 0.35/0.42 ! [X1 : $i,X0 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
% 0.35/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_injective)).
% 0.35/0.42 thf(f3,axiom,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (((X0 @ one) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1)))) => ! [X2 : $i] : (X0 @ X2))),
% 0.35/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction)).
% 0.35/0.42 thf(f4,conjecture,(
% 0.35/0.42 ! [X0 : $i] : (((succ @ X0)) != X0)),
% 0.35/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz2)).
% 0.35/0.42 thf(f5,negated_conjecture,(
% 0.35/0.42 ~ ! [X0 : $i] : (((succ @ X0)) != X0)),
% 0.35/0.42 inference(negated_conjecture,[status(cth)],[f4])).
% 0.35/0.42 thf(f6,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (((X0 @ one) & ! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1)))) => ! [X2 : $i] : (X0 @ X2))),
% 0.35/0.42 inference(rectify,[],[f3])).
% 0.35/0.42 thf(f7,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
% 0.35/0.42 inference(fool_elimination,[],[f6])).
% 0.35/0.42 thf(f8,plain,(
% 0.35/0.42 ! [X1 : $i,X0 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
% 0.35/0.42 inference(rectify,[],[f2])).
% 0.35/0.42 thf(f9,plain,(
% 0.35/0.42 ? [X0 : $i] : (((succ @ X0)) = X0)),
% 0.35/0.42 inference(ennf_transformation,[],[f5])).
% 0.35/0.42 thf(f10,plain,(
% 0.35/0.42 ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1))),
% 0.35/0.42 inference(ennf_transformation,[],[f8])).
% 0.35/0.42 thf(f11,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true)))),
% 0.35/0.42 inference(ennf_transformation,[],[f7])).
% 0.35/0.42 thf(f12,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (((X0 @ one)) != $true) | ? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)))),
% 0.35/0.42 inference(flattening,[],[f11])).
% 0.35/0.42 thf(f13,plain,(
% 0.35/0.42 (sK0 = ((succ @ sK0)))),
% 0.35/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f9])).
% 0.35/0.42 thf(f14,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (((X0 @ one)) != $true) | ? [X2 : $i] : ((((X0 @ (succ @ X2))) != $true) & (((X0 @ X2)) = $true)))),
% 0.35/0.42 inference(rectify,[],[f12])).
% 0.35/0.42 thf(f15,plain,(
% 0.35/0.42 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (((X0 @ one)) != $true) | ((((X0 @ (succ @ (sK1 @ X0)))) != $true) & (((X0 @ (sK1 @ X0))) = $true)))),
% 0.35/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK1 @ X0)],[f14])).
% 0.35/0.42 thf(f16,plain,(
% 0.35/0.42 (sK0 = ((succ @ sK0)))),
% 0.35/0.42 inference(cnf_transformation,[],[f13])).
% 0.35/0.42 thf(f17,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((succ @ X0)) != one)) )),
% 0.35/0.42 inference(cnf_transformation,[],[f1])).
% 0.35/0.42 thf(f18,plain,(
% 0.35/0.42 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ one)) != $true) | (((X0 @ (sK1 @ X0))) = $true) | (((X0 @ X1)) = $true)) )),
% 0.35/0.42 inference(cnf_transformation,[],[f15])).
% 0.35/0.42 thf(f19,plain,(
% 0.35/0.42 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (succ @ (sK1 @ X0)))) != $true) | (((X0 @ X1)) = $true) | (((X0 @ one)) != $true)) )),
% 0.35/0.42 inference(cnf_transformation,[],[f15])).
% 0.35/0.42 thf(f20,plain,(
% 0.35/0.42 ( ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1)) )),
% 0.35/0.42 inference(cnf_transformation,[],[f10])).
% 0.35/0.42 thf(f23,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((succ @ X0)) != sK0) | (sK0 = X0)) )),
% 0.35/0.42 inference(constrained_superposition,[],[f20,f16])).
% 0.35/0.42 thf(f26,plain,(
% 0.35/0.42 (one != sK0)),
% 0.35/0.42 inference(constrained_superposition,[],[f17,f16])).
% 0.35/0.42 thf(f30,plain,(
% 0.35/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (((((^[Y0 : $i]: (~ (X2 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ (X2 @ Y0)))))) = $true) | ((((^[Y0 : $i]: (~ (X2 @ Y0))) @ X1)) = $true) | ((((^[Y0 : $i]: (~ (X2 @ Y0))) @ one)) != $true)) )),
% 0.35/0.42 inference(primitive_instantiation,[],[f18])).
% 0.35/0.42 thf(f35,plain,(
% 0.35/0.42 ( ! [X2 : ($i > $o),X1 : $i] : ((((~ (X2 @ X1))) = $true) | (((~ (X2 @ one))) != $true) | (((~ (X2 @ (sK1 @ (^[Y0 : $i]: (~ (X2 @ Y0))))))) = $true)) )),
% 0.35/0.42 inference(beta-eta_normalization,[],[f30])).
% 0.35/0.42 thf(f36,plain,(
% 0.35/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((X2 @ X1))) | (((~ (X2 @ one))) != $true) | (((~ (X2 @ (sK1 @ (^[Y0 : $i]: (~ (X2 @ Y0))))))) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f35])).
% 0.35/0.42 thf(f37,plain,(
% 0.35/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((X2 @ X1))) | (((X2 @ one)) = $true) | (((~ (X2 @ (sK1 @ (^[Y0 : $i]: (~ (X2 @ Y0))))))) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f36])).
% 0.35/0.42 thf(f38,plain,(
% 0.35/0.42 ( ! [X2 : ($i > $o),X1 : $i] : (($false = ((X2 @ (sK1 @ (^[Y0 : $i]: (~ (X2 @ Y0))))))) | ($false = ((X2 @ X1))) | (((X2 @ one)) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f37])).
% 0.35/0.42 thf(f51,plain,(
% 0.35/0.42 ( ! [X0 : $i] : (((((^[Y0 : $i]: (~ (Y0 = X0))) @ one)) != $true) | (((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
% 0.35/0.42 inference(leibniz_equality_elimination,[],[f19])).
% 0.35/0.42 thf(f67,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((~ (one = X0))) != $true) | (((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
% 0.35/0.42 inference(beta-eta_normalization,[],[f51])).
% 0.35/0.42 thf(f68,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (((one = X0)) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f67])).
% 0.35/0.42 thf(f69,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((succ @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (one = X0)) )),
% 0.35/0.42 inference(equality_proxy_clausification,[],[f68])).
% 0.35/0.42 thf(f75,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((sK0 != X0) | (one = X0) | (((sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))))) = sK0)) )),
% 0.35/0.42 inference(constrained_superposition,[],[f23,f69])).
% 0.35/0.42 thf(f87,plain,(
% 0.35/0.42 (sK0 != sK0) | (one = sK0) | (sK0 = ((sK1 @ (^[Y0 : $i]: (~ (Y0 = sK0))))))),
% 0.35/0.42 inference(imitation,[],[f75])).
% 0.35/0.42 thf(f89,plain,(
% 0.35/0.42 (sK0 = ((sK1 @ (^[Y0 : $i]: (~ (Y0 = sK0)))))) | (one = sK0)),
% 0.35/0.42 inference(trivial_inequality_removal,[],[f87])).
% 0.35/0.42 thf(f90,plain,(
% 0.35/0.42 (sK0 = ((sK1 @ (^[Y0 : $i]: (~ (Y0 = sK0))))))),
% 0.35/0.42 inference(forward_subsumption_resolution,[],[f89,f26])).
% 0.35/0.42 thf(f119,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ (sK1 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (~ (X3 @ Y1))) @ Y0))))))) | ($false = (((^[Y0 : $i]: (~ (X3 @ Y0))) @ X1))) | ((((^[Y0 : $i]: (~ (X3 @ Y0))) @ one)) = $true)) )),
% 0.35/0.42 inference(primitive_instantiation,[],[f38])).
% 0.35/0.42 thf(f126,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((~ (X3 @ one))) = $true) | ($false = ((~ (X3 @ (sK1 @ (^[Y0 : $i]: (~ (~ (X3 @ Y0))))))))) | (((~ (X3 @ X1))) = $false)) )),
% 0.35/0.42 inference(beta-eta_normalization,[],[f119])).
% 0.35/0.42 thf(f127,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((X3 @ one)) = $false) | ($false = ((~ (X3 @ (sK1 @ (^[Y0 : $i]: (~ (~ (X3 @ Y0))))))))) | (((~ (X3 @ X1))) = $false)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f126])).
% 0.35/0.42 thf(f128,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((X3 @ one)) = $false) | (((X3 @ (sK1 @ (^[Y0 : $i]: (~ (~ (X3 @ Y0))))))) = $true) | (((~ (X3 @ X1))) = $false)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f127])).
% 0.35/0.42 thf(f129,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((X3 @ one)) = $false) | (((X3 @ X1)) = $true) | (((X3 @ (sK1 @ (^[Y0 : $i]: (~ (~ (X3 @ Y0))))))) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f128])).
% 0.35/0.42 thf(f130,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((X3 @ (sK1 @ (^[Y0 : $i]: (X3 @ Y0))))) = $true) | (((X3 @ X1)) = $true) | (((X3 @ one)) = $false)) )),
% 0.35/0.42 inference(boolean_simplification,[],[f129])).
% 0.35/0.42 thf(f131,plain,(
% 0.35/0.42 ( ! [X3 : ($i > $o),X1 : $i] : ((((X3 @ (sK1 @ X3))) = $true) | (((X3 @ X1)) = $true) | (((X3 @ one)) = $false)) )),
% 0.35/0.42 inference(beta-eta_normalization,[],[f130])).
% 0.35/0.42 thf(f197,plain,(
% 0.35/0.42 ( ! [X0 : $i] : (((((^[Y0 : $i]: (~ (Y0 = sK0))) @ sK0)) = $true) | ((((^[Y0 : $i]: (~ (Y0 = sK0))) @ X0)) = $true) | ($false = (((^[Y0 : $i]: (~ (Y0 = sK0))) @ one)))) )),
% 0.35/0.42 inference(constrained_superposition,[],[f131,f90])).
% 0.35/0.42 thf(f234,plain,(
% 0.35/0.42 ( ! [X0 : $i] : (($false = ((~ (one = sK0)))) | (((~ (X0 = sK0))) = $true) | (((~ (sK0 = sK0))) = $true)) )),
% 0.35/0.42 inference(beta-eta_normalization,[],[f197])).
% 0.35/0.42 thf(f235,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((~ (X0 = sK0))) = $true) | (((~ (sK0 = sK0))) = $true) | (((one = sK0)) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f234])).
% 0.35/0.42 thf(f236,plain,(
% 0.35/0.42 ( ! [X0 : $i] : (($false = ((X0 = sK0))) | (((~ (sK0 = sK0))) = $true) | (((one = sK0)) = $true)) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f235])).
% 0.35/0.42 thf(f237,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((((~ (sK0 = sK0))) = $true) | (sK0 != X0) | (((one = sK0)) = $true)) )),
% 0.35/0.42 inference(equality_proxy_clausification,[],[f236])).
% 0.35/0.42 thf(f238,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((sK0 != X0) | (((one = sK0)) = $true) | ($false = ((sK0 = sK0)))) )),
% 0.35/0.42 inference(not_proxy_clausification,[],[f237])).
% 0.35/0.42 thf(f239,plain,(
% 0.35/0.42 ( ! [X0 : $i] : (($false = ((sK0 = sK0))) | (one = sK0) | (sK0 != X0)) )),
% 0.35/0.42 inference(equality_proxy_clausification,[],[f238])).
% 0.35/0.42 thf(f240,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((one = sK0) | (sK0 != X0) | (sK0 != sK0)) )),
% 0.35/0.42 inference(equality_proxy_clausification,[],[f239])).
% 0.35/0.42 thf(f241,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((sK0 != X0) | (one = sK0)) )),
% 0.35/0.42 inference(trivial_inequality_removal,[],[f240])).
% 0.35/0.42 thf(f246,plain,(
% 0.35/0.42 ( ! [X0 : $i] : ((sK0 != X0)) )),
% 0.35/0.42 inference(forward_subsumption_resolution,[],[f241,f26])).
% 0.35/0.42 thf(f247,plain,(
% 0.35/0.42 (sK0 != sK0)),
% 0.35/0.42 inference(imitation,[],[f246])).
% 0.35/0.42 thf(f249,plain,(
% 0.35/0.42 $false),
% 0.35/0.42 inference(trivial_inequality_removal,[],[f247])).
% 0.35/0.42 % SZS output end Proof for theBenchmark
% 0.35/0.42 % (2427390)------------------------------
% 0.35/0.42 % (2427390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.42 % (2427390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.42 % (2427390)CaDiCaL version: 2.1.3
% 0.35/0.42 % (2427390)Termination reason: Refutation
% 0.35/0.42 % (2427390)Time elapsed: 0.006 s
% 0.35/0.42 % (2427390)Peak memory usage: 12 MB
% 0.35/0.42 % (2427390)Instructions burned: 10 (million)
% 0.35/0.42 % (2427385)Success in time 0.042 s
% 0.35/0.42 % Vampire exiting
%------------------------------------------------------------------------------