%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM636^3 : 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 : n004.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 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^3 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 12:07:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24 Running first-order model finding
% 0.08/0.24 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
% 0.21/0.29 % (1209562)Will run a generic schedule for satisfiability detection.
% 0.21/0.29 % (1209568)% WARNING: option uhcvi not known.
% 0.21/0.29 % (1209572)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2639342796:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.29 % (1209568)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3876742217:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.29 % (1209567)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=404046707_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.29 % (1209568)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % (1209570)dis+10_1_sil=32000:sp=arity:random_seed=2818682324:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.29 % (1209569)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2867062373:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.29 % (1209568)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.29 % Exception at run slice level
% 0.21/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.29 % (1209571)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3513247966:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.29 % (1209571)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.29 % (1209572) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1209562-1209572"...
% 0.21/0.29 % (1209572)...printing done.
% 0.21/0.29 % (1209572)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_1, type, succ: ($i > $i)).
% 0.21/0.29 thf(func_def_3, type, m: ($i > $o)).
% 0.21/0.29 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.29 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(func_def_10, type, sK0: (($i > $o) > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ! [X0 : $i] : (((succ @ X0)) != one)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first)).
% 0.21/0.29 thf(f2,axiom,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective)).
% 0.21/0.29 thf(f3,axiom,(
% 0.21/0.29 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction)).
% 0.21/0.29 thf(f4,axiom,(
% 0.21/0.29 (m = (^[X0 : $i] : ((((succ @ X0)) != X0))))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_defn)).
% 0.21/0.29 thf(f7,conjecture,(
% 0.21/0.29 ! [X0 : $i] : (m @ X0)),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_is_all)).
% 0.21/0.29 thf(f8,negated_conjecture,(
% 0.21/0.29 ~ ! [X0 : $i] : (m @ X0)),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.21/0.29 inference(rectify,[],[f3])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
% 0.21/0.29 inference(fool_elimination,[],[f9])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 (m = (^[Y0 : $i]: (~ ((succ @ Y0) = Y0))))),
% 0.21/0.29 inference(fool_elimination,[],[f4])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ~ ! [X0 : $i] : (m @ X0)),
% 0.21/0.29 inference(rectify,[],[f8])).
% 0.21/0.29 thf(f17,plain,(
% 0.21/0.29 ~ ! [X0 : $i] : (((m @ X0)) = $true)),
% 0.21/0.29 inference(fool_elimination,[],[f16])).
% 0.21/0.29 thf(f18,plain,(
% 0.21/0.29 ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((succ @ X0)) != ((succ @ X1))))),
% 0.21/0.29 inference(ennf_transformation,[],[f2])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true)))),
% 0.21/0.29 inference(ennf_transformation,[],[f10])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | ? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true))),
% 0.21/0.29 inference(flattening,[],[f19])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ? [X0 : $i] : (((m @ X0)) != $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f17])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | ? [X2 : $i] : (($true != ((X0 @ (succ @ X2)))) & (((X0 @ X2)) = $true)) | (((X0 @ one)) != $true))),
% 0.21/0.29 inference(rectify,[],[f20])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (($true != ((X0 @ (succ @ (sK0 @ X0))))) & ($true = ((X0 @ (sK0 @ X0))))) | (((X0 @ one)) != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f23])).
% 0.21/0.29 thf(f25,plain,(
% 0.21/0.29 ($true != ((m @ sK1)))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f22])).
% 0.21/0.29 thf(f26,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ X0)) != one)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f1])).
% 0.21/0.29 thf(f27,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f18])).
% 0.21/0.29 thf(f28,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ one)) != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (succ @ (sK0 @ X0))))) | (((X0 @ X1)) = $true) | (((X0 @ one)) != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f24])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 (m = (^[Y0 : $i]: (~ ((succ @ Y0) = Y0))))),
% 0.21/0.29 inference(cnf_transformation,[],[f11])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ($true != ((m @ sK1)))),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f35,definition,(
% 0.21/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 ($true != (((^[Y0 : $i]: (~ ((succ @ Y0) = Y0))) @ sK1)))),
% 0.21/0.29 inference(definition_unfolding,[],[f33,f30])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 ($true != ((~ ((succ @ sK1) = sK1))))),
% 0.21/0.29 inference(beta-eta_normalization,[],[f38])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 ($true = (((succ @ sK1) = sK1)))),
% 0.21/0.29 inference(not_proxy_clausification,[],[f39])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 (sK1 = ((succ @ sK1)))),
% 0.21/0.29 inference(equality_proxy_clausification,[],[f40])).
% 0.21/0.29 thf(f57,plain,(
% 0.21/0.29 (one != sK1)),
% 0.21/0.29 inference(constrained_superposition,[],[f26,f41])).
% 0.21/0.29 thf(f59,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ X0)) != sK1) | (sK1 = X0)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f27,f41])).
% 0.21/0.29 thf(f66,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true) | (((X0 @ one)) = $false)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f28,f35])).
% 0.21/0.29 thf(f70,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true) | (((X0 @ one)) = $false)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.29 thf(f90,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true != (((^[Y0 : $i]: (~ (Y0 = X0))) @ one)))) )),
% 0.21/0.29 inference(leibniz_equality_elimination,[],[f29])).
% 0.21/0.29 thf(f113,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true != ((~ (one = X0))))) )),
% 0.21/0.29 inference(beta-eta_normalization,[],[f90])).
% 0.21/0.29 thf(f114,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true = ((one = X0)))) )),
% 0.21/0.29 inference(not_proxy_clausification,[],[f113])).
% 0.21/0.29 thf(f115,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (one = X0)) )),
% 0.21/0.29 inference(equality_proxy_clausification,[],[f114])).
% 0.21/0.29 thf(f137,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ one)) != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ one)) = $false) | (((X0 @ X1)) != $false)) )),
% 0.21/0.29 inference(equality_factoring,[],[f70])).
% 0.21/0.29 thf(f192,plain,(
% 0.21/0.29 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $false) | (((X0 @ one)) = $false) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f137,f70])).
% 0.21/0.29 thf(f230,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((one = X0) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))))) )),
% 0.21/0.29 inference(leibniz_equality_elimination,[],[f192])).
% 0.21/0.29 thf(f250,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((one = X0) | ($true = ((~ ((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0))))) )),
% 0.21/0.29 inference(beta-eta_normalization,[],[f230])).
% 0.21/0.29 thf(f251,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((one = X0) | ($false = (((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0)))) )),
% 0.21/0.29 inference(not_proxy_clausification,[],[f250])).
% 0.21/0.29 thf(f252,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((one = X0) | (((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))))) != X0)) )),
% 0.21/0.29 inference(equality_proxy_clausification,[],[f251])).
% 0.21/0.29 thf(f255,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((sK1 != X0) | (sK1 = ((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) | (one = X0)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f59,f115])).
% 0.21/0.29 thf(f269,plain,(
% 0.21/0.29 (sK1 = ((sK0 @ (^[Y0 : $i]: (~ (Y0 = sK1)))))) | (one = sK1)),
% 0.21/0.29 inference(equality_resolution,[],[f255])).
% 0.21/0.29 thf(f270,plain,(
% 0.21/0.29 (one = sK1)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f269,f252])).
% 0.21/0.29 thf(f271,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f270,f57])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (1209572)------------------------------
% 0.21/0.29 % (1209572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1209572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1209572)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1209572)Termination reason: Refutation
% 0.21/0.29 % (1209572)Time elapsed: 0.007 s
% 0.21/0.29 % (1209572)Peak memory usage: 12 MB
% 0.21/0.29 % (1209572)Instructions burned: 11 (million)
% 0.21/0.29 % (1209562)Success in time 0.04 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------