%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM636^2 : 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 : n007.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 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n007.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 12:01:26 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.22/0.26 % (3268244)Will run a generic schedule for satisfiability detection.
% 0.22/0.26 % (3268251)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1320971643:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.26 % (3268250)% WARNING: option uhcvi not known.
% 0.22/0.26 % (3268249)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1532319789_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.26 % (3268250)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3439364073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.26 % (3268252)dis+10_1_sil=32000:sp=arity:random_seed=3969993562:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.26 % (3268253)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3034241465:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.26 % (3268250)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.26 % Exception at run slice level
% 0.22/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.26 % (3268250)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.26 % (3268253)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.26 % (3268251) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3268244-3268251"...
% 0.22/0.26 % (3268251)...printing done.
% 0.22/0.26 % (3268251)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% 0.22/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.26 thf(func_def_1, type, succ: ($i > $i)).
% 0.22/0.26 thf(func_def_5, type, sK0: (($i > $o) > $i)).
% 0.22/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.22/0.26 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.26 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.26 thf(f1,axiom,(
% 0.22/0.26 ! [X0 : $i] : (((succ @ X0)) != one)),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first)).
% 0.22/0.26 thf(f2,axiom,(
% 0.22/0.26 ! [X0 : $i,X1 : $i] : ((((succ @ X0)) = ((succ @ X1))) => (X0 = X1))),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective)).
% 0.22/0.26 thf(f3,axiom,(
% 0.22/0.26 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction)).
% 0.22/0.26 thf(f4,conjecture,(
% 0.22/0.26 ! [X0 : $i] : (((succ @ X0)) != X0)),
% 0.22/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz2)).
% 0.22/0.26 thf(f5,negated_conjecture,(
% 0.22/0.26 ~ ! [X0 : $i] : (((succ @ X0)) != X0)),
% 0.22/0.26 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.26 thf(f6,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.22/0.26 inference(rectify,[],[f3])).
% 0.22/0.26 thf(f7,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
% 0.22/0.26 inference(fool_elimination,[],[f6])).
% 0.22/0.26 thf(f8,plain,(
% 0.22/0.26 ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((succ @ X0)) != ((succ @ X1))))),
% 0.22/0.26 inference(ennf_transformation,[],[f2])).
% 0.22/0.26 thf(f9,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true)))),
% 0.22/0.26 inference(ennf_transformation,[],[f7])).
% 0.22/0.26 thf(f10,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | ? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true))),
% 0.22/0.26 inference(flattening,[],[f9])).
% 0.22/0.26 thf(f11,plain,(
% 0.22/0.26 ? [X0 : $i] : (((succ @ X0)) = X0)),
% 0.22/0.26 inference(ennf_transformation,[],[f5])).
% 0.22/0.26 thf(f12,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | ? [X2 : $i] : (($true != ((X0 @ (succ @ X2)))) & (((X0 @ X2)) = $true)) | (((X0 @ one)) != $true))),
% 0.22/0.26 inference(rectify,[],[f10])).
% 0.22/0.26 thf(f13,plain,(
% 0.22/0.26 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (($true != ((X0 @ (succ @ (sK0 @ X0))))) & ($true = ((X0 @ (sK0 @ X0))))) | (((X0 @ one)) != $true))),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f12])).
% 0.22/0.26 thf(f14,plain,(
% 0.22/0.26 (sK1 = ((succ @ sK1)))),
% 0.22/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11])).
% 0.22/0.26 thf(f15,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ X0)) != one)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f1])).
% 0.22/0.26 thf(f16,plain,(
% 0.22/0.26 ( ! [X0 : $i,X1 : $i] : ((((succ @ X0)) != ((succ @ X1))) | (X0 = X1)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f8])).
% 0.22/0.26 thf(f17,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ one)) != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f13])).
% 0.22/0.26 thf(f18,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (succ @ (sK0 @ X0))))) | (((X0 @ X1)) = $true) | (((X0 @ one)) != $true)) )),
% 0.22/0.26 inference(cnf_transformation,[],[f13])).
% 0.22/0.26 thf(f19,plain,(
% 0.22/0.26 (sK1 = ((succ @ sK1)))),
% 0.22/0.26 inference(cnf_transformation,[],[f14])).
% 0.22/0.26 thf(f21,definition,(
% 0.22/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.26 thf(f22,plain,(
% 0.22/0.26 (one != sK1)),
% 0.22/0.26 inference(constrained_superposition,[],[f15,f19])).
% 0.22/0.26 thf(f64,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ X0)) != sK1) | (sK1 = X0)) )),
% 0.22/0.26 inference(constrained_superposition,[],[f16,f19])).
% 0.22/0.26 thf(f128,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true) | (((X0 @ one)) = $false)) )),
% 0.22/0.26 inference(constrained_superposition,[],[f17,f21])).
% 0.22/0.26 thf(f135,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ X1)) = $true) | (((X0 @ one)) = $false)) )),
% 0.22/0.26 inference(trivial_inequality_removal,[],[f128])).
% 0.22/0.26 thf(f237,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ one)) != $true) | ($true = ((X0 @ (sK0 @ X0)))) | (((X0 @ one)) = $false) | (((X0 @ X1)) != $false)) )),
% 0.22/0.26 inference(equality_factoring,[],[f135])).
% 0.22/0.26 thf(f284,plain,(
% 0.22/0.26 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $false) | (((X0 @ one)) = $false) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.22/0.26 inference(forward_subsumption_resolution,[],[f237,f21])).
% 0.22/0.26 thf(f334,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((one = X0) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))))) )),
% 0.22/0.26 inference(leibniz_equality_elimination,[],[f284])).
% 0.22/0.26 thf(f354,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((one = X0) | ($true = ((~ ((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0))))) )),
% 0.22/0.26 inference(beta-eta_normalization,[],[f334])).
% 0.22/0.26 thf(f355,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((one = X0) | ($false = (((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))) = X0)))) )),
% 0.22/0.26 inference(not_proxy_clausification,[],[f354])).
% 0.22/0.26 thf(f356,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))))) != X0) | (one = X0)) )),
% 0.22/0.26 inference(equality_proxy_clausification,[],[f355])).
% 0.22/0.26 thf(f431,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true != (((^[Y0 : $i]: (~ (Y0 = X0))) @ one)))) )),
% 0.22/0.26 inference(leibniz_equality_elimination,[],[f18])).
% 0.22/0.26 thf(f464,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true != ((~ (one = X0))))) )),
% 0.22/0.26 inference(beta-eta_normalization,[],[f431])).
% 0.22/0.26 thf(f465,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true = ((one = X0)))) )),
% 0.22/0.26 inference(not_proxy_clausification,[],[f464])).
% 0.22/0.26 thf(f466,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((((succ @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (one = X0)) )),
% 0.22/0.26 inference(equality_proxy_clausification,[],[f465])).
% 0.22/0.26 thf(f835,plain,(
% 0.22/0.26 ( ! [X0 : $i] : ((sK1 != X0) | (sK1 = ((sK0 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) | (one = X0)) )),
% 0.22/0.26 inference(constrained_superposition,[],[f64,f466])).
% 0.22/0.26 thf(f872,plain,(
% 0.22/0.26 (sK1 = ((sK0 @ (^[Y0 : $i]: (~ (Y0 = sK1)))))) | (one = sK1)),
% 0.22/0.26 inference(equality_resolution,[],[f835])).
% 0.22/0.26 thf(f876,plain,(
% 0.22/0.26 (one = sK1)),
% 0.22/0.26 inference(forward_subsumption_resolution,[],[f872,f356])).
% 0.22/0.26 thf(f877,plain,(
% 0.22/0.26 $false),
% 0.22/0.26 inference(forward_subsumption_resolution,[],[f876,f22])).
% 0.22/0.26 % SZS output end Proof for theBenchmark
% 0.22/0.26 % (3268251)------------------------------
% 0.22/0.26 % (3268251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.26 % (3268251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.26 % (3268251)CaDiCaL version: 2.1.3
% 0.22/0.26 % (3268251)Termination reason: Refutation
% 0.22/0.26 % (3268251)Time elapsed: 0.011 s
% 0.22/0.26 % (3268251)Peak memory usage: 12 MB
% 0.22/0.26 % (3268251)Instructions burned: 32 (million)
% 0.22/0.26 % (3268244)Success in time 0.039 s
% 0.22/0.26 % Vampire exiting
%------------------------------------------------------------------------------