%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:18:58 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:00:51 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.21/0.27 % (2067386)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (2067393)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=99590368:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.27 % (2067393)Refutation not found, incomplete strategy
% 0.21/0.27 % (2067393)------------------------------
% 0.21/0.27 % (2067393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2067393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2067393)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2067393)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (2067393)Time elapsed: 0.001 s
% 0.21/0.27 % (2067393)Peak memory usage: 12 MB
% 0.21/0.27 % (2067393)Instructions burned: 1 (million)
% 0.21/0.27 % (2067393)------------------------------
% 0.21/0.27 % (2067393)------------------------------
% 0.21/0.27 % (2067397)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (2067397)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.27 % (2067391)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=628074996:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (2067392)lrs+10_16_si=on:nwc=1.5:random_seed=3464350363:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.27 % (2067394)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2263013115:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.27 % (2067395)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1128527639:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (2067397)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1261286225:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.27 % (2067391) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2067386-2067391"...
% 0.21/0.27 % (2067395) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2067386-2067395"...
% 0.21/0.27 % (2067397)Refutation not found, incomplete strategy
% 0.21/0.27 % (2067397)------------------------------
% 0.21/0.27 % (2067397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2067397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2067397)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2067397)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.27 % (2067397)Time elapsed: 0.002 s
% 0.21/0.27 % (2067397)Peak memory usage: 12 MB
% 0.21/0.27 % (2067397)Instructions burned: 3 (million)
% 0.21/0.27 % (2067391)...printing done.
% 0.21/0.27 % (2067397)------------------------------
% 0.21/0.27 % (2067397)------------------------------
% 0.21/0.27 % (2067395)...printing done.
% 0.21/0.27 % (2067394) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2067386-2067394"...
% 0.21/0.27 % (2067391)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_1, type, cS: ($i > $i)).
% 0.21/0.27 thf(func_def_2, type, cIND: $o).
% 0.21/0.27 thf(func_def_7, type, sK1: (($i > $o) > $i)).
% 0.21/0.27 thf(func_def_8, type, sK2: ($i > $o)).
% 0.21/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.21/0.27 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.27 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.27 thf(f1,axiom,(
% 0.21/0.27 (cIND = ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X1 : $i] : (X0 @ X1)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cIND_def)).
% 0.21/0.27 thf(f2,conjecture,(
% 0.21/0.27 cIND => ! [X0 : $i] : (? [X1 : $i] : (X0 = ((cS @ X1))) | (X0 = c0))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM578)).
% 0.21/0.27 thf(f3,negated_conjecture,(
% 0.21/0.27 ~(cIND => ! [X0 : $i] : (? [X1 : $i] : (X0 = ((cS @ X1))) | (X0 = c0)))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f2])).
% 0.21/0.27 thf(f4,plain,(
% 0.21/0.27 (cIND = ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2 : $i] : (X0 @ X2)))),
% 0.21/0.27 inference(rectify,[],[f1])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (cS @ X1))) = $true)) & (((X0 @ c0)) = $true)) => ! [X2 : $i] : ($true = ((X0 @ X2)))) <=> (cIND = $true)),
% 0.21/0.27 inference(fool_elimination,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 ~(cIND => ! [X0 : $i] : (? [X1 : $i] : (X0 = ((cS @ X1))) | (X0 = c0)))),
% 0.21/0.27 inference(rectify,[],[f3])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 ~((cIND = $true) => ! [X0 : $i] : (? [X1 : $i] : (((cS @ X1)) = X0) | (c0 = X0)))),
% 0.21/0.27 inference(fool_elimination,[],[f6])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 ! [X0 : ($i > $o)] : (! [X2 : $i] : ($true = ((X0 @ X2))) | (? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true)) | (((X0 @ c0)) != $true))) <=> (cIND = $true)),
% 0.21/0.27 inference(ennf_transformation,[],[f5])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 ! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true)) | ! [X2 : $i] : ($true = ((X0 @ X2)))) <=> (cIND = $true)),
% 0.21/0.27 inference(flattening,[],[f8])).
% 0.21/0.27 thf(f10,plain,(
% 0.21/0.27 (cIND = $true) & ? [X0 : $i] : (! [X1 : $i] : (((cS @ X1)) != X0) & (c0 != X0))),
% 0.21/0.27 inference(ennf_transformation,[],[f7])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 (cIND = $true) & (! [X1 : $i] : (((cS @ X1)) != sK0) & (c0 != sK0))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10])).
% 0.21/0.27 thf(f12,plain,(
% 0.21/0.27 (! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true)) | ! [X2 : $i] : ($true = ((X0 @ X2)))) | (cIND != $true)) & ((cIND = $true) | ? [X0 : ($i > $o)] : ((((X0 @ c0)) = $true) & ! [X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (cS @ X1))) = $true)) & ? [X2 : $i] : ($true != ((X0 @ X2)))))),
% 0.21/0.27 inference(nnf_transformation,[],[f9])).
% 0.21/0.27 thf(f13,plain,(
% 0.21/0.27 (! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((X0 @ (cS @ X1))) != $true)) | ! [X2 : $i] : ($true = ((X0 @ X2)))) | (cIND != $true)) & ((cIND = $true) | ? [X3 : ($i > $o)] : (($true = ((X3 @ c0))) & ! [X4 : $i] : (($true != ((X3 @ X4))) | ($true = ((X3 @ (cS @ X4))))) & ? [X5 : $i] : ($true != ((X3 @ X5)))))),
% 0.21/0.27 inference(rectify,[],[f12])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 (! [X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | (($true = ((X0 @ (sK1 @ X0)))) & ($true != ((X0 @ (cS @ (sK1 @ X0)))))) | ! [X2 : $i] : ($true = ((X0 @ X2)))) | (cIND != $true)) & ((cIND = $true) | (($true = ((sK2 @ c0))) & ! [X4 : $i] : (($true != ((sK2 @ X4))) | ($true = ((sK2 @ (cS @ X4))))) & ($true != ((sK2 @ sK3)))))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK2,sK3]),skolemize(X1,sK1 @ X0),skolemize(X3,sK2),skolemize(X5,sK3)],[f13])).
% 0.21/0.27 thf(f15,plain,(
% 0.21/0.27 (c0 != sK0)),
% 0.21/0.27 inference(cnf_transformation,[],[f11])).
% 0.21/0.27 thf(f16,plain,(
% 0.21/0.27 ( ! [X1 : $i] : ((((cS @ X1)) != sK0)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f11])).
% 0.21/0.27 thf(f17,plain,(
% 0.21/0.27 (cIND = $true)),
% 0.21/0.27 inference(cnf_transformation,[],[f11])).
% 0.21/0.27 thf(f21,plain,(
% 0.21/0.27 ( ! [X2 : $i,X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ($true != ((X0 @ (cS @ (sK1 @ X0))))) | ($true = ((X0 @ X2))) | (cIND != $true)) )),
% 0.21/0.27 inference(cnf_transformation,[],[f14])).
% 0.21/0.27 thf(f26,plain,(
% 0.21/0.27 ( ! [X2 : $i,X0 : ($i > $o)] : ((((X0 @ c0)) != $true) | ($true != $true) | ($true != ((X0 @ (cS @ (sK1 @ X0))))) | ($true = ((X0 @ X2)))) )),
% 0.21/0.27 inference(definition_unfolding,[],[f21,f17])).
% 0.21/0.27 thf(f30,plain,(
% 0.21/0.27 ( ! [X2 : $i,X0 : ($i > $o)] : (($true != ((X0 @ (cS @ (sK1 @ X0))))) | (((X0 @ c0)) != $true) | ($true = ((X0 @ X2)))) )),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f26])).
% 0.21/0.27 thf(f63,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($true != (((^[Y0 : $i]: (~ (Y0 = X0))) @ c0))) | (((cS @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
% 0.21/0.27 inference(leibniz_equality_elimination,[],[f30])).
% 0.21/0.27 thf(f69,plain,(
% 0.21/0.27 ( ! [X0 : $i] : ((((cS @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | ($true != ((~ (c0 = X0))))) )),
% 0.21/0.27 inference(beta-eta_normalization,[],[f63])).
% 0.21/0.27 thf(f70,plain,(
% 0.21/0.27 ( ! [X0 : $i] : (($true = ((c0 = X0))) | (((cS @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0)) )),
% 0.21/0.27 inference(not_proxy_clausification,[],[f69])).
% 0.21/0.27 thf(f71,plain,(
% 0.21/0.27 ( ! [X0 : $i] : ((((cS @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0)))))) = X0) | (c0 = X0)) )),
% 0.21/0.27 inference(equality_proxy_clausification,[],[f70])).
% 0.21/0.27 thf(f91,plain,(
% 0.21/0.27 ( ! [X0 : $i] : ((sK0 != X0) | (c0 = X0)) )),
% 0.21/0.27 inference(constrained_superposition,[],[f16,f71])).
% 0.21/0.27 thf(f101,plain,(
% 0.21/0.27 (sK0 != sK0) | (c0 = sK0)),
% 0.21/0.27 inference(imitation,[],[f91])).
% 0.21/0.27 thf(f103,plain,(
% 0.21/0.27 (c0 = sK0)),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f101])).
% 0.21/0.27 thf(f104,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(forward_subsumption_resolution,[],[f103,f15])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (2067391)------------------------------
% 0.21/0.27 % (2067391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2067391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2067391)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2067391)Termination reason: Refutation
% 0.21/0.27 % (2067391)Time elapsed: 0.004 s
% 0.21/0.27 % (2067391)Peak memory usage: 12 MB
% 0.21/0.27 % (2067391)Instructions burned: 4 (million)
% 0.21/0.27 % (2067386)Success in time 0.04 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------