%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:47:25 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n016.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 16:49:50 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.26 % (600994)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (601008)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.26 % (601008)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
% 0.08/0.26 % (601008)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=1939578147:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.26 % (601008)Refutation not found, incomplete strategy
% 0.08/0.26 % (601008)------------------------------
% 0.08/0.26 % (601008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (601008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (601008)CaDiCaL version: 2.1.3
% 0.08/0.26 % (601008)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.26 % (601008)Time elapsed: 0.003 s
% 0.08/0.26 % (601008)Peak memory usage: 12 MB
% 0.08/0.26 % (601008)Instructions burned: 9 (million)
% 0.08/0.26 % (601008)------------------------------
% 0.08/0.26 % (601008)------------------------------
% 0.08/0.26 % (601002)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2676085382:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (601004)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=832850376:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.26 % (601003)lrs+10_16_si=on:nwc=1.5:random_seed=3290773400:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.26 % (601006)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1219078472:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.26 % (601005)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=3608919588: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)
% 0.08/0.26 % (601007)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1492875743:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.26 % (601004) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-600994-601004"...
% 0.08/0.26 % (601002) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-600994-601002"...
% 0.08/0.26 % (601005) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-600994-601005"...
% 0.08/0.26 % (601003) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-600994-601003"...
% 0.08/0.26 % (601007) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-600994-601007"...
% 0.08/0.26 % (601004)...printing done.
% 0.08/0.26 % (601004)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_4, type, sK0: ($o > $o)).
% 0.08/0.26 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.26 thf(func_def_10, type, vOR: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(f1,conjecture,(
% 0.08/0.26 ? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & ~(X0 @ $false @ $false) & (X0 @ $true @ $true)) & ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cOMEGA_EXAMPLE2)).
% 0.08/0.26 thf(f2,negated_conjecture,(
% 0.08/0.26 ~(? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & ~(X0 @ $false @ $false) & (X0 @ $true @ $true)) & ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.26 thf(f3,plain,(
% 0.08/0.26 ~(? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & ~(X0 @ $false @ $false) & (X0 @ $true @ $true)) & ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~(? [X0 : ($o > $o > $o)] : (~ (((X0 @ $true @ $false)) = $true) & ~ (((X0 @ $false @ $true)) = $true) & ~ (((X0 @ $false @ $false)) = $true) & (((X0 @ $true @ $true)) = $true)) & ! [X1 : ($o > $o)] : (((X1 @ $true)) = ((X1 @ ($true => $true)))))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ~(! [X1 : ($o > $o)] : (((X1 @ $true)) = ((X1 @ ($true => $true)))) & ? [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $false)) != $true) & (((X0 @ $true @ $true)) = $true) & (((X0 @ $false @ $true)) != $true) & (((X0 @ $false @ $false)) != $true)))),
% 0.08/0.26 inference(flattening,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $false)) = $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $true)) != $true)) | ? [X1 : ($o > $o)] : (((X1 @ $true)) != ((X1 @ ($true => $true))))),
% 0.08/0.26 inference(ennf_transformation,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $false)) = $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $true)) != $true)) | (((sK0 @ ($true => $true))) != ((sK0 @ $true)))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f6])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 ( ! [X0 : ($o > $o > $o)] : ((((sK0 @ ($true => $true))) != ((sK0 @ $true))) | (((X0 @ $true @ $true)) != $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $false)) = $true) | (((X0 @ $false @ $true)) = $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f7])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) != ((sK0 @ $true))) | (((X0 @ $false @ $false)) = $true)) )),
% 0.08/0.26 inference(boolean_simplification,[],[f8])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $false @ $false)) = $true) | (((X0 @ $true @ $false)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f11])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $true @ $true)) != $true) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $true @ $false))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $false @ $true))) | ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $false @ $false)) = $true)),
% 0.08/0.26 inference(primitive_instantiation,[],[f12])).
% 0.08/0.26 thf(f49,plain,(
% 0.08/0.26 ((($false & $false)) = $true) | ((($false & $true)) = $true) | ($true != (($true & $true))) | ((($true & $false)) = $true)),
% 0.08/0.26 inference(beta-eta_normalization,[],[f18])).
% 0.08/0.26 thf(f50,plain,(
% 0.08/0.26 ($false = $true) | ($true != (($true & $true))) | ((($true & $false)) = $true) | ((($false & $true)) = $true)),
% 0.08/0.26 inference(boolean_simplification,[],[f49])).
% 0.08/0.26 thf(f51,plain,(
% 0.08/0.26 ((($true & $false)) = $true) | ($true != (($true & $true))) | ((($false & $true)) = $true)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f50])).
% 0.08/0.26 thf(f52,plain,(
% 0.08/0.26 ($false = $true) | ($true != (($true & $true))) | ((($false & $true)) = $true)),
% 0.08/0.26 inference(boolean_simplification,[],[f51])).
% 0.08/0.26 thf(f53,plain,(
% 0.08/0.26 ($true != (($true & $true))) | ((($false & $true)) = $true)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f52])).
% 0.08/0.26 thf(f54,plain,(
% 0.08/0.26 ((($false & $true)) = $true) | ($true != $true)),
% 0.08/0.26 inference(boolean_simplification,[],[f53])).
% 0.08/0.26 thf(f55,plain,(
% 0.08/0.26 ((($false & $true)) = $true)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f54])).
% 0.08/0.26 thf(f56,plain,(
% 0.08/0.26 ($false = $true)),
% 0.08/0.26 inference(boolean_simplification,[],[f55])).
% 0.08/0.26 thf(f57,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f56])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (601004)------------------------------
% 0.08/0.26 % (601004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (601004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (601004)CaDiCaL version: 2.1.3
% 0.08/0.26 % (601004)Termination reason: Refutation
% 0.08/0.26 % (601004)Time elapsed: 0.002 s
% 0.08/0.26 % (601004)Peak memory usage: 12 MB
% 0.08/0.26 % (601004)Instructions burned: 3 (million)
% 0.08/0.26 % (600994)Success in time 0.041 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------