%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO310^5 : 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 : n006.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 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO310^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:44:39 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.23/0.30 % (997021)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (997028)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2577358516:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (997028)Refutation not found, incomplete strategy
% 0.23/0.30 % (997028)------------------------------
% 0.23/0.30 % (997028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (997028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (997028)CaDiCaL version: 2.1.3
% 0.23/0.30 % (997028)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.30 % (997028)Time elapsed: 0.001 s
% 0.23/0.30 % (997028)Peak memory usage: 12 MB
% 0.23/0.30 % (997028)Instructions burned: 2 (million)
% 0.23/0.30 % (997028)------------------------------
% 0.23/0.30 % (997028)------------------------------
% 0.23/0.30 % (997032)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (997032)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
% 0.23/0.30 % (997026)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=301129062:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (997027)lrs+10_16_si=on:nwc=1.5:random_seed=3822646808:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (997030)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=708042160:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (997031)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3373576581:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (997032)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=3608860275:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (997026) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-997021-997026"...
% 0.23/0.30 % (997030) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-997021-997030"...
% 0.23/0.30 % (997027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-997021-997027"...
% 0.23/0.30 % (997029)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=3387548945: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)
% 0.23/0.30 % (997031) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-997021-997031"...
% 0.23/0.30 % (997026)...printing done.
% 0.23/0.30 % (997030)...printing done.
% 0.23/0.30 % (997034)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3616611252:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.30 % (997027)...printing done.
% 0.23/0.30 % (997026)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% 0.23/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.30 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.23/0.30 thf(func_def_4, type, sK0: ($o > $o)).
% 0.23/0.30 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.23/0.30 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.23/0.30 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.23/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.23/0.30 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.23/0.30 thf(func_def_12, type, vAND: ($o > $o > $o)).
% 0.23/0.30 thf(f1,conjecture,(
% 0.23/0.30 ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : ((X0 @ $false @ $false) & ~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & (X0 @ $true @ $true))),
% 0.23/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cOMEGA_EXAMPLE)).
% 0.23/0.30 thf(f2,negated_conjecture,(
% 0.23/0.30 ~(! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : ((X0 @ $false @ $false) & ~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & (X0 @ $true @ $true)))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.30 thf(f3,plain,(
% 0.23/0.30 ~(! [X0 : ($o > $o)] : ((X0 @ $true) <=> (X0 @ $true => $true)) & ? [X1 : ($o > $o > $o)] : ((X1 @ $false @ $false) & ~(X1 @ $true @ $false) & ~(X1 @ $false @ $true) & (X1 @ $true @ $true)))),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f4,plain,(
% 0.23/0.30 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : ((((X1 @ $false @ $false)) = $true) & ~ (((X1 @ $true @ $false)) = $true) & ~ (((X1 @ $false @ $true)) = $true) & ($true = ((X1 @ $true @ $true)))))),
% 0.23/0.30 inference(fool_elimination,[],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : ((((X1 @ $false @ $false)) = $true) & ($true = ((X1 @ $true @ $true))) & (((X1 @ $false @ $true)) != $true) & (((X1 @ $true @ $false)) != $true)))),
% 0.23/0.30 inference(flattening,[],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ! [X1 : ($o > $o > $o)] : (($true != ((X1 @ $true @ $true))) | (((X1 @ $false @ $false)) != $true) | (((X1 @ $false @ $true)) = $true) | (((X1 @ $true @ $false)) = $true)) | ? [X0 : ($o > $o)] : (((X0 @ $true)) != ((X0 @ ($true => $true))))),
% 0.23/0.30 inference(ennf_transformation,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true)) | ? [X1 : ($o > $o)] : (((X1 @ ($true => $true))) != ((X1 @ $true)))),
% 0.23/0.30 inference(rectify,[],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true)) | (((sK0 @ ($true => $true))) != ((sK0 @ $true)))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $true)) = $true) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $true @ $true)) != $true) | (((sK0 @ ($true => $true))) != ((sK0 @ $true)))) )),
% 0.23/0.30 inference(cnf_transformation,[],[f8])).
% 0.23/0.30 thf(f12,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $true @ $false)) = $true) | (((sK0 @ ($true => $true))) = $true) | (((sK0 @ $true)) = $true) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $false @ $true)) = $true)) )),
% 0.23/0.30 inference(xor_proxy_clausification,[],[f9])).
% 0.23/0.30 thf(f13,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $true)) = $true) | (((X0 @ $false @ $false)) != $true) | (((sK0 @ ($true => $true))) = $false) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) = $false)) )),
% 0.23/0.30 inference(xor_proxy_clausification,[],[f9])).
% 0.23/0.30 thf(f14,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) = $false) | (((X0 @ $true @ $false)) = $true) | (((sK0 @ $true)) = $false) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $false @ $true)) = $true)) )),
% 0.23/0.30 inference(boolean_simplification,[],[f13])).
% 0.23/0.30 thf(f15,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) = $false) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $true)) = $true)) )),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f14])).
% 0.23/0.30 thf(f16,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((sK0 @ $true)) = $true) | (((X0 @ $false @ $false)) != $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) = $true)) )),
% 0.23/0.30 inference(boolean_simplification,[],[f12])).
% 0.23/0.30 thf(f17,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $false @ $false)) != $true) | (((X0 @ $true @ $true)) != $true) | (((sK0 @ $true)) = $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true)) )),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f16])).
% 0.23/0.30 thf(f19,definition,(
% 0.23/0.30 spl1_1 <=> (((sK0 @ $true)) = $false)),
% 0.23/0.30 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.23/0.30 thf(f21,plain,(
% 0.23/0.30 (((sK0 @ $true)) = $false) | ~spl1_1),
% 0.23/0.30 inference(avatar_component_clause,[],[f19])).
% 0.23/0.30 thf(f23,definition,(
% 0.23/0.30 spl1_2 <=> ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $false)) != $true))),
% 0.23/0.30 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.23/0.30 thf(f24,plain,(
% 0.23/0.30 ( ! [X0 : ($o > $o > $o)] : ((((X0 @ $true @ $true)) != $true) | (((X0 @ $true @ $false)) = $true) | (((X0 @ $false @ $true)) = $true) | (((X0 @ $false @ $false)) != $true)) ) | ~spl1_2),
% 0.23/0.30 inference(avatar_component_clause,[],[f23])).
% 0.23/0.30 thf(f25,plain,(
% 0.23/0.30 spl1_1 | spl1_2),
% 0.23/0.30 inference(avatar_split_clause,[],[f15,f23,f19])).
% 0.23/0.30 thf(f27,definition,(
% 0.23/0.30 spl1_3 <=> (((sK0 @ $true)) = $true)),
% 0.23/0.30 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.23/0.30 thf(f29,plain,(
% 0.23/0.30 (((sK0 @ $true)) = $true) | ~spl1_3),
% 0.23/0.30 inference(avatar_component_clause,[],[f27])).
% 0.23/0.30 thf(f30,plain,(
% 0.23/0.30 spl1_2 | spl1_3),
% 0.23/0.30 inference(avatar_split_clause,[],[f17,f27,f23])).
% 0.23/0.30 thf(f33,plain,(
% 0.23/0.30 ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $true @ $true)) != $true) | ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $false @ $false)) != $true) | ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $false @ $true)) = $true) | ((((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 = Y1)))) @ $true @ $false)) = $true) | ~spl1_2),
% 0.23/0.30 inference(primitive_instantiation,[],[f24])).
% 0.23/0.30 thf(f43,plain,(
% 0.23/0.30 ((($false = $true)) = $true) | ((($false = $false)) != $true) | ((($true = $true)) != $true) | ((($true = $false)) = $true) | ~spl1_2),
% 0.23/0.30 inference(beta-eta_normalization,[],[f33])).
% 0.23/0.30 thf(f44,plain,(
% 0.23/0.30 ((($true = $true)) != $true) | ($false = $true) | ((($true = $false)) = $true) | ((($false = $false)) != $true) | ~spl1_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f43])).
% 0.23/0.30 thf(f45,plain,(
% 0.23/0.30 ($false = $true) | ((($true = $false)) = $true) | ((($false = $false)) != $true) | ($true != $true) | ~spl1_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f44])).
% 0.23/0.30 thf(f46,plain,(
% 0.23/0.30 ($false = $true) | ($true != $true) | ($false = $true) | ((($false = $false)) != $true) | ~spl1_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f45])).
% 0.23/0.30 thf(f47,plain,(
% 0.23/0.30 ($false = $true) | ($true != $true) | ($false = $true) | ($false != $false) | ~spl1_2),
% 0.23/0.30 inference(equality_proxy_clausification,[],[f46])).
% 0.23/0.30 thf(f48,plain,(
% 0.23/0.30 ($false != $false) | ($true != $true) | ($false = $true) | ~spl1_2),
% 0.23/0.30 inference(duplicate_literal_removal,[],[f47])).
% 0.23/0.30 thf(f49,plain,(
% 0.23/0.30 $false | ~spl1_2),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f48])).
% 0.23/0.30 thf(f50,plain,(
% 0.23/0.30 ~spl1_2),
% 0.23/0.30 inference(avatar_contradiction_clause,[],[f49])).
% 0.23/0.30 thf(f109,plain,(
% 0.23/0.30 ($false = $true) | (~spl1_1 | ~spl1_3)),
% 0.23/0.30 inference(forward_demodulation,[],[f29,f21])).
% 0.23/0.30 thf(f110,plain,(
% 0.23/0.30 $false | (~spl1_1 | ~spl1_3)),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f109])).
% 0.23/0.30 thf(f111,plain,(
% 0.23/0.30 ~spl1_1 | ~spl1_3),
% 0.23/0.30 inference(avatar_contradiction_clause,[],[f110])).
% 0.23/0.30 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f25])).
% 0.23/0.30 cnf(s2, plain, spl1_2 | spl1_3, inference(sat_conversion,[],[f30])).
% 0.23/0.30 cnf(s3, plain, ~spl1_2, inference(sat_conversion,[],[f50])).
% 0.23/0.30 cnf(s4, plain, ~spl1_1 | ~spl1_3, inference(sat_conversion,[],[f111])).
% 0.23/0.30 cnf(s5, plain, spl1_3, inference(rat,[],[s2,s3])).
% 0.23/0.30 cnf(s6, plain, ~spl1_1, inference(rat,[],[s4,s5])).
% 0.23/0.30 cnf(s7, plain, $false, inference(rat,[],[s1,s3,s6])).
% 0.23/0.30 thf(f112,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(avatar_sat_refutation,[],[s7])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (997026)------------------------------
% 0.23/0.30 % (997026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (997026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (997026)CaDiCaL version: 2.1.3
% 0.23/0.30 % (997026)Termination reason: Refutation
% 0.23/0.30 % (997026)Time elapsed: 0.003 s
% 0.23/0.30 % (997026)Peak memory usage: 13 MB
% 0.23/0.30 % (997026)Instructions burned: 4 (million)
% 0.23/0.30 % (997021)Success in time 0.046 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------