%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:48:10 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO513^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n015.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:15:18 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (3828795)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (3828804)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3873058706:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (3828804)Refutation not found, incomplete strategy
% 0.20/0.28 % (3828804)------------------------------
% 0.20/0.28 % (3828804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828804)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828804)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3828804)Time elapsed: 0.0000 s
% 0.20/0.28 % (3828804)Peak memory usage: 12 MB
% 0.20/0.28 % (3828804)------------------------------
% 0.20/0.28 % (3828804)------------------------------
% 0.20/0.28 % (3828806)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (3828806)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
% 0.20/0.28 % (3828800)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1868272459:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (3828801)lrs+10_16_si=on:nwc=1.5:random_seed=2692938653:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (3828802)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4034114223:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (3828803)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=2810645831: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)
% 0.20/0.28 % (3828805)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1919894818:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (3828806)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=3847594426:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (3828800)Refutation not found, incomplete strategy
% 0.20/0.28 % (3828800)------------------------------
% 0.20/0.28 % (3828800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828802)Refutation not found, incomplete strategy
% 0.20/0.28 % (3828802)------------------------------
% 0.20/0.28 % (3828802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828800)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828800)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3828800)Time elapsed: 0.001 s
% 0.20/0.28 % (3828802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828800)Peak memory usage: 12 MB
% 0.20/0.28 % (3828802)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828802)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3828802)Time elapsed: 0.001 s
% 0.20/0.28 % (3828802)Peak memory usage: 12 MB
% 0.20/0.28 % (3828800)------------------------------
% 0.20/0.28 % (3828800)------------------------------
% 0.20/0.28 % (3828802)------------------------------
% 0.20/0.28 % (3828802)------------------------------
% 0.20/0.28 % (3828803)Refutation not found, incomplete strategy
% 0.20/0.28 % (3828803)------------------------------
% 0.20/0.28 % (3828803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828803)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828803)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3828803)Time elapsed: 0.003 s
% 0.20/0.28 % (3828803)Peak memory usage: 12 MB
% 0.20/0.28 % (3828803)Instructions burned: 3 (million)
% 0.20/0.28 % (3828808)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3970543996:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (3828803)------------------------------
% 0.20/0.28 % (3828803)------------------------------
% 0.20/0.28 % (3828808)Instruction limit reached!
% 0.20/0.28 % (3828808)------------------------------
% 0.20/0.28 % (3828808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828808)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828808)Termination reason: Instruction limit
% 0.20/0.28 % (3828808)Termination phase: Saturation
% 0.20/0.28 % (3828808)Time elapsed: 0.001 s
% 0.20/0.28 % (3828808)Peak memory usage: 12 MB
% 0.20/0.28 % (3828808)Instructions burned: 3 (million)
% 0.20/0.28 % (3828806)Refutation not found, incomplete strategy
% 0.20/0.28 % (3828806)------------------------------
% 0.20/0.28 % (3828806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828806)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828806)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (3828806)Time elapsed: 0.004 s
% 0.20/0.28 % (3828806)Peak memory usage: 12 MB
% 0.20/0.28 % (3828806)Instructions burned: 6 (million)
% 0.20/0.28 % (3828806)------------------------------
% 0.20/0.28 % (3828806)------------------------------
% 0.20/0.28 % (3828801)Instruction limit reached!
% 0.20/0.28 % (3828801)------------------------------
% 0.20/0.28 % (3828801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828801)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828801)Termination reason: Instruction limit
% 0.20/0.28 % (3828801)Termination phase: Saturation
% 0.20/0.28 % (3828801)Time elapsed: 0.010 s
% 0.20/0.28 % (3828801)Peak memory usage: 12 MB
% 0.20/0.28 % (3828801)Instructions burned: 20 (million)
% 0.20/0.28 % (3828819)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
% 0.20/0.28 % (3828819)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.28 % (3828819)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3925676247:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.28 % (3828817)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.28 % (3828816)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2990305277:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.28 % (3828817)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1862731832:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.28 % (3828819)Instruction limit reached!
% 0.20/0.28 % (3828819)------------------------------
% 0.20/0.28 % (3828819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828819)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828819)Termination reason: Instruction limit
% 0.20/0.28 % (3828819)Termination phase: Saturation
% 0.20/0.28 % (3828819)Time elapsed: 0.007 s
% 0.20/0.28 % (3828819)Peak memory usage: 12 MB
% 0.20/0.28 % (3828819)Instructions burned: 30 (million)
% 0.20/0.28 % (3828818)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2179005056:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.28 % (3828816) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3828795-3828816"...
% 0.20/0.28 % (3828820)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3853961042:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.28 % (3828816)...printing done.
% 0.20/0.28 % (3828816)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.20/0.28 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.28 thf(func_def_5, type, sK0: ((($o > $o) > $o) > $o > $o)).
% 0.20/0.28 thf(func_def_6, type, sK1: ((($o > $o) > $o) > $o)).
% 0.20/0.28 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceo)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 thf(f3,plain,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (X1 @ X2) => (X1 @ (X0 @ X1)))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ? [X0 : (($o > $o) > $o)] : ! [X1 : ($o > $o)] : (? [X2 : $o] : (((X1 @ X2)) = $true) => (((X1 @ (X0 @ X1))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X1 : (X0 > $o)] : (($true = ((X1 @ (vEPSILON @ X0 @ X1)))) | (((X1 @ X2)) = $false)) )),
% 0.20/0.28 introduced(theory,[Hilbert's_choice_axiom_instance])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X0 : (($o > $o) > $o)] : ? [X1 : ($o > $o)] : (? [X2 : $o] : (((X1 @ X2)) = $true) & (((X1 @ (X0 @ X1))) != $true))),
% 0.20/0.28 inference(ennf_transformation,[],[f4])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [X0 : (($o > $o) > $o)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true) & ($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ( ! [X0 : (($o > $o) > $o)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f8])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ( ! [X0 : $o] : (($true != $true) | (((sK0 @ vEPSILON @ $o @ X0)) = $false)) )),
% 0.20/0.28 inference(superposition,[],[f9,f6])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ( ! [X0 : $o] : ((((sK0 @ vEPSILON @ $o @ X0)) = $false)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f29])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 ($true = $false)),
% 0.20/0.28 inference(superposition,[],[f30,f10])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f31])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (3828816)------------------------------
% 0.20/0.28 % (3828816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3828816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3828816)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3828816)Termination reason: Refutation
% 0.20/0.28 % (3828816)Time elapsed: 0.002 s
% 0.20/0.28 % (3828816)Peak memory usage: 12 MB
% 0.20/0.28 % (3828816)Instructions burned: 3 (million)
% 0.20/0.28 % (3828795)Success in time 0.058 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------