%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO276^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:47:20 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO276^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:42:30 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.30 % (2906232)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2906243)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2906243)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
% 0.22/0.30 % (2906239)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=153674441:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2906241)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3320558657:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2906237)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1424860673:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2906238)lrs+10_16_si=on:nwc=1.5:random_seed=3749370773:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2906240)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=3325592289: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)
% 0.22/0.30 % (2906242)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1948649053:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2906243)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=2344190092:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2906239)Refutation not found, incomplete strategy
% 0.22/0.30 % (2906239)------------------------------
% 0.22/0.30 % (2906239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2906241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906232-2906241"...
% 0.22/0.30 % (2906239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2906239)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2906239)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2906239)Time elapsed: 0.002 s
% 0.22/0.30 % (2906239)Peak memory usage: 12 MB
% 0.22/0.30 % (2906239)Instructions burned: 3 (million)
% 0.22/0.30 % (2906237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906232-2906237"...
% 0.22/0.30 % (2906238) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906232-2906238"...
% 0.22/0.30 % (2906240) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906232-2906240"...
% 0.22/0.30 % (2906239)------------------------------
% 0.22/0.30 % (2906239)------------------------------
% 0.22/0.30 % (2906242) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2906232-2906242"...
% 0.22/0.30 % (2906241)...printing done.
% 0.22/0.30 % (2906243)Refutation not found, incomplete strategy
% 0.22/0.30 % (2906243)------------------------------
% 0.22/0.30 % (2906243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2906243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2906243)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2906243)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2906243)Time elapsed: 0.004 s
% 0.22/0.30 % (2906243)Peak memory usage: 12 MB
% 0.22/0.30 % (2906243)Instructions burned: 5 (million)
% 0.22/0.30 % (2906237)...printing done.
% 0.22/0.30 % (2906238)...printing done.
% 0.22/0.30 % (2906241)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_1, type, cP: ($i > $o)).
% 0.22/0.30 thf(func_def_3, type, s: ($i > $i)).
% 0.22/0.30 thf(func_def_8, type, sK0: (($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_9, type, sK1: (($i > $i > $o) > $i)).
% 0.22/0.30 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(f1,conjecture,(
% 0.22/0.30 (! [X0 : ($i > $i > $o)] : (((X0 @ cO @ cO) & ! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m)),
% 0.22/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I2)).
% 0.22/0.30 thf(f2,negated_conjecture,(
% 0.22/0.30 ~((! [X0 : ($i > $i > $o)] : (((X0 @ cO @ cO) & ! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.30 thf(f3,plain,(
% 0.22/0.30 ~((! [X0 : ($i > $i > $o)] : (((X0 @ cO @ cO) & ! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f4,plain,(
% 0.22/0.30 ~((! [X0 : ($i > $i > $o)] : (((((X0 @ cO @ cO)) = $true) & ! [X2 : $i,X1 : $i] : ((((X0 @ X1 @ X2)) = $true) => (((X0 @ (s @ X1) @ (s @ X2))) = $true))) => (((X0 @ n @ m)) = $true)) & (((cP @ n)) = $true)) => (((cP @ m)) = $true))),
% 0.22/0.30 inference(fool_elimination,[],[f3])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 (((cP @ m)) != $true) & (! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | ((((X0 @ cO @ cO)) != $true) | ? [X1 : $i,X2 : $i] : ((((X0 @ (s @ X1) @ (s @ X2))) != $true) & (((X0 @ X1 @ X2)) = $true)))) & (((cP @ n)) = $true))),
% 0.22/0.30 inference(ennf_transformation,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | ? [X1 : $i,X2 : $i] : ((((X0 @ (s @ X1) @ (s @ X2))) != $true) & (((X0 @ X1 @ X2)) = $true)) | (((X0 @ cO @ cO)) != $true)) & (((cP @ n)) = $true) & (((cP @ m)) != $true)),
% 0.22/0.30 inference(flattening,[],[f5])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 ! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | (($true != ((X0 @ (s @ (sK0 @ X0)) @ (s @ (sK1 @ X0))))) & (((X0 @ (sK0 @ X0) @ (sK1 @ X0))) = $true)) | (((X0 @ cO @ cO)) != $true)) & (((cP @ n)) = $true) & (((cP @ m)) != $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 (((cP @ m)) != $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f7])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 (((cP @ n)) = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f7])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $i > $o)] : ((((X0 @ (sK0 @ X0) @ (sK1 @ X0))) = $true) | (((X0 @ n @ m)) = $true) | (((X0 @ cO @ cO)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f7])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ( ! [X0 : ($i > $i > $o)] : (($true != ((X0 @ (s @ (sK0 @ X0)) @ (s @ (sK1 @ X0))))) | (((X0 @ n @ m)) = $true) | (((X0 @ cO @ cO)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f7])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 ((((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))))) = $true) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ n @ m))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ cO @ cO)) != $true)),
% 0.22/0.30 inference(primitive_instantiation,[],[f10])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ($true = ((n = m))) | (((cO = cO)) != $true) | ((((sK0 @ =) = (sK1 @ =))) = $true)),
% 0.22/0.30 inference(beta-eta_normalization,[],[f13])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 (((cO = cO)) != $true) | (n = m) | ((((sK0 @ =) = (sK1 @ =))) = $true)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f18])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 (cO != cO) | ((((sK0 @ =) = (sK1 @ =))) = $true) | (n = m)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f19])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 (((sK1 @ =)) = ((sK0 @ =))) | (n = m) | (cO != cO)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f20])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 (((sK1 @ =)) = ((sK0 @ =))) | (n = m)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f21])).
% 0.22/0.30 thf(f49,plain,(
% 0.22/0.30 ($true != (((s @ (sK0 @ =)) = (s @ (sK0 @ =))))) | (n = m) | (((cO = cO)) != $true) | ($true = ((n = m)))),
% 0.22/0.30 inference(superposition,[],[f11,f22])).
% 0.22/0.30 thf(f55,plain,(
% 0.22/0.30 (n = m) | (((cO = cO)) != $true) | (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | ($true = ((n = m)))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f49])).
% 0.22/0.30 thf(f56,plain,(
% 0.22/0.30 (cO != cO) | (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | (n = m) | ($true = ((n = m)))),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f55])).
% 0.22/0.30 thf(f57,plain,(
% 0.22/0.30 (n = m) | (n = m) | (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | (cO != cO)),
% 0.22/0.30 inference(equality_proxy_clausification,[],[f56])).
% 0.22/0.30 thf(f58,plain,(
% 0.22/0.30 (n = m) | (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | (cO != cO)),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f57])).
% 0.22/0.30 thf(f59,plain,(
% 0.22/0.30 (n = m)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f58])).
% 0.22/0.30 thf(f80,plain,(
% 0.22/0.30 (((cP @ m)) = $true)),
% 0.22/0.30 inference(superposition,[],[f9,f59])).
% 0.22/0.30 thf(f81,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f80,f8])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (2906241)------------------------------
% 0.22/0.30 % (2906241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2906241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2906241)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2906241)Termination reason: Refutation
% 0.22/0.30 % (2906241)Time elapsed: 0.003 s
% 0.22/0.30 % (2906241)Peak memory usage: 12 MB
% 0.22/0.30 % (2906241)Instructions burned: 5 (million)
% 0.22/0.30 % (2906232)Success in time 0.043 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------