%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV096^5 : 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 : n017.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 08:37:38 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV096^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:05:37 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.32 % (442849)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (442855)lrs+10_16_si=on:nwc=1.5:random_seed=2295066204:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (442860)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (442860)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
% 0.22/0.32 % (442855) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-442849-442855"...
% 0.22/0.32 % (442858)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=971972160:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (442856)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2055847956:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (442858) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-442849-442858"...
% 0.22/0.32 % (442855)...printing done.
% 0.22/0.32 % (442860)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=2715734227:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (442855)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, a: $tType).
% 0.22/0.32 thf(type_def_6, type, b: $tType).
% 0.22/0.32 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_0, type, z: a).
% 0.22/0.32 thf(func_def_1, type, cR: (a > a > $o)).
% 0.22/0.32 thf(func_def_2, type, f: (a > b > $o)).
% 0.22/0.32 thf(func_def_3, type, cS: (b > b > $o)).
% 0.22/0.32 thf(func_def_7, type, sK0: b).
% 0.22/0.32 thf(func_def_8, type, sK1: (a > a)).
% 0.22/0.32 thf(func_def_9, type, sK2: (a > b)).
% 0.22/0.32 thf(f1,conjecture,(
% 0.22/0.32 (! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X4 : b,X8 : a,X7 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X6 : b,X5 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : ((f @ X3 @ X4) | ((cR @ X3 @ z) & ~(f @ X2 @ X4))))),
% 0.22/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM552E_pme)).
% 0.22/0.32 thf(f2,negated_conjecture,(
% 0.22/0.32 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X0 @ X1) & (cR @ X2 @ X1)) => (cR @ X0 @ X2))) => ((! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4) & ! [X4 : b,X8 : a,X7 : a] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X6 : b,X5 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6))) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : ((f @ X3 @ X4) | ((cR @ X3 @ z) & ~(f @ X2 @ X4)))))),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.32 thf(f3,plain,(
% 0.22/0.32 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X1 @ X2) & (cR @ X3 @ X2)) => (cR @ X1 @ X3))) => ((! [X4 : a] : ? [X5 : b] : (f @ X4 @ X5) & ! [X6 : b,X7 : a,X8 : a] : (((f @ X7 @ X6) & (f @ X8 @ X6)) => (cR @ X8 @ X7)) & ! [X9 : a,X10 : b,X11 : b] : (((f @ X9 @ X10) & (f @ X9 @ X11)) => (cS @ X11 @ X10))) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : ((f @ X13 @ X12) | ((cR @ X13 @ z) & ~(f @ X14 @ X12)))))),
% 0.22/0.32 inference(rectify,[],[f2])).
% 0.22/0.32 thf(f4,plain,(
% 0.22/0.32 ~((! [X3 : a,X1 : a,X2 : a] : (((((cR @ X1 @ X2)) = $true) & ($true = ((cR @ X3 @ X2)))) => (((cR @ X1 @ X3)) = $true)) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true)) => ((! [X10 : b,X11 : b,X9 : a] : (((((f @ X9 @ X10)) = $true) & (((f @ X9 @ X11)) = $true)) => (((cS @ X11 @ X10)) = $true)) & ! [X6 : b,X8 : a,X7 : a] : (((((f @ X7 @ X6)) = $true) & ($true = ((f @ X8 @ X6)))) => ($true = ((cR @ X8 @ X7)))) & ! [X4 : a] : ? [X5 : b] : (((f @ X4 @ X5)) = $true)) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : ((((f @ X13 @ X12)) = $true) | (($true = ((cR @ X13 @ z))) & ~ (((f @ X14 @ X12)) = $true)))))),
% 0.22/0.32 inference(fool_elimination,[],[f3])).
% 0.22/0.32 thf(f5,plain,(
% 0.22/0.32 ~((! [X3 : a,X1 : a,X2 : a] : (((((cR @ X1 @ X2)) = $true) & ($true = ((cR @ X3 @ X2)))) => (((cR @ X1 @ X3)) = $true)) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true)) => ((! [X10 : b,X11 : b,X9 : a] : (((((f @ X9 @ X10)) = $true) & (((f @ X9 @ X11)) = $true)) => (((cS @ X11 @ X10)) = $true)) & ! [X6 : b,X8 : a,X7 : a] : (((((f @ X7 @ X6)) = $true) & ($true = ((f @ X8 @ X6)))) => ($true = ((cR @ X8 @ X7)))) & ! [X4 : a] : ? [X5 : b] : (((f @ X4 @ X5)) = $true)) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : ((((f @ X13 @ X12)) = $true) | ((((f @ X14 @ X12)) != $true) & ($true = ((cR @ X13 @ z)))))))),
% 0.22/0.32 inference(flattening,[],[f4])).
% 0.22/0.32 thf(f6,plain,(
% 0.22/0.32 (? [X12 : b] : ! [X13 : a] : ? [X14 : a] : ((((f @ X13 @ X12)) != $true) & (($true != ((cR @ X13 @ z))) | (((f @ X14 @ X12)) = $true))) & (! [X10 : b,X11 : b,X9 : a] : ((((cS @ X11 @ X10)) = $true) | ((((f @ X9 @ X10)) != $true) | (((f @ X9 @ X11)) != $true))) & ! [X6 : b,X8 : a,X7 : a] : (($true = ((cR @ X8 @ X7))) | ((((f @ X7 @ X6)) != $true) | ($true != ((f @ X8 @ X6))))) & ! [X4 : a] : ? [X5 : b] : (((f @ X4 @ X5)) = $true))) & (! [X3 : a,X1 : a,X2 : a] : ((((cR @ X1 @ X3)) = $true) | ((((cR @ X1 @ X2)) != $true) | ($true != ((cR @ X3 @ X2))))) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true))),
% 0.22/0.32 inference(ennf_transformation,[],[f5])).
% 0.22/0.32 thf(f7,plain,(
% 0.22/0.32 ? [X12 : b] : ! [X13 : a] : ? [X14 : a] : ((((f @ X13 @ X12)) != $true) & (($true != ((cR @ X13 @ z))) | (((f @ X14 @ X12)) = $true))) & ! [X4 : a] : ? [X5 : b] : (((f @ X4 @ X5)) = $true) & ! [X6 : b,X8 : a,X7 : a] : (($true != ((f @ X8 @ X6))) | ($true = ((cR @ X8 @ X7))) | (((f @ X7 @ X6)) != $true)) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X2 : a,X3 : a,X1 : a] : ((((cR @ X1 @ X3)) = $true) | (((cR @ X1 @ X2)) != $true) | ($true != ((cR @ X3 @ X2)))) & ! [X9 : a,X11 : b,X10 : b] : ((((f @ X9 @ X11)) != $true) | (((f @ X9 @ X10)) != $true) | (((cS @ X11 @ X10)) = $true))),
% 0.22/0.32 inference(flattening,[],[f6])).
% 0.22/0.32 thf(f8,plain,(
% 0.22/0.32 ? [X0 : b] : ! [X1 : a] : ? [X2 : a] : ((((f @ X1 @ X0)) != $true) & ((((cR @ X1 @ z)) != $true) | ($true = ((f @ X2 @ X0))))) & ! [X3 : a] : ? [X4 : b] : (((f @ X3 @ X4)) = $true) & ! [X5 : b,X6 : a,X7 : a] : ((((f @ X6 @ X5)) != $true) | (((cR @ X6 @ X7)) = $true) | (((f @ X7 @ X5)) != $true)) & ! [X8 : a] : (((cR @ X8 @ X8)) = $true) & ! [X9 : a,X10 : a,X11 : a] : ((((cR @ X11 @ X10)) = $true) | (((cR @ X11 @ X9)) != $true) | ($true != ((cR @ X10 @ X9)))) & ! [X12 : a,X13 : b,X14 : b] : (($true != ((f @ X12 @ X13))) | (((f @ X12 @ X14)) != $true) | (((cS @ X13 @ X14)) = $true))),
% 0.22/0.32 inference(rectify,[],[f7])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 ! [X1 : a] : (($true != ((f @ X1 @ sK0))) & ((((cR @ X1 @ z)) != $true) | ($true = ((f @ (sK1 @ X1) @ sK0))))) & ! [X3 : a] : (((f @ X3 @ (sK2 @ X3))) = $true) & ! [X5 : b,X6 : a,X7 : a] : ((((f @ X6 @ X5)) != $true) | (((cR @ X6 @ X7)) = $true) | (((f @ X7 @ X5)) != $true)) & ! [X8 : a] : (((cR @ X8 @ X8)) = $true) & ! [X9 : a,X10 : a,X11 : a] : ((((cR @ X11 @ X10)) = $true) | (((cR @ X11 @ X9)) != $true) | ($true != ((cR @ X10 @ X9)))) & ! [X12 : a,X13 : b,X14 : b] : (($true != ((f @ X12 @ X13))) | (((f @ X12 @ X14)) != $true) | (((cS @ X13 @ X14)) = $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X4,sK2 @ X3),skolemize(X4,sK2 @ X3)],[f8])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ( ! [X8 : a] : ((((cR @ X8 @ X8)) = $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f9])).
% 0.22/0.32 thf(f15,plain,(
% 0.22/0.32 ( ! [X1 : a] : ((((cR @ X1 @ z)) != $true) | ($true = ((f @ (sK1 @ X1) @ sK0)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f9])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 ( ! [X1 : a] : (($true != ((f @ X1 @ sK0)))) )),
% 0.22/0.32 inference(cnf_transformation,[],[f9])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 ( ! [X1 : a] : ((((cR @ X1 @ z)) != $true)) )),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f15,f16])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 ($true != $true)),
% 0.22/0.32 inference(constrained_superposition,[],[f19,f12])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f20])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (442855)------------------------------
% 0.22/0.32 % (442855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (442855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (442855)CaDiCaL version: 2.1.3
% 0.22/0.32 % (442855)Termination reason: Refutation
% 0.22/0.32 % (442855)Time elapsed: 0.005 s
% 0.22/0.32 % (442855)Peak memory usage: 12 MB
% 0.22/0.32 % (442855)Instructions burned: 3 (million)
% 0.22/0.32 % (442849)Success in time 0.06 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------