%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV200^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:39:08 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV200^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:20:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (858780)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (858787)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1203265351:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (858787) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-858780-858787"...
% 0.09/0.25 % (858787)...printing done.
% 0.09/0.25 % (858786)% WARNING: option uhcvi not known.
% 0.09/0.25 % (858787)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, a: $tType).
% 0.09/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, x: a).
% 0.09/0.25 thf(func_def_1, type, cZ: a).
% 0.09/0.25 thf(func_def_2, type, cP: (a > a > a)).
% 0.09/0.25 thf(func_def_6, type, sK0: (a > a > a > $o)).
% 0.09/0.25 thf(func_def_7, type, sK1: ((a > $o) > a)).
% 0.09/0.25 thf(func_def_8, type, sK2: ((a > $o) > a)).
% 0.09/0.25 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 (! [X4 : (a > $o)] : ((! [X0 : a,X1 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ cZ)) => ! [X0 : a] : (X4 @ X0)) & ! [X0 : a,X1 : a,X2 : a,X3 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : a,X1 : a] : (((cP @ X0 @ X1)) != cZ)) => ! [X5 : (a > a > a > $o)] : ((! [X6 : a,X7 : a,X8 : a] : ((? [X9 : a,X10 : a,X11 : a,X12 : a,X13 : a,X14 : a] : ((X5 @ X10 @ X12 @ X14) & (X5 @ X9 @ X11 @ X13) & (X8 = ((cP @ X13 @ X14))) & (X7 = ((cP @ X11 @ X12))) & (X6 = ((cP @ X9 @ X10)))) | ((X6 = X8) & (X7 = cZ)) | ((X7 = X8) & (X6 = cZ))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ cZ @ x @ x))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_LEM1C_pme)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~((! [X4 : (a > $o)] : ((! [X0 : a,X1 : a] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ cZ)) => ! [X0 : a] : (X4 @ X0)) & ! [X0 : a,X1 : a,X2 : a,X3 : a] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : a,X1 : a] : (((cP @ X0 @ X1)) != cZ)) => ! [X5 : (a > a > a > $o)] : ((! [X6 : a,X7 : a,X8 : a] : ((? [X9 : a,X10 : a,X11 : a,X12 : a,X13 : a,X14 : a] : ((X5 @ X10 @ X12 @ X14) & (X5 @ X9 @ X11 @ X13) & (X8 = ((cP @ X13 @ X14))) & (X7 = ((cP @ X11 @ X12))) & (X6 = ((cP @ X9 @ X10)))) | ((X6 = X8) & (X7 = cZ)) | ((X7 = X8) & (X6 = cZ))) => (X5 @ X6 @ X7 @ X8)) & $true) => (X5 @ cZ @ x @ x)))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~((! [X0 : (a > $o)] : ((! [X1 : a,X2 : a] : (((X0 @ X2) & (X0 @ X1)) => (X0 @ (cP @ X1 @ X2))) & (X0 @ cZ)) => ! [X3 : a] : (X0 @ X3)) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9)))) => ! [X10 : (a > a > a > $o)] : ((! [X11 : a,X12 : a,X13 : a] : ((? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((X10 @ X15 @ X17 @ X19) & (X10 @ X14 @ X16 @ X18) & (((cP @ X18 @ X19)) = X13) & (((cP @ X16 @ X17)) = X12) & (((cP @ X14 @ X15)) = X11)) | ((X11 = X13) & (cZ = X12)) | ((X12 = X13) & (cZ = X11))) => (X10 @ X11 @ X12 @ X13)) & $true) => (X10 @ cZ @ x @ x)))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~((! [X0 : (a > $o)] : ((! [X1 : a,X2 : a] : (((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ (cP @ X1 @ X2))) = $true)) & (((X0 @ cZ)) = $true)) => ! [X3 : a] : (((X0 @ X3)) = $true)) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9)))) => ! [X10 : (a > a > a > $o)] : ((! [X11 : a,X12 : a,X13 : a] : ((? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X10 @ X15 @ X17 @ X19)) = $true) & (((X10 @ X14 @ X16 @ X18)) = $true) & (((cP @ X18 @ X19)) = X13) & (((cP @ X16 @ X17)) = X12) & (((cP @ X14 @ X15)) = X11)) | ((X11 = X13) & (cZ = X12)) | ((X12 = X13) & (cZ = X11))) => (((X10 @ X11 @ X12 @ X13)) = $true)) & $true) => (((X10 @ cZ @ x @ x)) = $true)))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ~((! [X0 : (a > $o)] : ((! [X1 : a,X2 : a] : (((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ (cP @ X1 @ X2))) = $true)) & (((X0 @ cZ)) = $true)) => ! [X3 : a] : (((X0 @ X3)) = $true)) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9)))) => ! [X10 : (a > a > a > $o)] : (! [X11 : a,X12 : a,X13 : a] : ((? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X10 @ X15 @ X17 @ X19)) = $true) & (((X10 @ X14 @ X16 @ X18)) = $true) & (((cP @ X18 @ X19)) = X13) & (((cP @ X16 @ X17)) = X12) & (((cP @ X14 @ X15)) = X11)) | ((X11 = X13) & (cZ = X12)) | ((X12 = X13) & (cZ = X11))) => (((X10 @ X11 @ X12 @ X13)) = $true)) => (((X10 @ cZ @ x @ x)) = $true)))),
% 0.09/0.25 inference(true_and_false_elimination,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ? [X10 : (a > a > a > $o)] : ((((X10 @ cZ @ x @ x)) != $true) & ! [X11 : a,X12 : a,X13 : a] : ((((X10 @ X11 @ X12 @ X13)) = $true) | (! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X10 @ X15 @ X17 @ X19)) != $true) | (((X10 @ X14 @ X16 @ X18)) != $true) | (((cP @ X18 @ X19)) != X13) | (((cP @ X16 @ X17)) != X12) | (((cP @ X14 @ X15)) != X11)) & ((X11 != X13) | (cZ != X12)) & ((X12 != X13) | (cZ != X11))))) & (! [X0 : (a > $o)] : (! [X3 : a] : (((X0 @ X3)) = $true) | (? [X1 : a,X2 : a] : ((((X0 @ (cP @ X1 @ X2))) != $true) & ((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true))) | (((X0 @ cZ)) != $true))) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9))))),
% 0.09/0.25 inference(ennf_transformation,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ? [X10 : (a > a > a > $o)] : ((((X10 @ cZ @ x @ x)) != $true) & ! [X11 : a,X12 : a,X13 : a] : ((((X10 @ X11 @ X12 @ X13)) = $true) | (! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X10 @ X15 @ X17 @ X19)) != $true) | (((X10 @ X14 @ X16 @ X18)) != $true) | (((cP @ X18 @ X19)) != X13) | (((cP @ X16 @ X17)) != X12) | (((cP @ X14 @ X15)) != X11)) & ((X11 != X13) | (cZ != X12)) & ((X12 != X13) | (cZ != X11))))) & ! [X0 : (a > $o)] : (! [X3 : a] : (((X0 @ X3)) = $true) | ? [X1 : a,X2 : a] : ((((X0 @ (cP @ X1 @ X2))) != $true) & (((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) | (((X0 @ cZ)) != $true)) & ! [X4 : a,X5 : a,X6 : a,X7 : a] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : a,X9 : a] : (cZ != ((cP @ X8 @ X9)))),
% 0.09/0.25 inference(flattening,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ? [X0 : (a > a > a > $o)] : (($true != ((X0 @ cZ @ x @ x))) & ! [X1 : a,X2 : a,X3 : a] : (($true = ((X0 @ X1 @ X2 @ X3))) | (! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (($true != ((X0 @ X5 @ X7 @ X9))) | ($true != ((X0 @ X4 @ X6 @ X8))) | (((cP @ X8 @ X9)) != X3) | (((cP @ X6 @ X7)) != X2) | (((cP @ X4 @ X5)) != X1)) & ((X1 != X3) | (cZ != X2)) & ((X2 != X3) | (cZ != X1))))) & ! [X10 : (a > $o)] : (! [X11 : a] : ($true = ((X10 @ X11))) | ? [X12 : a,X13 : a] : (($true != ((X10 @ (cP @ X12 @ X13)))) & ($true = ((X10 @ X13))) & ($true = ((X10 @ X12)))) | ($true != ((X10 @ cZ)))) & ! [X14 : a,X15 : a,X16 : a,X17 : a] : (((X16 = X17) & (X14 = X15)) | (((cP @ X14 @ X16)) != ((cP @ X15 @ X17)))) & ! [X18 : a,X19 : a] : (cZ != ((cP @ X18 @ X19)))),
% 0.09/0.25 inference(rectify,[],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 (($true != ((sK0 @ cZ @ x @ x))) & ! [X1 : a,X2 : a,X3 : a] : (($true = ((sK0 @ X1 @ X2 @ X3))) | (! [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : (($true != ((sK0 @ X5 @ X7 @ X9))) | ($true != ((sK0 @ X4 @ X6 @ X8))) | (((cP @ X8 @ X9)) != X3) | (((cP @ X6 @ X7)) != X2) | (((cP @ X4 @ X5)) != X1)) & ((X1 != X3) | (cZ != X2)) & ((X2 != X3) | (cZ != X1))))) & ! [X10 : (a > $o)] : (! [X11 : a] : ($true = ((X10 @ X11))) | (($true != ((X10 @ (cP @ (sK1 @ X10) @ (sK2 @ X10))))) & ($true = ((X10 @ (sK2 @ X10)))) & ($true = ((X10 @ (sK1 @ X10))))) | ($true != ((X10 @ cZ)))) & ! [X14 : a,X15 : a,X16 : a,X17 : a] : (((X16 = X17) & (X14 = X15)) | (((cP @ X14 @ X16)) != ((cP @ X15 @ X17)))) & ! [X18 : a,X19 : a] : (cZ != ((cP @ X18 @ X19)))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X13,sK2 @ X10),skolemize(X13,sK2 @ X10)],[f8])).
% 0.09/0.25 thf(f16,plain,(
% 0.09/0.25 ( ! [X2 : a,X3 : a,X1 : a] : (($true = ((sK0 @ X1 @ X2 @ X3))) | (X2 != X3) | (cZ != X1)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f19,plain,(
% 0.09/0.25 ($true != ((sK0 @ cZ @ x @ x)))),
% 0.09/0.25 inference(cnf_transformation,[],[f9])).
% 0.09/0.25 thf(f27,plain,(
% 0.09/0.25 ( ! [X3 : a,X1 : a] : (($true = ((sK0 @ X1 @ X3 @ X3))) | (cZ != X1)) )),
% 0.09/0.25 inference(equality_resolution,[],[f16])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 ( ! [X3 : a] : (($true = ((sK0 @ cZ @ X3 @ X3)))) )),
% 0.09/0.25 inference(equality_resolution,[],[f27])).
% 0.09/0.25 thf(f29,plain,(
% 0.09/0.25 ($true != $true)),
% 0.09/0.25 inference(constrained_superposition,[],[f19,f28])).
% 0.09/0.25 thf(f30,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f29])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (858787)------------------------------
% 0.09/0.25 % (858787)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (858787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (858787)CaDiCaL version: 2.1.3
% 0.09/0.25 % (858787)Termination reason: Refutation
% 0.09/0.25 % (858787)Time elapsed: 0.002 s
% 0.09/0.25 % (858787)Peak memory usage: 12 MB
% 0.09/0.25 % (858787)Instructions burned: 5 (million)
% 0.09/0.25 % (858780)Success in time 0.034 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------