%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV259^5 : 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 : 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 08:39:13 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV259^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 15:23:52 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.27 % (460493)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (460499)% WARNING: option uhcvi not known.
% 0.20/0.27 % (460499)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1977372495:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (460499)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (460499)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.27 % (460499) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-460493-460499"...
% 0.20/0.27 % (460499)...printing done.
% 0.20/0.27 % (460499)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, b: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.27 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.20/0.27 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_9, type, sK0: ((b > $o) > $o)).
% 0.20/0.27 thf(func_def_10, type, sK1: (b > $o)).
% 0.20/0.27 thf(func_def_11, type, sK2: b).
% 0.20/0.27 thf(func_def_12, type, sK3: (b > $o)).
% 0.20/0.27 thf(func_def_13, type, sK4: (((b > $o) > $o) > b > $o)).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ! [X0 : ((b > $o) > $o)] : ((! [X5 : (b > $o),X6 : (b > $o),X4 : (b > $o)] : (((X4 = (^[X2 : b] : ((X6 @ X2) & (X5 @ X2)))) & (X0 @ X6) & (X0 @ X5)) => (X0 @ X4)) & ! [X3 : ((b > $o) > $o),X1 : (b > $o)] : (((X1 = (^[X2 : b] : (? [X4 : (b > $o)] : ((X4 @ X2) & (X3 @ X4))))) & ! [X2 : (b > $o)] : ((X3 @ X2) => (X0 @ X2))) => (X0 @ X1)) & ! [X1 : (b > $o)] : ((X1 = (^[X2 : b] : (~$false))) => (X0 @ X1)) & ! [X1 : (b > $o)] : ((X1 = (^[X2 : b] : ($false))) => (X0 @ X1))) => ! [X7 : (b > $o),X2 : b] : ((X7 @ X2) => ! [X4 : (b > $o)] : ((! [X1 : (b > $o)] : ((X1 = (^[X8 : b] : (~(X4 @ X8)))) => (X0 @ X1)) & ! [X8 : b] : ((X7 @ X8) => (X4 @ X8))) => (X4 @ X2))))),
% 0.20/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCLOSURE_THM0_pme)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ! [X0 : ((b > $o) > $o)] : ((! [X5 : (b > $o),X6 : (b > $o),X4 : (b > $o)] : (((X4 = (^[X2 : b] : ((X6 @ X2) & (X5 @ X2)))) & (X0 @ X6) & (X0 @ X5)) => (X0 @ X4)) & ! [X3 : ((b > $o) > $o),X1 : (b > $o)] : (((X1 = (^[X2 : b] : (? [X4 : (b > $o)] : ((X4 @ X2) & (X3 @ X4))))) & ! [X2 : (b > $o)] : ((X3 @ X2) => (X0 @ X2))) => (X0 @ X1)) & ! [X1 : (b > $o)] : ((X1 = (^[X2 : b] : (~$false))) => (X0 @ X1)) & ! [X1 : (b > $o)] : ((X1 = (^[X2 : b] : ($false))) => (X0 @ X1))) => ! [X7 : (b > $o),X2 : b] : ((X7 @ X2) => ! [X4 : (b > $o)] : ((! [X1 : (b > $o)] : ((X1 = (^[X8 : b] : (~(X4 @ X8)))) => (X0 @ X1)) & ! [X8 : b] : ((X7 @ X8) => (X4 @ X8))) => (X4 @ X2))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o),X2 : (b > $o),X3 : (b > $o)] : (((X3 = (^[X4 : b] : ((X2 @ X4) & (X1 @ X4)))) & (X0 @ X2) & (X0 @ X1)) => (X0 @ X3)) & ! [X5 : ((b > $o) > $o),X6 : (b > $o)] : (((X6 = (^[X7 : b] : (? [X8 : (b > $o)] : ((X8 @ X7) & (X5 @ X8))))) & ! [X9 : (b > $o)] : ((X5 @ X9) => (X0 @ X9))) => (X0 @ X6)) & ! [X10 : (b > $o)] : ((X10 = (^[X11 : b] : (~$false))) => (X0 @ X10)) & ! [X12 : (b > $o)] : ((X12 = (^[X13 : b] : ($false))) => (X0 @ X12))) => ! [X14 : (b > $o),X15 : b] : ((X14 @ X15) => ! [X16 : (b > $o)] : ((! [X17 : (b > $o)] : ((X17 = (^[X18 : b] : (~(X16 @ X18)))) => (X0 @ X17)) & ! [X19 : b] : ((X14 @ X19) => (X16 @ X19))) => (X16 @ X15))))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o),X2 : (b > $o),X3 : (b > $o)] : ((((^[Y0 : b]: ((X1 @ Y0) & (X2 @ Y0))) = X3) & (((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ X3)) = $true)) & ! [X5 : ((b > $o) > $o),X6 : (b > $o)] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X5 @ Y1) & (Y1 @ Y0))))) = X6) & ! [X9 : (b > $o)] : ((((X5 @ X9)) = $true) => (((X0 @ X9)) = $true))) => (((X0 @ X6)) = $true)) & ! [X10 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X10) => (((X0 @ X10)) = $true)) & ! [X12 : (b > $o)] : (((^[Y0 : b]: ($false)) = X12) => (((X0 @ X12)) = $true))) => ! [X14 : (b > $o),X15 : b] : ((((X14 @ X15)) = $true) => ! [X16 : (b > $o)] : ((! [X17 : (b > $o)] : (((^[Y0 : b]: (~ (X16 @ Y0))) = X17) => (((X0 @ X17)) = $true)) & ! [X19 : b] : ((((X14 @ X19)) = $true) => (((X16 @ X19)) = $true))) => (((X16 @ X15)) = $true))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ~ ! [X0 : ((b > $o) > $o)] : ((! [X1 : (b > $o),X2 : (b > $o),X3 : (b > $o)] : ((((^[Y0 : b]: ((X1 @ Y0) & (X2 @ Y0))) = X3) & (((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ X3)) = $true)) & ! [X4 : ((b > $o) > $o),X5 : (b > $o)] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) & (Y1 @ Y0))))) = X5) & ! [X6 : (b > $o)] : (($true = ((X4 @ X6))) => (((X0 @ X6)) = $true))) => (((X0 @ X5)) = $true)) & ! [X7 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X7) => ($true = ((X0 @ X7)))) & ! [X8 : (b > $o)] : (((^[Y0 : b]: ($false)) = X8) => ($true = ((X0 @ X8))))) => ! [X9 : (b > $o),X10 : b] : (($true = ((X9 @ X10))) => ! [X11 : (b > $o)] : ((! [X12 : (b > $o)] : (((^[Y0 : b]: (~ (X11 @ Y0))) = X12) => (((X0 @ X12)) = $true)) & ! [X13 : b] : (($true = ((X9 @ X13))) => ($true = ((X11 @ X13))))) => ($true = ((X11 @ X10))))))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ? [X0 : ((b > $o) > $o)] : (? [X9 : (b > $o),X10 : b] : (? [X11 : (b > $o)] : (($true != ((X11 @ X10))) & (! [X12 : (b > $o)] : ((((X0 @ X12)) = $true) | ((^[Y0 : b]: (~ (X11 @ Y0))) != X12)) & ! [X13 : b] : (($true = ((X11 @ X13))) | ($true != ((X9 @ X13)))))) & ($true = ((X9 @ X10)))) & (! [X1 : (b > $o),X2 : (b > $o),X3 : (b > $o)] : ((((X0 @ X3)) = $true) | (((^[Y0 : b]: ((X1 @ Y0) & (X2 @ Y0))) != X3) | (((X0 @ X2)) != $true) | (((X0 @ X1)) != $true))) & ! [X4 : ((b > $o) > $o),X5 : (b > $o)] : ((((X0 @ X5)) = $true) | (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) & (Y1 @ Y0))))) != X5) | ? [X6 : (b > $o)] : ((((X0 @ X6)) != $true) & ($true = ((X4 @ X6)))))) & ! [X7 : (b > $o)] : (($true = ((X0 @ X7))) | ((^[Y0 : b]: (~ $false)) != X7)) & ! [X8 : (b > $o)] : (($true = ((X0 @ X8))) | ((^[Y0 : b]: ($false)) != X8))))),
% 0.20/0.27 inference(ennf_transformation,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ? [X0 : ((b > $o) > $o)] : (? [X9 : (b > $o),X10 : b] : (? [X11 : (b > $o)] : (($true != ((X11 @ X10))) & ! [X12 : (b > $o)] : ((((X0 @ X12)) = $true) | ((^[Y0 : b]: (~ (X11 @ Y0))) != X12)) & ! [X13 : b] : (($true = ((X11 @ X13))) | ($true != ((X9 @ X13))))) & ($true = ((X9 @ X10)))) & ! [X1 : (b > $o),X2 : (b > $o),X3 : (b > $o)] : ((((X0 @ X3)) = $true) | ((^[Y0 : b]: ((X1 @ Y0) & (X2 @ Y0))) != X3) | (((X0 @ X2)) != $true) | (((X0 @ X1)) != $true)) & ! [X4 : ((b > $o) > $o),X5 : (b > $o)] : ((((X0 @ X5)) = $true) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X4 @ Y1) & (Y1 @ Y0))))) != X5) | ? [X6 : (b > $o)] : ((((X0 @ X6)) != $true) & ($true = ((X4 @ X6))))) & ! [X7 : (b > $o)] : (($true = ((X0 @ X7))) | ((^[Y0 : b]: (~ $false)) != X7)) & ! [X8 : (b > $o)] : (($true = ((X0 @ X8))) | ((^[Y0 : b]: ($false)) != X8)))),
% 0.20/0.27 inference(flattening,[],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ? [X0 : ((b > $o) > $o)] : (? [X1 : (b > $o),X2 : b] : (? [X3 : (b > $o)] : (($true != ((X3 @ X2))) & ! [X4 : (b > $o)] : ((((X0 @ X4)) = $true) | ((^[Y0 : b]: (~ (X3 @ Y0))) != X4)) & ! [X5 : b] : (($true = ((X3 @ X5))) | ($true != ((X1 @ X5))))) & ($true = ((X1 @ X2)))) & ! [X6 : (b > $o),X7 : (b > $o),X8 : (b > $o)] : (($true = ((X0 @ X8))) | ((^[Y0 : b]: ((X6 @ Y0) & (X7 @ Y0))) != X8) | ($true != ((X0 @ X7))) | (((X0 @ X6)) != $true)) & ! [X9 : ((b > $o) > $o),X10 : (b > $o)] : ((((X0 @ X10)) = $true) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X9 @ Y1) & (Y1 @ Y0))))) != X10) | ? [X11 : (b > $o)] : (($true != ((X0 @ X11))) & ($true = ((X9 @ X11))))) & ! [X12 : (b > $o)] : ((((X0 @ X12)) = $true) | ((^[Y0 : b]: (~ $false)) != X12)) & ! [X13 : (b > $o)] : (($true = ((X0 @ X13))) | ((^[Y0 : b]: ($false)) != X13)))),
% 0.20/0.27 inference(rectify,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ((($true != ((sK3 @ sK2))) & ! [X4 : (b > $o)] : (($true = ((sK0 @ X4))) | ((^[Y0 : b]: (~ (sK3 @ Y0))) != X4)) & ! [X5 : b] : (($true = ((sK3 @ X5))) | ($true != ((sK1 @ X5))))) & ($true = ((sK1 @ sK2)))) & ! [X6 : (b > $o),X7 : (b > $o),X8 : (b > $o)] : (($true = ((sK0 @ X8))) | ((^[Y0 : b]: ((X6 @ Y0) & (X7 @ Y0))) != X8) | ($true != ((sK0 @ X7))) | ($true != ((sK0 @ X6)))) & ! [X9 : ((b > $o) > $o),X10 : (b > $o)] : (($true = ((sK0 @ X10))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X9 @ Y1) & (Y1 @ Y0))))) != X10) | (($true != ((sK0 @ (sK4 @ X9)))) & ($true = ((X9 @ (sK4 @ X9)))))) & ! [X12 : (b > $o)] : (($true = ((sK0 @ X12))) | ((^[Y0 : b]: (~ $false)) != X12)) & ! [X13 : (b > $o)] : (($true = ((sK0 @ X13))) | ((^[Y0 : b]: ($false)) != X13))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X11,sK4 @ X9)],[f8])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK2)))),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ( ! [X5 : b] : (($true != ((sK1 @ X5))) | ($true = ((sK3 @ X5)))) )),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ($true != ((sK3 @ sK2)))),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ($true != $true) | ($true = ((sK3 @ sK2)))),
% 0.20/0.27 inference(constrained_superposition,[],[f16,f15])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 ($true = ((sK3 @ sK2)))),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f28])).
% 0.20/0.27 thf(f30,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f29,f18])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (460499)------------------------------
% 0.20/0.27 % (460499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (460499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (460499)CaDiCaL version: 2.1.3
% 0.20/0.27 % (460499)Termination reason: Refutation
% 0.20/0.27 % (460499)Time elapsed: 0.002 s
% 0.20/0.27 % (460499)Peak memory usage: 12 MB
% 0.20/0.27 % (460499)Instructions burned: 5 (million)
% 0.20/0.27 % (460493)Success in time 0.038 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------