%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV097^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV097^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:12:27 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.27 % (201751)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (201760)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=312930733:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.27 % (201760) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-201751-201760"...
% 0.21/0.27 % (201760)...printing done.
% 0.21/0.27 % (201760)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% 0.21/0.27 thf(type_def_5, type, a: $tType).
% 0.21/0.27 thf(type_def_6, type, b: $tType).
% 0.21/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.27 thf(func_def_0, type, z: a).
% 0.21/0.27 thf(func_def_1, type, cR: (a > a > $o)).
% 0.21/0.27 thf(func_def_2, type, f: (a > b > $o)).
% 0.21/0.27 thf(func_def_3, type, cS: (b > b > $o)).
% 0.21/0.27 thf(func_def_7, type, sK0: (a > b)).
% 0.21/0.27 thf(func_def_8, type, sK1: a).
% 0.21/0.27 thf(func_def_9, type, sK2: (b > a)).
% 0.21/0.27 thf(f1,conjecture,(
% 0.21/0.27 (! [X0 : a,X2 : a,X1 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X8 : a,X4 : b,X7 : a] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4)) => ! [X3 : a] : ? [X4 : b] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4)))),
% 0.21/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM552C_pme)).
% 0.21/0.27 thf(f2,negated_conjecture,(
% 0.21/0.27 ~((! [X0 : a,X2 : a,X1 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X8 : a,X4 : b,X7 : a] : (((f @ X7 @ X4) & (f @ X8 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X5) & (f @ X3 @ X6)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4)) => ! [X3 : a] : ? [X4 : b] : ! [X2 : a] : ((~(f @ X2 @ X4) & (cR @ X3 @ z)) | (f @ X3 @ X4))))),
% 0.21/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.27 thf(f3,plain,(
% 0.21/0.27 ~((! [X0 : a,X1 : a,X2 : a] : (((cR @ X1 @ X2) & (cR @ X0 @ X2)) => (cR @ X0 @ X1)) & ! [X3 : a] : (cR @ X3 @ X3)) => ((! [X4 : a,X5 : b,X6 : a] : (((f @ X6 @ X5) & (f @ X4 @ X5)) => (cR @ X6 @ X4)) & ! [X7 : a,X8 : b,X9 : b] : (((f @ X7 @ X8) & (f @ X7 @ X9)) => (cS @ X8 @ X9)) & ! [X10 : a] : ? [X11 : b] : (f @ X10 @ X11)) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : ((~(f @ X14 @ X13) & (cR @ X12 @ z)) | (f @ X12 @ X13))))),
% 0.21/0.27 inference(rectify,[],[f2])).
% 0.21/0.27 thf(f4,plain,(
% 0.21/0.27 ~((! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X0 : a,X2 : a,X1 : a] : (((((cR @ X1 @ X2)) = $true) & (((cR @ X0 @ X2)) = $true)) => (((cR @ X0 @ X1)) = $true))) => ((! [X8 : b,X9 : b,X7 : a] : (((((f @ X7 @ X8)) = $true) & ($true = ((f @ X7 @ X9)))) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true) & ! [X5 : b,X6 : a,X4 : a] : ((($true = ((f @ X4 @ X5))) & (((f @ X6 @ X5)) = $true)) => (((cR @ X6 @ X4)) = $true))) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : ((~ ($true = ((f @ X14 @ X13))) & ($true = ((cR @ X12 @ z)))) | ($true = ((f @ X12 @ X13))))))),
% 0.21/0.27 inference(fool_elimination,[],[f3])).
% 0.21/0.27 thf(f5,plain,(
% 0.21/0.27 ~((! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X0 : a,X2 : a,X1 : a] : (((((cR @ X1 @ X2)) = $true) & (((cR @ X0 @ X2)) = $true)) => (((cR @ X0 @ X1)) = $true))) => ((! [X8 : b,X9 : b,X7 : a] : (((((f @ X7 @ X8)) = $true) & ($true = ((f @ X7 @ X9)))) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true) & ! [X5 : b,X6 : a,X4 : a] : ((($true = ((f @ X4 @ X5))) & (((f @ X6 @ X5)) = $true)) => (((cR @ X6 @ X4)) = $true))) => ! [X12 : a] : ? [X13 : b] : ! [X14 : a] : (($true = ((f @ X12 @ X13))) | (($true != ((f @ X14 @ X13))) & ($true = ((cR @ X12 @ z)))))))),
% 0.21/0.27 inference(flattening,[],[f4])).
% 0.21/0.27 thf(f6,plain,(
% 0.21/0.27 (? [X12 : a] : ! [X13 : b] : ? [X14 : a] : (($true != ((f @ X12 @ X13))) & (($true = ((f @ X14 @ X13))) | ($true != ((cR @ X12 @ z))))) & (! [X8 : b,X9 : b,X7 : a] : ((((cS @ X8 @ X9)) = $true) | ((((f @ X7 @ X8)) != $true) | ($true != ((f @ X7 @ X9))))) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true) & ! [X5 : b,X6 : a,X4 : a] : ((((cR @ X6 @ X4)) = $true) | (($true != ((f @ X4 @ X5))) | (((f @ X6 @ X5)) != $true))))) & (! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X0 : a,X2 : a,X1 : a] : ((((cR @ X0 @ X1)) = $true) | ((((cR @ X1 @ X2)) != $true) | (((cR @ X0 @ X2)) != $true))))),
% 0.21/0.27 inference(ennf_transformation,[],[f5])).
% 0.21/0.27 thf(f7,plain,(
% 0.21/0.27 ! [X1 : a,X0 : a,X2 : a] : ((((cR @ X1 @ X2)) != $true) | (((cR @ X0 @ X1)) = $true) | (((cR @ X0 @ X2)) != $true)) & ! [X6 : a,X5 : b,X4 : a] : (($true != ((f @ X4 @ X5))) | (((f @ X6 @ X5)) != $true) | (((cR @ X6 @ X4)) = $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true) & ! [X3 : a] : (((cR @ X3 @ X3)) = $true) & ! [X8 : b,X7 : a,X9 : b] : ((((f @ X7 @ X8)) != $true) | (((cS @ X8 @ X9)) = $true) | ($true != ((f @ X7 @ X9)))) & ? [X12 : a] : ! [X13 : b] : ? [X14 : a] : (($true != ((f @ X12 @ X13))) & (($true = ((f @ X14 @ X13))) | ($true != ((cR @ X12 @ z)))))),
% 0.21/0.27 inference(flattening,[],[f6])).
% 0.21/0.27 thf(f8,plain,(
% 0.21/0.27 ! [X0 : a,X1 : a,X2 : a] : ((((cR @ X0 @ X2)) != $true) | ($true = ((cR @ X1 @ X0))) | (((cR @ X1 @ X2)) != $true)) & ! [X3 : a,X4 : b,X5 : a] : ((((f @ X5 @ X4)) != $true) | (((f @ X3 @ X4)) != $true) | (((cR @ X3 @ X5)) = $true)) & ! [X6 : a] : ? [X7 : b] : (((f @ X6 @ X7)) = $true) & ! [X8 : a] : (((cR @ X8 @ X8)) = $true) & ! [X9 : b,X10 : a,X11 : b] : ((((f @ X10 @ X9)) != $true) | ($true = ((cS @ X9 @ X11))) | (((f @ X10 @ X11)) != $true)) & ? [X12 : a] : ! [X13 : b] : ? [X14 : a] : (($true != ((f @ X12 @ X13))) & (($true = ((f @ X14 @ X13))) | ($true != ((cR @ X12 @ z)))))),
% 0.21/0.27 inference(rectify,[],[f7])).
% 0.21/0.27 thf(f9,plain,(
% 0.21/0.27 ! [X0 : a,X1 : a,X2 : a] : ((((cR @ X0 @ X2)) != $true) | ($true = ((cR @ X1 @ X0))) | (((cR @ X1 @ X2)) != $true)) & ! [X3 : a,X4 : b,X5 : a] : ((((f @ X5 @ X4)) != $true) | (((f @ X3 @ X4)) != $true) | (((cR @ X3 @ X5)) = $true)) & ! [X6 : a] : ($true = ((f @ X6 @ (sK0 @ X6)))) & ! [X8 : a] : (((cR @ X8 @ X8)) = $true) & ! [X9 : b,X10 : a,X11 : b] : ((((f @ X10 @ X9)) != $true) | ($true = ((cS @ X9 @ X11))) | (((f @ X10 @ X11)) != $true)) & ! [X13 : b] : (($true != ((f @ sK1 @ X13))) & ((((f @ (sK2 @ X13) @ X13)) = $true) | (((cR @ sK1 @ z)) != $true)))),
% 0.21/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,vAPP]),skolemize(X14,sK2 @ X13),skolemize(X12,sK1),skolemize(X14,sK2 @ X13)],[f8])).
% 0.21/0.27 thf(f11,plain,(
% 0.21/0.27 ( ! [X13 : b] : (($true != ((f @ sK1 @ X13)))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f9])).
% 0.21/0.27 thf(f14,plain,(
% 0.21/0.27 ( ! [X6 : a] : (($true = ((f @ X6 @ (sK0 @ X6))))) )),
% 0.21/0.27 inference(cnf_transformation,[],[f9])).
% 0.21/0.27 thf(f18,plain,(
% 0.21/0.27 ($true != $true)),
% 0.21/0.27 inference(superposition,[],[f11,f14])).
% 0.21/0.27 thf(f19,plain,(
% 0.21/0.27 $false),
% 0.21/0.27 inference(trivial_inequality_removal,[],[f18])).
% 0.21/0.27 % SZS output end Proof for theBenchmark
% 0.21/0.27 % (201760)------------------------------
% 0.21/0.27 % (201760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (201760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (201760)CaDiCaL version: 2.1.3
% 0.21/0.27 % (201760)Termination reason: Refutation
% 0.21/0.27 % (201760)Time elapsed: 0.001 s
% 0.21/0.27 % (201760)Peak memory usage: 12 MB
% 0.21/0.27 % (201760)Instructions burned: 3 (million)
% 0.21/0.27 % (201751)Success in time 0.03 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------