%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n010.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 08:38:59 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV096^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n010.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 15:10:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25 % (2976962)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (2976971)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2671315947:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (2976971)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (2976971) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2976962-2976971"...
% 0.08/0.25 % (2976971)...printing done.
% 0.08/0.25 % (2976968)% WARNING: option uhcvi not known.
% 0.08/0.25 % (2976971)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, a: $tType).
% 0.08/0.25 thf(type_def_6, type, b: $tType).
% 0.08/0.25 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, z: a).
% 0.08/0.25 thf(func_def_1, type, cR: (a > a > $o)).
% 0.08/0.25 thf(func_def_2, type, f: (a > b > $o)).
% 0.08/0.25 thf(func_def_3, type, cS: (b > b > $o)).
% 0.08/0.25 thf(func_def_7, type, sK0: b).
% 0.08/0.25 thf(func_def_8, type, sK1: (a > a)).
% 0.08/0.25 thf(func_def_9, type, sK2: (a > b)).
% 0.08/0.25 thf(f1,conjecture,(
% 0.08/0.25 (! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X7 : a,X8 : a,X4 : b] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4)) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM552E_pme)).
% 0.08/0.25 thf(f2,negated_conjecture,(
% 0.08/0.25 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X7 : a,X8 : a,X4 : b] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : b,X6 : b] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : b] : (f @ X3 @ X4)) => ! [X4 : b] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4))))),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.25 thf(f3,plain,(
% 0.08/0.25 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X3 @ X2) & (cR @ X1 @ X2)) => (cR @ X1 @ X3))) => ((! [X4 : a,X5 : a,X6 : b] : (((f @ X5 @ X6) & (f @ X4 @ X6)) => (cR @ X4 @ X5)) & ! [X7 : a,X8 : b,X9 : b] : (((f @ X7 @ X9) & (f @ X7 @ X8)) => (cS @ X8 @ X9)) & ! [X10 : a] : ? [X11 : b] : (f @ X10 @ X11)) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : (((cR @ X13 @ z) & ~(f @ X14 @ X12)) | (f @ X13 @ X12))))),
% 0.08/0.25 inference(rectify,[],[f2])).
% 0.08/0.25 thf(f4,plain,(
% 0.08/0.25 ~((! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : (((((cR @ X3 @ X2)) = $true) & (((cR @ X1 @ X2)) = $true)) => (((cR @ X1 @ X3)) = $true))) => ((! [X4 : a,X5 : a,X6 : b] : (((((f @ X5 @ X6)) = $true) & (((f @ X4 @ X6)) = $true)) => (((cR @ X4 @ X5)) = $true)) & ! [X7 : a,X8 : b,X9 : b] : (((((f @ X7 @ X9)) = $true) & (((f @ X7 @ X8)) = $true)) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true)) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : (((((cR @ X13 @ z)) = $true) & ~ (((f @ X14 @ X12)) = $true)) | (((f @ X13 @ X12)) = $true))))),
% 0.08/0.25 inference(fool_elimination,[],[f3])).
% 0.08/0.25 thf(f5,plain,(
% 0.08/0.25 ~((! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : (((((cR @ X3 @ X2)) = $true) & (((cR @ X1 @ X2)) = $true)) => (((cR @ X1 @ X3)) = $true))) => ((! [X4 : a,X5 : a,X6 : b] : (((((f @ X5 @ X6)) = $true) & (((f @ X4 @ X6)) = $true)) => (((cR @ X4 @ X5)) = $true)) & ! [X7 : a,X8 : b,X9 : b] : (((((f @ X7 @ X9)) = $true) & (((f @ X7 @ X8)) = $true)) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true)) => ! [X12 : b] : ? [X13 : a] : ! [X14 : a] : (((((cR @ X13 @ z)) = $true) & (((f @ X14 @ X12)) != $true)) | (((f @ X13 @ X12)) = $true))))),
% 0.08/0.25 inference(flattening,[],[f4])).
% 0.08/0.25 thf(f6,plain,(
% 0.08/0.25 (? [X12 : b] : ! [X13 : a] : ? [X14 : a] : (((((cR @ X13 @ z)) != $true) | (((f @ X14 @ X12)) = $true)) & (((f @ X13 @ X12)) != $true)) & (! [X4 : a,X5 : a,X6 : b] : ((((cR @ X4 @ X5)) = $true) | ((((f @ X5 @ X6)) != $true) | (((f @ X4 @ X6)) != $true))) & ! [X7 : a,X8 : b,X9 : b] : ((((cS @ X8 @ X9)) = $true) | ((((f @ X7 @ X9)) != $true) | (((f @ X7 @ X8)) != $true))) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true))) & (! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((cR @ X1 @ X3)) = $true) | ((((cR @ X3 @ X2)) != $true) | (((cR @ X1 @ X2)) != $true))))),
% 0.08/0.25 inference(ennf_transformation,[],[f5])).
% 0.08/0.25 thf(f7,plain,(
% 0.08/0.25 ? [X12 : b] : ! [X13 : a] : ? [X14 : a] : (((((cR @ X13 @ z)) != $true) | (((f @ X14 @ X12)) = $true)) & (((f @ X13 @ X12)) != $true)) & ! [X4 : a,X5 : a,X6 : b] : ((((cR @ X4 @ X5)) = $true) | (((f @ X5 @ X6)) != $true) | (((f @ X4 @ X6)) != $true)) & ! [X7 : a,X8 : b,X9 : b] : ((((cS @ X8 @ X9)) = $true) | (((f @ X7 @ X9)) != $true) | (((f @ X7 @ X8)) != $true)) & ! [X10 : a] : ? [X11 : b] : (((f @ X10 @ X11)) = $true) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((cR @ X1 @ X3)) = $true) | (((cR @ X3 @ X2)) != $true) | (((cR @ X1 @ X2)) != $true))),
% 0.08/0.25 inference(flattening,[],[f6])).
% 0.08/0.25 thf(f8,plain,(
% 0.08/0.25 ? [X0 : b] : ! [X1 : a] : ? [X2 : a] : ((($true != ((cR @ X1 @ z))) | ($true = ((f @ X2 @ X0)))) & ($true != ((f @ X1 @ X0)))) & ! [X3 : a,X4 : a,X5 : b] : (($true = ((cR @ X3 @ X4))) | ($true != ((f @ X4 @ X5))) | (((f @ X3 @ X5)) != $true)) & ! [X6 : a,X7 : b,X8 : b] : (($true = ((cS @ X7 @ X8))) | ($true != ((f @ X6 @ X8))) | ($true != ((f @ X6 @ X7)))) & ! [X9 : a] : ? [X10 : b] : ($true = ((f @ X9 @ X10))) & ! [X11 : a] : ($true = ((cR @ X11 @ X11))) & ! [X12 : a,X13 : a,X14 : a] : (($true = ((cR @ X12 @ X14))) | ($true != ((cR @ X14 @ X13))) | ($true != ((cR @ X12 @ X13))))),
% 0.08/0.25 inference(rectify,[],[f7])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 ! [X1 : a] : ((($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK1 @ X1) @ sK0)))) & ($true != ((f @ X1 @ sK0)))) & ! [X3 : a,X4 : a,X5 : b] : (($true = ((cR @ X3 @ X4))) | ($true != ((f @ X4 @ X5))) | (((f @ X3 @ X5)) != $true)) & ! [X6 : a,X7 : b,X8 : b] : (($true = ((cS @ X7 @ X8))) | ($true != ((f @ X6 @ X8))) | ($true != ((f @ X6 @ X7)))) & ! [X9 : a] : ($true = ((f @ X9 @ (sK2 @ X9)))) & ! [X11 : a] : ($true = ((cR @ X11 @ X11))) & ! [X12 : a,X13 : a,X14 : a] : (($true = ((cR @ X12 @ X14))) | ($true != ((cR @ X14 @ X13))) | ($true != ((cR @ X12 @ X13))))),
% 0.08/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X10,sK2 @ X9),skolemize(X10,sK2 @ X9)],[f8])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 ( ! [X11 : a] : (($true = ((cR @ X11 @ X11)))) )),
% 0.08/0.25 inference(cnf_transformation,[],[f9])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ( ! [X1 : a] : (($true != ((f @ X1 @ sK0)))) )),
% 0.08/0.25 inference(cnf_transformation,[],[f9])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 ( ! [X1 : a] : (($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK1 @ X1) @ sK0)))) )),
% 0.08/0.25 inference(cnf_transformation,[],[f9])).
% 0.08/0.25 thf(f19,plain,(
% 0.08/0.25 ( ! [X1 : a] : (($true != ((cR @ X1 @ z)))) )),
% 0.08/0.25 inference(forward_subsumption_resolution,[],[f16,f15])).
% 0.08/0.25 thf(f20,plain,(
% 0.08/0.25 ($true != $true)),
% 0.08/0.25 inference(constrained_superposition,[],[f19,f11])).
% 0.08/0.25 thf(f21,plain,(
% 0.08/0.25 $false),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f20])).
% 0.08/0.25 % SZS output end Proof for theBenchmark
% 0.08/0.25 % (2976971)------------------------------
% 0.08/0.25 % (2976971)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2976971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2976971)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2976971)Termination reason: Refutation
% 0.08/0.25 % (2976971)Time elapsed: 0.002 s
% 0.08/0.25 % (2976971)Peak memory usage: 12 MB
% 0.08/0.25 % (2976971)Instructions burned: 3 (million)
% 0.08/0.25 % (2976962)Success in time 0.035 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------