%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV197^5 : 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 : n014.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 08:38:00 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV197^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 15:19:45 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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
% 0.21/0.29 % (2796214)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2796232)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=321800089:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2796232) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2796214-2796232"...
% 0.21/0.29 % (2796232)...printing done.
% 0.21/0.29 % (2796232)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, iS: $tType).
% 0.21/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, c0: iS).
% 0.21/0.29 thf(func_def_1, type, cP: (iS > iS > iS)).
% 0.21/0.29 thf(func_def_5, type, sK0: ((iS > $o) > iS)).
% 0.21/0.29 thf(func_def_6, type, sK1: ((iS > $o) > iS)).
% 0.21/0.29 thf(func_def_7, type, sK2: iS).
% 0.21/0.29 thf(func_def_8, type, sK3: iS).
% 0.21/0.29 thf(func_def_9, type, sK4: iS).
% 0.21/0.29 thf(func_def_10, type, sK5: iS).
% 0.21/0.29 thf(func_def_11, type, sK6: iS).
% 0.21/0.29 thf(func_def_12, type, sK7: iS).
% 0.21/0.29 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(f1,conjecture,(
% 0.21/0.29 (! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X1 : iS,X0 : iS] : (((cP @ X0 @ X1)) != c0) & ! [X2 : iS,X1 : iS,X0 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3)))) => (! [X3 : iS,X1 : iS,X0 : iS,X2 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3))) & ! [X1 : iS,X0 : iS] : (((cP @ X0 @ X1)) != c0))),
% 0.21/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_ALG02_pme)).
% 0.21/0.29 thf(f2,negated_conjecture,(
% 0.21/0.29 ~((! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X0) & (X4 @ X1)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X1 : iS,X0 : iS] : (((cP @ X0 @ X1)) != c0) & ! [X2 : iS,X1 : iS,X0 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3)))) => (! [X3 : iS,X1 : iS,X0 : iS,X2 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X0 = X1) & (X2 = X3))) & ! [X1 : iS,X0 : iS] : (((cP @ X0 @ X1)) != c0)))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.29 thf(f3,plain,(
% 0.21/0.29 ~((! [X0 : (iS > $o)] : ((! [X1 : iS,X2 : iS] : (((X0 @ X1) & (X0 @ X2)) => (X0 @ (cP @ X1 @ X2))) & (X0 @ c0)) => ! [X3 : iS] : (X0 @ X3)) & ! [X4 : iS,X5 : iS] : (c0 != ((cP @ X5 @ X4))) & ! [X6 : iS,X7 : iS,X8 : iS,X9 : iS] : ((((cP @ X7 @ X9)) = ((cP @ X8 @ X6))) => ((X7 = X8) & (X6 = X9)))) => (! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : ((((cP @ X12 @ X13)) = ((cP @ X11 @ X10))) => ((X11 = X12) & (X10 = X13))) & ! [X14 : iS,X15 : iS] : (c0 != ((cP @ X15 @ X14)))))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f4,plain,(
% 0.21/0.29 ~((! [X4 : iS,X5 : iS] : (c0 != ((cP @ X5 @ X4))) & ! [X6 : iS,X7 : iS,X9 : iS,X8 : iS] : ((((cP @ X7 @ X9)) = ((cP @ X8 @ X6))) => ((X7 = X8) & (X6 = X9))) & ! [X0 : (iS > $o)] : ((($true = ((X0 @ c0))) & ! [X1 : iS,X2 : iS] : ((($true = ((X0 @ X1))) & ($true = ((X0 @ X2)))) => ($true = ((X0 @ (cP @ X1 @ X2)))))) => ! [X3 : iS] : ($true = ((X0 @ X3))))) => (! [X11 : iS,X10 : iS,X13 : iS,X12 : iS] : ((((cP @ X12 @ X13)) = ((cP @ X11 @ X10))) => ((X10 = X13) & (X11 = X12))) & ! [X14 : iS,X15 : iS] : (c0 != ((cP @ X15 @ X14)))))),
% 0.21/0.29 inference(fool_elimination,[],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 (? [X15 : iS,X14 : iS] : (c0 = ((cP @ X15 @ X14))) | ? [X11 : iS,X13 : iS,X10 : iS,X12 : iS] : (((X11 != X12) | (X10 != X13)) & (((cP @ X12 @ X13)) = ((cP @ X11 @ X10))))) & (! [X4 : iS,X5 : iS] : (c0 != ((cP @ X5 @ X4))) & ! [X7 : iS,X9 : iS,X6 : iS,X8 : iS] : (((X7 = X8) & (X6 = X9)) | (((cP @ X7 @ X9)) != ((cP @ X8 @ X6)))) & ! [X0 : (iS > $o)] : (! [X3 : iS] : ($true = ((X0 @ X3))) | (($true != ((X0 @ c0))) | ? [X1 : iS,X2 : iS] : (($true != ((X0 @ (cP @ X1 @ X2)))) & (($true = ((X0 @ X1))) & ($true = ((X0 @ X2))))))))),
% 0.21/0.29 inference(ennf_transformation,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ! [X0 : (iS > $o)] : (($true != ((X0 @ c0))) | ? [X1 : iS,X2 : iS] : (($true = ((X0 @ X1))) & ($true != ((X0 @ (cP @ X1 @ X2)))) & ($true = ((X0 @ X2)))) | ! [X3 : iS] : ($true = ((X0 @ X3)))) & (? [X15 : iS,X14 : iS] : (c0 = ((cP @ X15 @ X14))) | ? [X11 : iS,X13 : iS,X10 : iS,X12 : iS] : (((X11 != X12) | (X10 != X13)) & (((cP @ X12 @ X13)) = ((cP @ X11 @ X10))))) & ! [X4 : iS,X5 : iS] : (c0 != ((cP @ X5 @ X4))) & ! [X7 : iS,X9 : iS,X6 : iS,X8 : iS] : (((X7 = X8) & (X6 = X9)) | (((cP @ X7 @ X9)) != ((cP @ X8 @ X6))))),
% 0.21/0.29 inference(flattening,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ! [X0 : (iS > $o)] : (($true != ((X0 @ c0))) | ? [X1 : iS,X2 : iS] : (($true = ((X0 @ X1))) & ($true != ((X0 @ (cP @ X1 @ X2)))) & ($true = ((X0 @ X2)))) | ! [X3 : iS] : ($true = ((X0 @ X3)))) & (? [X4 : iS,X5 : iS] : (c0 = ((cP @ X4 @ X5))) | ? [X6 : iS,X7 : iS,X8 : iS,X9 : iS] : (((X6 != X9) | (X7 != X8)) & (((cP @ X6 @ X8)) = ((cP @ X9 @ X7))))) & ! [X10 : iS,X11 : iS] : (c0 != ((cP @ X11 @ X10))) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X12 = X15) & (X13 = X14)) | (((cP @ X12 @ X13)) != ((cP @ X15 @ X14))))),
% 0.21/0.29 inference(rectify,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ! [X0 : (iS > $o)] : (($true != ((X0 @ c0))) | (($true = ((X0 @ (sK0 @ X0)))) & ($true != ((X0 @ (cP @ (sK0 @ X0) @ (sK1 @ X0))))) & ($true = ((X0 @ (sK1 @ X0))))) | ! [X3 : iS] : ($true = ((X0 @ X3)))) & ((c0 = ((cP @ sK2 @ sK3))) | (((sK4 != sK7) | (sK6 != sK5)) & (((cP @ sK4 @ sK6)) = ((cP @ sK7 @ sK5))))) & ! [X10 : iS,X11 : iS] : (c0 != ((cP @ X11 @ X10))) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X12 = X15) & (X13 = X14)) | (((cP @ X12 @ X13)) != ((cP @ X15 @ X14))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X6,sK4),skolemize(X7,sK5),skolemize(X8,sK6),skolemize(X9,sK7)],[f7])).
% 0.21/0.29 thf(f9,plain,(
% 0.21/0.29 ( ! [X14 : iS,X15 : iS,X12 : iS,X13 : iS] : ((((cP @ X12 @ X13)) != ((cP @ X15 @ X14))) | (X13 = X14)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ( ! [X14 : iS,X15 : iS,X12 : iS,X13 : iS] : ((((cP @ X12 @ X13)) != ((cP @ X15 @ X14))) | (X12 = X15)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ( ! [X10 : iS,X11 : iS] : ((c0 != ((cP @ X11 @ X10)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 (c0 = ((cP @ sK2 @ sK3))) | (((cP @ sK4 @ sK6)) = ((cP @ sK7 @ sK5)))),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 (sK4 != sK7) | (sK6 != sK5) | (c0 = ((cP @ sK2 @ sK3)))),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f19,plain,(
% 0.21/0.29 (((cP @ sK4 @ sK6)) = ((cP @ sK7 @ sK5)))),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f12,f11])).
% 0.21/0.29 thf(f20,plain,(
% 0.21/0.29 (sK4 != sK7) | (sK6 != sK5)),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f13,f11])).
% 0.21/0.29 thf(f22,definition,(
% 0.21/0.29 spl8_1 <=> (sK4 = sK7)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (sK4 != sK7) | spl8_1),
% 0.21/0.29 inference(avatar_component_clause,[],[f22])).
% 0.21/0.29 thf(f26,definition,(
% 0.21/0.29 spl8_2 <=> (sK6 = sK5)),
% 0.21/0.29 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 ~spl8_1 | ~spl8_2),
% 0.21/0.29 inference(avatar_split_clause,[],[f20,f26,f22])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 ( ! [X0 : iS,X1 : iS] : ((((cP @ X0 @ X1)) != ((cP @ sK7 @ sK5))) | (sK6 = X1)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f9,f19])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 ( ! [X0 : iS,X1 : iS] : ((((cP @ X0 @ X1)) != ((cP @ sK7 @ sK5))) | (sK4 = X0)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f10,f19])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 (sK6 = sK5)),
% 0.21/0.29 inference(equality_resolution,[],[f31])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 spl8_2),
% 0.21/0.29 inference(avatar_split_clause,[],[f37,f26])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 (sK4 = sK7)),
% 0.21/0.29 inference(equality_resolution,[],[f35])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 $false | spl8_1),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f41,f24])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 spl8_1),
% 0.21/0.29 inference(avatar_contradiction_clause,[],[f42])).
% 0.21/0.29 cnf(s1, plain, ~spl8_1 | ~spl8_2, inference(sat_conversion,[],[f29])).
% 0.21/0.29 cnf(s2, plain, spl8_2, inference(sat_conversion,[],[f38])).
% 0.21/0.29 cnf(s3, plain, spl8_1, inference(sat_conversion,[],[f43])).
% 0.21/0.29 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(avatar_sat_refutation,[],[s4])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (2796232)------------------------------
% 0.21/0.29 % (2796232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2796232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2796232)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2796232)Termination reason: Refutation
% 0.21/0.29 % (2796232)Time elapsed: 0.002 s
% 0.21/0.29 % (2796232)Peak memory usage: 13 MB
% 0.21/0.29 % (2796232)Instructions burned: 4 (million)
% 0.21/0.29 % (2796214)Success in time 0.039 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------