%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU961^5 : 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 : n002.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 08:34:28 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU961^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:53:52 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.09/0.27 % (1398017)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (1398025)dis+10_1_sil=32000:sp=arity:random_seed=1889769353:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.27 % (1398025) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1398017-1398025"...
% 0.09/0.27 % (1398025)...printing done.
% 0.09/0.27 % (1398023)% WARNING: option uhcvi not known.
% 0.09/0.27 % (1398025)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% 0.09/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.27 thf(func_def_3, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.27 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.27 thf(func_def_5, type, sK0: ($i > $i)).
% 0.09/0.27 thf(func_def_6, type, sK1: ($i > $i)).
% 0.09/0.27 thf(func_def_7, type, sK2: (($i > $i) > $o)).
% 0.09/0.27 thf(func_def_8, type, sK3: ((($i > $i) > $o) > $i > $i)).
% 0.09/0.27 thf(func_def_9, type, sK4: (($i > $i) > ($i > $i) > $i)).
% 0.09/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.09/0.27 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.27 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.09/0.27 thf(f1,conjecture,(
% 0.09/0.27 (! [X2 : ($i > $i),X3 : ($i > $i)] : (! [X4 : $i] : (((X2 @ X4)) = ((X3 @ X4))) => (X2 = X3)) & ! [X0 : $i,X1 : $i] : (X0 = X1)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : ((X5 @ (X8 @ X4)))))) & (X7 @ X5)) => (X7 @ (^[X4 : $i] : ((X6 @ (X5 @ X4)))))) => ! [X7 : (($i > $i) > $o)] : ((! [X9 : ($i > $i)] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : ((X5 @ (X9 @ X4)))))) & (X7 @ X5)) => (X7 @ X6)))),
% 0.09/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196C_pme)).
% 0.09/0.27 thf(f2,negated_conjecture,(
% 0.09/0.27 ~((! [X2 : ($i > $i),X3 : ($i > $i)] : (! [X4 : $i] : (((X2 @ X4)) = ((X3 @ X4))) => (X2 = X3)) & ! [X0 : $i,X1 : $i] : (X0 = X1)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X4 : $i] : ((X5 @ (X8 @ X4)))))) & (X7 @ X5)) => (X7 @ (^[X4 : $i] : ((X6 @ (X5 @ X4)))))) => ! [X7 : (($i > $i) > $o)] : ((! [X9 : ($i > $i)] : ((X7 @ X9) => (X7 @ (^[X4 : $i] : ((X5 @ (X9 @ X4)))))) & (X7 @ X5)) => (X7 @ X6))))),
% 0.09/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.27 thf(f3,plain,(
% 0.09/0.27 ~((! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((X7 @ X8) => (X7 @ (^[X9 : $i] : ((X5 @ (X8 @ X9)))))) & (X7 @ X5)) => (X7 @ (^[X10 : $i] : ((X6 @ (X5 @ X10)))))) => ! [X11 : (($i > $i) > $o)] : ((! [X12 : ($i > $i)] : ((X11 @ X12) => (X11 @ (^[X13 : $i] : ((X5 @ (X12 @ X13)))))) & (X11 @ X5)) => (X11 @ X6))))),
% 0.09/0.27 inference(rectify,[],[f2])).
% 0.09/0.27 thf(f4,plain,(
% 0.09/0.27 ~((! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((((X7 @ X8)) = $true) => ($true = ((X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0))))))) & (((X7 @ X5)) = $true)) => ($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))))) => ! [X11 : (($i > $i) > $o)] : ((! [X12 : ($i > $i)] : ((((X11 @ X12)) = $true) => ($true = ((X11 @ (^[Y0 : $i]: (X5 @ (X12 @ Y0))))))) & (((X11 @ X5)) = $true)) => (((X11 @ X6)) = $true))))),
% 0.09/0.27 inference(fool_elimination,[],[f3])).
% 0.09/0.27 thf(f5,plain,(
% 0.09/0.27 ~((! [X0 : ($i > $i),X1 : ($i > $i)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => (X0 = X1)) & ! [X3 : $i,X4 : $i] : (X3 = X4)) => ! [X5 : ($i > $i),X6 : ($i > $i)] : (! [X7 : (($i > $i) > $o)] : ((! [X8 : ($i > $i)] : ((((X7 @ X8)) = $true) => ($true = ((X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0))))))) & (((X7 @ X5)) = $true)) => ($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0))))))) => ! [X9 : (($i > $i) > $o)] : ((! [X10 : ($i > $i)] : (($true = ((X9 @ X10))) => ($true = ((X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0))))))) & ($true = ((X9 @ X5)))) => ($true = ((X9 @ X6))))))),
% 0.09/0.27 inference(rectify,[],[f4])).
% 0.09/0.27 thf(f6,plain,(
% 0.09/0.27 ? [X5 : ($i > $i),X6 : ($i > $i)] : (? [X9 : (($i > $i) > $o)] : (($true != ((X9 @ X6))) & (! [X10 : ($i > $i)] : (($true = ((X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) | ($true != ((X9 @ X10)))) & ($true = ((X9 @ X5))))) & ! [X7 : (($i > $i) > $o)] : (($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0)))))) | (? [X8 : ($i > $i)] : (($true != ((X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0)))))) & (((X7 @ X8)) = $true)) | (((X7 @ X5)) != $true)))) & (! [X0 : ($i > $i),X1 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2)))) & ! [X3 : $i,X4 : $i] : (X3 = X4))),
% 0.09/0.27 inference(ennf_transformation,[],[f5])).
% 0.09/0.27 thf(f7,plain,(
% 0.09/0.27 ? [X5 : ($i > $i),X6 : ($i > $i)] : (? [X9 : (($i > $i) > $o)] : (($true != ((X9 @ X6))) & ! [X10 : ($i > $i)] : (($true = ((X9 @ (^[Y0 : $i]: (X5 @ (X10 @ Y0)))))) | ($true != ((X9 @ X10)))) & ($true = ((X9 @ X5)))) & ! [X7 : (($i > $i) > $o)] : (($true = ((X7 @ (^[Y0 : $i]: (X6 @ (X5 @ Y0)))))) | ? [X8 : ($i > $i)] : (($true != ((X7 @ (^[Y0 : $i]: (X5 @ (X8 @ Y0)))))) & (((X7 @ X8)) = $true)) | (((X7 @ X5)) != $true))) & ! [X0 : ($i > $i),X1 : ($i > $i)] : ((X0 = X1) | ? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2)))) & ! [X3 : $i,X4 : $i] : (X3 = X4)),
% 0.09/0.27 inference(flattening,[],[f6])).
% 0.09/0.27 thf(f8,plain,(
% 0.09/0.27 ? [X0 : ($i > $i),X1 : ($i > $i)] : (? [X2 : (($i > $i) > $o)] : (($true != ((X2 @ X1))) & ! [X3 : ($i > $i)] : (($true = ((X2 @ (^[Y0 : $i]: (X0 @ (X3 @ Y0)))))) | ($true != ((X2 @ X3)))) & ($true = ((X2 @ X0)))) & ! [X4 : (($i > $i) > $o)] : (($true = ((X4 @ (^[Y0 : $i]: (X1 @ (X0 @ Y0)))))) | ? [X5 : ($i > $i)] : (($true != ((X4 @ (^[Y0 : $i]: (X0 @ (X5 @ Y0)))))) & ($true = ((X4 @ X5)))) | ($true != ((X4 @ X0))))) & ! [X6 : ($i > $i),X7 : ($i > $i)] : ((X6 = X7) | ? [X8 : $i] : (((X6 @ X8)) != ((X7 @ X8)))) & ! [X9 : $i,X10 : $i] : (X9 = X10)),
% 0.09/0.27 inference(rectify,[],[f7])).
% 0.09/0.27 thf(f9,plain,(
% 0.09/0.27 ((($true != ((sK2 @ sK1))) & ! [X3 : ($i > $i)] : (($true = ((sK2 @ (^[Y0 : $i]: (sK0 @ (X3 @ Y0)))))) | ($true != ((sK2 @ X3)))) & ($true = ((sK2 @ sK0)))) & ! [X4 : (($i > $i) > $o)] : (($true = ((X4 @ (^[Y0 : $i]: (sK1 @ (sK0 @ Y0)))))) | (($true != ((X4 @ (^[Y0 : $i]: (sK0 @ (sK3 @ X4 @ Y0)))))) & ($true = ((X4 @ (sK3 @ X4))))) | ($true != ((X4 @ sK0))))) & ! [X6 : ($i > $i),X7 : ($i > $i)] : ((X6 = X7) | (((X6 @ (sK4 @ X7 @ X6))) != ((X7 @ (sK4 @ X7 @ X6))))) & ! [X9 : $i,X10 : $i] : (X9 = X10)),
% 0.09/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X8,sK4 @ X7 @ X6),skolemize(X8,sK4 @ X7 @ X6)],[f8])).
% 0.09/0.27 thf(f10,plain,(
% 0.09/0.27 ( ! [X10 : $i,X9 : $i] : ((X9 = X10)) )),
% 0.09/0.27 inference(cnf_transformation,[],[f9])).
% 0.09/0.27 thf(f11,plain,(
% 0.09/0.27 ( ! [X6 : ($i > $i),X7 : ($i > $i)] : ((X6 = X7) | (((X6 @ (sK4 @ X7 @ X6))) != ((X7 @ (sK4 @ X7 @ X6))))) )),
% 0.09/0.27 inference(cnf_transformation,[],[f9])).
% 0.09/0.27 thf(f14,plain,(
% 0.09/0.27 ($true = ((sK2 @ sK0)))),
% 0.09/0.27 inference(cnf_transformation,[],[f9])).
% 0.09/0.27 thf(f16,plain,(
% 0.09/0.27 ($true != ((sK2 @ sK1)))),
% 0.09/0.27 inference(cnf_transformation,[],[f9])).
% 0.09/0.27 thf(f27,plain,(
% 0.09/0.27 ( ! [X6 : ($i > $i),X7 : ($i > $i)] : ((X6 = X7)) )),
% 0.09/0.27 inference(forward_subsumption_resolution,[],[f11,f10])).
% 0.09/0.27 thf(f31,plain,(
% 0.09/0.27 ( ! [X0 : ($i > $i)] : (($true = ((sK2 @ X0)))) )),
% 0.09/0.27 inference(constrained_superposition,[],[f14,f27])).
% 0.09/0.27 thf(f80,plain,(
% 0.09/0.27 ($true != $true)),
% 0.09/0.27 inference(constrained_superposition,[],[f16,f31])).
% 0.09/0.27 thf(f84,plain,(
% 0.09/0.27 $false),
% 0.09/0.27 inference(trivial_inequality_removal,[],[f80])).
% 0.09/0.27 % SZS output end Proof for theBenchmark
% 0.09/0.27 % (1398025)------------------------------
% 0.09/0.27 % (1398025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.27 % (1398025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.27 % (1398025)CaDiCaL version: 2.1.3
% 0.09/0.27 % (1398025)Termination reason: Refutation
% 0.09/0.27 % (1398025)Time elapsed: 0.003 s
% 0.09/0.27 % (1398025)Peak memory usage: 12 MB
% 0.09/0.27 % (1398025)Instructions burned: 8 (million)
% 0.09/0.27 % (1398017)Success in time 0.032 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------