%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV076^5 : 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 : 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 08:38:57 AM UTC 2026
% Result : Theorem 0.29s 0.38s
% Output : Refutation 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV076^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.27 % Computer : n017.cluster.edu
% 0.13/0.27 % Model : x86_64 x86_64
% 0.13/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.27 % Memory : 8046.5625MB
% 0.13/0.27 % OS : Linux 6.8.0-71-generic
% 0.13/0.27 % CPULimit : 300
% 0.13/0.27 % WCLimit : 300
% 0.13/0.27 % DateTime : Tue Sep 29 15:02:07 UTC 2026
% 0.13/0.28 % CPUTime :
% 0.13/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.33 Running first-order model finding
% 0.29/0.33 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
% 0.29/0.38 % (440938)Will run a generic schedule for satisfiability detection.
% 0.29/0.38 % (440947)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2432495068:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.29/0.38 % (440947)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.29/0.38 % (440947) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-440938-440947"...
% 0.29/0.38 % (440947)...printing done.
% 0.29/0.38 % (440947)Refutation found. Thanks to Tanya!
% 0.29/0.38 % SZS status Theorem for theBenchmark
% 0.29/0.38 % SZS output start Proof for theBenchmark
% 0.29/0.38 thf(type_def_5, type, a: $tType).
% 0.29/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.29/0.38 thf(func_def_3, type, sK0: (a > a > $o)).
% 0.29/0.38 thf(func_def_4, type, sK1: ((a > $o) > a)).
% 0.29/0.38 thf(func_def_5, type, sK2: (a > $o)).
% 0.29/0.38 thf(func_def_6, type, sK3: (a > a)).
% 0.29/0.38 thf(func_def_7, type, sK4: (a > (a > $o) > a)).
% 0.29/0.38 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.29/0.38 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.29/0.38 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.29/0.38 thf(f1,conjecture,(
% 0.29/0.38 ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X5 : (a > $o)] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5)))) & ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4))) => ! [X5 : (a > $o)] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 0.29/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM401B_pme)).
% 0.29/0.38 thf(f2,negated_conjecture,(
% 0.29/0.38 ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X5 : (a > $o)] : (! [X6 : a] : (! [X7 : a] : ((X5 @ X7) => (X0 @ X7 @ X6)) => (X0 @ (X1 @ X5) @ X6)) & ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ (X1 @ X5)))) & ! [X2 : a,X3 : a,X4 : a] : (((X0 @ X3 @ X4) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X4))) => ! [X5 : (a > $o)] : ? [X8 : a] : ! [X4 : a] : ((X5 @ X4) => (X0 @ X4 @ X8)))),
% 0.29/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.29/0.38 thf(f3,plain,(
% 0.29/0.38 ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X3 : a] : (! [X4 : a] : ((X2 @ X4) => (X0 @ X4 @ X3)) => (X0 @ (X1 @ X2) @ X3)) & ! [X5 : a] : ((X2 @ X5) => (X0 @ X5 @ (X1 @ X2)))) & ! [X6 : a,X7 : a,X8 : a] : (((X0 @ X7 @ X8) & (X0 @ X6 @ X7)) => (X0 @ X6 @ X8))) => ! [X9 : (a > $o)] : ? [X10 : a] : ! [X11 : a] : ((X9 @ X11) => (X0 @ X11 @ X10)))),
% 0.29/0.38 inference(rectify,[],[f2])).
% 0.29/0.38 thf(f4,plain,(
% 0.29/0.38 ~ ! [X0 : (a > a > $o),X1 : ((a > $o) > a)] : ((! [X2 : (a > $o)] : (! [X3 : a] : (! [X4 : a] : ((((X2 @ X4)) = $true) => (((X0 @ X4 @ X3)) = $true)) => (((X0 @ (X1 @ X2) @ X3)) = $true)) & ! [X5 : a] : ((((X2 @ X5)) = $true) => (((X0 @ X5 @ (X1 @ X2))) = $true))) & ! [X6 : a,X7 : a,X8 : a] : (((((X0 @ X7 @ X8)) = $true) & (((X0 @ X6 @ X7)) = $true)) => (((X0 @ X6 @ X8)) = $true))) => ! [X9 : (a > $o)] : ? [X10 : a] : ! [X11 : a] : ((((X9 @ X11)) = $true) => (((X0 @ X11 @ X10)) = $true)))),
% 0.29/0.38 inference(fool_elimination,[],[f3])).
% 0.29/0.38 thf(f5,plain,(
% 0.29/0.38 ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X9 : (a > $o)] : ! [X10 : a] : ? [X11 : a] : ((((X0 @ X11 @ X10)) != $true) & (((X9 @ X11)) = $true)) & (! [X2 : (a > $o)] : (! [X3 : a] : ((((X0 @ (X1 @ X2) @ X3)) = $true) | ? [X4 : a] : ((((X0 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true))) & ! [X5 : a] : ((((X0 @ X5 @ (X1 @ X2))) = $true) | (((X2 @ X5)) != $true))) & ! [X6 : a,X7 : a,X8 : a] : ((((X0 @ X6 @ X8)) = $true) | ((((X0 @ X7 @ X8)) != $true) | (((X0 @ X6 @ X7)) != $true)))))),
% 0.29/0.38 inference(ennf_transformation,[],[f4])).
% 0.29/0.38 thf(f6,plain,(
% 0.29/0.38 ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X9 : (a > $o)] : ! [X10 : a] : ? [X11 : a] : ((((X0 @ X11 @ X10)) != $true) & (((X9 @ X11)) = $true)) & ! [X2 : (a > $o)] : (! [X3 : a] : ((((X0 @ (X1 @ X2) @ X3)) = $true) | ? [X4 : a] : ((((X0 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true))) & ! [X5 : a] : ((((X0 @ X5 @ (X1 @ X2))) = $true) | (((X2 @ X5)) != $true))) & ! [X6 : a,X7 : a,X8 : a] : ((((X0 @ X6 @ X8)) = $true) | (((X0 @ X7 @ X8)) != $true) | (((X0 @ X6 @ X7)) != $true)))),
% 0.29/0.38 inference(flattening,[],[f5])).
% 0.29/0.38 thf(f7,plain,(
% 0.29/0.38 ? [X0 : (a > a > $o),X1 : ((a > $o) > a)] : (? [X2 : (a > $o)] : ! [X3 : a] : ? [X4 : a] : ((((X0 @ X4 @ X3)) != $true) & (((X2 @ X4)) = $true)) & ! [X5 : (a > $o)] : (! [X6 : a] : ((((X0 @ (X1 @ X5) @ X6)) = $true) | ? [X7 : a] : ((((X0 @ X7 @ X6)) != $true) & (((X5 @ X7)) = $true))) & ! [X8 : a] : (($true = ((X0 @ X8 @ (X1 @ X5)))) | ($true != ((X5 @ X8))))) & ! [X9 : a,X10 : a,X11 : a] : (($true = ((X0 @ X9 @ X11))) | ($true != ((X0 @ X10 @ X11))) | ($true != ((X0 @ X9 @ X10)))))),
% 0.29/0.38 inference(rectify,[],[f6])).
% 0.29/0.38 thf(f8,plain,(
% 0.29/0.38 ! [X3 : a] : (($true != ((sK0 @ (sK3 @ X3) @ X3))) & ($true = ((sK2 @ (sK3 @ X3))))) & ! [X5 : (a > $o)] : (! [X6 : a] : (($true = ((sK0 @ (sK1 @ X5) @ X6))) | (($true != ((sK0 @ (sK4 @ X6 @ X5) @ X6))) & ($true = ((X5 @ (sK4 @ X6 @ X5)))))) & ! [X8 : a] : (($true = ((sK0 @ X8 @ (sK1 @ X5)))) | ($true != ((X5 @ X8))))) & ! [X9 : a,X10 : a,X11 : a] : (($true = ((sK0 @ X9 @ X11))) | ($true != ((sK0 @ X10 @ X11))) | ($true != ((sK0 @ X9 @ X10))))),
% 0.29/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X7,sK4 @ X6 @ X5),skolemize(X7,sK4 @ X6 @ X5)],[f7])).
% 0.29/0.38 thf(f10,plain,(
% 0.29/0.38 ( ! [X8 : a,X5 : (a > $o)] : (($true = ((sK0 @ X8 @ (sK1 @ X5)))) | ($true != ((X5 @ X8)))) )),
% 0.29/0.38 inference(cnf_transformation,[],[f8])).
% 0.29/0.38 thf(f14,plain,(
% 0.29/0.38 ( ! [X3 : a] : (($true != ((sK0 @ (sK3 @ X3) @ X3)))) )),
% 0.29/0.38 inference(cnf_transformation,[],[f8])).
% 0.29/0.38 thf(f17,plain,(
% 0.29/0.38 ( ! [X0 : (a > $o)] : (($true != $true) | ($true != ((X0 @ (sK3 @ (sK1 @ X0)))))) )),
% 0.29/0.38 inference(constrained_superposition,[],[f14,f10])).
% 0.29/0.38 thf(f18,plain,(
% 0.29/0.38 ( ! [X0 : (a > $o)] : (($true != ((X0 @ (sK3 @ (sK1 @ X0)))))) )),
% 0.29/0.38 inference(trivial_inequality_removal,[],[f17])).
% 0.29/0.38 thf(f25,plain,(
% 0.29/0.38 $false),
% 0.29/0.38 inference(equality_resolution,[],[f18])).
% 0.29/0.38 % SZS output end Proof for theBenchmark
% 0.29/0.38 % (440947)------------------------------
% 0.29/0.38 % (440947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.38 % (440947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.38 % (440947)CaDiCaL version: 2.1.3
% 0.29/0.38 % (440947)Termination reason: Refutation
% 0.29/0.38 % (440947)Time elapsed: 0.003 s
% 0.29/0.38 % (440947)Peak memory usage: 12 MB
% 0.29/0.38 % (440947)Instructions burned: 4 (million)
% 0.29/0.38 % (440938)Success in time 0.034 s
% 0.29/0.38 % Vampire exiting
%------------------------------------------------------------------------------