%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:46:17 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:21:59 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.19/0.28 % (933768)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (933773)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3450755737:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (933773) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-933768-933773"...
% 0.19/0.28 % (933773)...printing done.
% 0.19/0.28 % (933773)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, f: ($o > $i > $i)).
% 0.19/0.28 thf(func_def_1, type, p: (($i > $i) > $o)).
% 0.19/0.28 thf(func_def_2, type, a: (($i > $i) > $o)).
% 0.19/0.28 thf(func_def_3, type, b: $o).
% 0.19/0.28 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.19/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(f1,conjecture,(
% 0.19/0.28 (p @ (^[X0 : $i] : ((f @ b & (a @ (^[X0 : $i] : ((f @ b @ X0)))) @ X0)))) => (p @ (f @ b & (a @ (f @ b))))),
% 0.19/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.19/0.28 thf(f2,negated_conjecture,(
% 0.19/0.28 ~((p @ (^[X0 : $i] : ((f @ b & (a @ (^[X0 : $i] : ((f @ b @ X0)))) @ X0)))) => (p @ (f @ b & (a @ (f @ b)))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.28 thf(f3,plain,(
% 0.19/0.28 ~((p @ (^[X0 : $i] : ((f @ b & (a @ (^[X1 : $i] : ((f @ b @ X1)))) @ X0)))) => (p @ (f @ b & (a @ (f @ b)))))),
% 0.19/0.28 inference(rectify,[],[f2])).
% 0.19/0.28 thf(f4,plain,(
% 0.19/0.28 ~(($true = ((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0))))) => (((p @ (f @ ((a @ (f @ b)) & b)))) = $true))),
% 0.19/0.28 inference(fool_elimination,[],[f3])).
% 0.19/0.28 thf(f5,plain,(
% 0.19/0.28 ($true = ((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0))))) & (((p @ (f @ ((a @ (f @ b)) & b)))) != $true)),
% 0.19/0.28 inference(ennf_transformation,[],[f4])).
% 0.19/0.28 thf(f6,plain,(
% 0.19/0.28 (((p @ (f @ ((a @ (f @ b)) & b)))) != $true)),
% 0.19/0.28 inference(cnf_transformation,[],[f5])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 ($true = ((p @ (^[Y0 : $i]: (f @ ((a @ (^[Y1 : $i]: (f @ b @ Y1))) & b) @ Y0)))))),
% 0.19/0.28 inference(cnf_transformation,[],[f5])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 (((p @ (f @ ((a @ (f @ b)) & b)))) = $true)),
% 0.19/0.28 inference(beta-eta_normalization,[],[f7])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 $false),
% 0.19/0.28 inference(forward_subsumption_resolution,[],[f10,f6])).
% 0.19/0.28 % SZS output end Proof for theBenchmark
% 0.19/0.28 % (933773)------------------------------
% 0.19/0.28 % (933773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (933773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (933773)CaDiCaL version: 2.1.3
% 0.19/0.28 % (933773)Termination reason: Refutation
% 0.19/0.28 % (933773)Time elapsed: 0.001 s
% 0.19/0.28 % (933773)Peak memory usage: 12 MB
% 0.19/0.28 % (933773)Instructions burned: 1 (million)
% 0.19/0.28 % (933768)Success in time 0.028 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------