%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU525^2 : 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 : n026.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 08:29:55 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
% 0.00/0.03 % Problem : SEU525^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:50:57 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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
% 0.21/0.29 % (620277)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (620282)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=878642711:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (620282) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-620277-620282"...
% 0.21/0.29 % (620282)...printing done.
% 0.21/0.29 % (620282)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, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, exu: (($i > $o) > $o)).
% 0.21/0.29 thf(func_def_2, type, exuE1: $o).
% 0.21/0.29 thf(func_def_3, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.29 thf(func_def_4, type, vAND: ($o > $o > $o)).
% 0.21/0.29 thf(func_def_5, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.29 thf(func_def_6, type, vIMP: ($o > $o > $o)).
% 0.21/0.29 thf(func_def_7, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.29 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.29 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.29 thf(func_def_14, type, sK0: ($i > $o)).
% 0.21/0.29 thf(func_def_15, type, sK1: ($i > $i)).
% 0.21/0.29 thf(func_def_16, type, sK2: ($i > $o)).
% 0.21/0.29 thf(func_def_17, type, sK3: ($i > $i)).
% 0.21/0.29 thf(func_def_18, type, sK4: (($i > $o) > $i)).
% 0.21/0.29 thf(func_def_19, type, vNOT: ($o > $o)).
% 0.21/0.29 thf(func_def_21, type, sK6: (($i > $o) > $i > $i)).
% 0.21/0.29 thf(func_def_22, type, sK7: (($i > $o) > $i > $i)).
% 0.21/0.29 thf(f1,axiom,(
% 0.21/0.29 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 0.21/0.29 thf(f3,conjecture,(
% 0.21/0.29 exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1)))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2)).
% 0.21/0.29 thf(f4,negated_conjecture,(
% 0.21/0.29 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X2 = X1))))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ((^[X0 : ($i > $o)] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 0.21/0.29 inference(rectify,[],[f1])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 0.21/0.29 inference(fool_elimination,[],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ~(exuE1 => ! [X0 : ($i > $o)] : ((exu @ (^[X1 : $i] : ((X0 @ X1)))) => ? [X2 : $i] : ! [X3 : $i] : ((X0 @ X3) <=> (X2 = X3))))),
% 0.21/0.29 inference(rectify,[],[f4])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X2 : $i] : ! [X3 : $i] : ((((X0 @ X3)) = $true) <=> (X2 = X3))))),
% 0.21/0.29 inference(fool_elimination,[],[f7])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ~((exuE1 = $true) => ! [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> (((X0 @ X2)) = $true))))),
% 0.21/0.29 inference(rectify,[],[f8])).
% 0.21/0.29 thf(f14,plain,(
% 0.21/0.29 ? [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ! [X1 : $i] : ? [X2 : $i] : ((((X0 @ X2)) = $true) <~> (X1 = X2))) & (exuE1 = $true)),
% 0.21/0.29 inference(ennf_transformation,[],[f11])).
% 0.21/0.29 thf(f15,plain,(
% 0.21/0.29 ? [X0 : ($i > $o)] : ((((exu @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | (((X0 @ X2)) != $true)) & ((X1 = X2) | (((X0 @ X2)) = $true)))) & (exuE1 = $true)),
% 0.21/0.29 inference(nnf_transformation,[],[f14])).
% 0.21/0.29 thf(f16,plain,(
% 0.21/0.29 ((((exu @ (^[Y0 : $i]: (sK0 @ Y0)))) = $true) & ! [X1 : $i] : (((((sK1 @ X1)) != X1) | ($true != ((sK0 @ (sK1 @ X1))))) & ((((sK1 @ X1)) = X1) | ($true = ((sK0 @ (sK1 @ X1))))))) & (exuE1 = $true)),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f15])).
% 0.21/0.29 thf(f21,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (($true = ((sK0 @ (sK1 @ X1)))) | (((sK1 @ X1)) = X1)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f16])).
% 0.21/0.29 thf(f22,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (($true != ((sK0 @ (sK1 @ X1)))) | (((sK1 @ X1)) != X1)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f16])).
% 0.21/0.29 thf(f23,plain,(
% 0.21/0.29 (((exu @ (^[Y0 : $i]: (sK0 @ Y0)))) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f16])).
% 0.21/0.29 thf(f24,plain,(
% 0.21/0.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 0.21/0.29 inference(cnf_transformation,[],[f6])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ((((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0)))) = $true)),
% 0.21/0.29 inference(definition_unfolding,[],[f23,f24])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 (((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))))) = $true)),
% 0.21/0.29 inference(beta-eta_normalization,[],[f32])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK5)) = $true)),
% 0.21/0.29 inference(sigma_proxy_clausification,[],[f38])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 ((((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK5 = Y0)))) & (sK0 @ sK5))) = $true)),
% 0.21/0.29 inference(beta-eta_normalization,[],[f39])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 ($true = ((sK0 @ sK5)))),
% 0.21/0.29 inference(and_proxy_clausification,[],[f40])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK5 = Y0))))) = $true)),
% 0.21/0.29 inference(and_proxy_clausification,[],[f40])).
% 0.21/0.29 thf(f43,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK0 @ Y0) => (sK5 = Y0))) @ X1)) = $true)) )),
% 0.21/0.29 inference(pi_proxy_clausification,[],[f42])).
% 0.21/0.29 thf(f44,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (((((sK0 @ X1) => (sK5 = X1))) = $true)) )),
% 0.21/0.29 inference(beta-eta_normalization,[],[f43])).
% 0.21/0.29 thf(f45,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (($false = ((sK0 @ X1))) | (((sK5 = X1)) = $true)) )),
% 0.21/0.29 inference(imp_proxy_clausification,[],[f44])).
% 0.21/0.29 thf(f46,plain,(
% 0.21/0.29 ( ! [X1 : $i] : (($false = ((sK0 @ X1))) | (sK5 = X1)) )),
% 0.21/0.29 inference(equality_proxy_clausification,[],[f45])).
% 0.21/0.29 thf(f67,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((sK1 @ X0)) = X0) | (sK5 = ((sK1 @ X0))) | ($false = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f46,f21])).
% 0.21/0.29 thf(f69,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((sK5 = ((sK1 @ X0))) | (((sK1 @ X0)) = X0)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f67])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((sK5 != X0) | (((sK1 @ X0)) = X0)) )),
% 0.21/0.29 inference(equality_factoring,[],[f69])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 (sK5 != sK5) | (((sK1 @ sK5)) = sK5)),
% 0.21/0.29 inference(imitation,[],[f72])).
% 0.21/0.29 thf(f76,plain,(
% 0.21/0.29 (((sK1 @ sK5)) = sK5)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f74])).
% 0.21/0.29 thf(f82,plain,(
% 0.21/0.29 (sK5 != sK5) | ($true != ((sK0 @ sK5)))),
% 0.21/0.29 inference(constrained_superposition,[],[f22,f76])).
% 0.21/0.29 thf(f85,plain,(
% 0.21/0.29 ($true != ((sK0 @ sK5)))),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f82])).
% 0.21/0.29 thf(f87,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f85,f41])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (620282)------------------------------
% 0.21/0.29 % (620282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (620282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (620282)CaDiCaL version: 2.1.3
% 0.21/0.29 % (620282)Termination reason: Refutation
% 0.21/0.29 % (620282)Time elapsed: 0.002 s
% 0.21/0.29 % (620282)Peak memory usage: 12 MB
% 0.21/0.29 % (620282)Instructions burned: 5 (million)
% 0.21/0.29 % (620277)Success in time 0.027 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------