%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:46:19 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO030^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:23:16 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.08/0.25 % (2873610)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (2873615)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4176296299:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.25 % (2873615) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2873610-2873615"...
% 0.08/0.25 % (2873615)...printing done.
% 0.08/0.25 % (2873621)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.25 % (2873621)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.25 % (2873615)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% 0.08/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.25 thf(func_def_0, type, leibeq: ($o > $o > $o)).
% 0.08/0.25 thf(func_def_2, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.25 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.08/0.25 thf(func_def_4, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.25 thf(func_def_5, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.25 thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.25 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.25 thf(func_def_10, type, sK0: (($o > $o) > $o)).
% 0.08/0.25 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.08/0.25 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.08/0.25 thf(f1,axiom,(
% 0.08/0.25 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leibeq)).
% 0.08/0.25 thf(f2,conjecture,(
% 0.08/0.25 ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.08/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.08/0.25 thf(f3,negated_conjecture,(
% 0.08/0.25 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.25 thf(f4,plain,(
% 0.08/0.25 (leibeq = (^[X0 : $o, X1 : $o] : (! [X2 : ($o > $o)] : ((X2 @ X0) => (X2 @ X1)))))),
% 0.08/0.25 inference(rectify,[],[f1])).
% 0.08/0.25 thf(f5,plain,(
% 0.08/0.25 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.08/0.25 inference(fool_elimination,[],[f4])).
% 0.08/0.25 thf(f6,plain,(
% 0.08/0.25 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (leibeq @ (X0 @ X1) @ X1)),
% 0.08/0.25 inference(rectify,[],[f3])).
% 0.08/0.25 thf(f7,plain,(
% 0.08/0.25 ~ ~ ! [X0 : ($o > $o)] : ? [X1 : $o] : (((leibeq @ (X0 @ X1) @ X1)) = $true)),
% 0.08/0.25 inference(fool_elimination,[],[f6])).
% 0.08/0.25 thf(f8,plain,(
% 0.08/0.25 ! [X0 : ($o > $o)] : ? [X1 : $o] : (((leibeq @ (X0 @ X1) @ X1)) = $true)),
% 0.08/0.25 inference(flattening,[],[f7])).
% 0.08/0.25 thf(f9,plain,(
% 0.08/0.25 ! [X0 : ($o > $o)] : (((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))) = $true)),
% 0.08/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f8])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 (leibeq = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 0.08/0.25 inference(cnf_transformation,[],[f5])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((leibeq @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))) = $true)) )),
% 0.08/0.25 inference(cnf_transformation,[],[f9])).
% 0.08/0.25 thf(f14,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : (((((^[Y0 : $o]: ((^[Y1 : $o]: (!! @ ($o > $o) @ (^[Y2 : $o > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (X0 @ (sK0 @ X0)) @ (sK0 @ X0))) = $true)) )),
% 0.08/0.25 inference(definition_unfolding,[],[f11,f10])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((!! @ ($o > $o) @ (^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0)))))) = $true)) )),
% 0.08/0.25 inference(beta-eta_normalization,[],[f14])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (((((^[Y0 : $o > $o]: ((Y0 @ (X0 @ (sK0 @ X0))) => (Y0 @ (sK0 @ X0)))) @ X1)) = $true)) )),
% 0.08/0.25 inference(pi_proxy_clausification,[],[f15])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($true = (((X1 @ (X0 @ (sK0 @ X0))) => (X1 @ (sK0 @ X0)))))) )),
% 0.08/0.25 inference(beta-eta_normalization,[],[f16])).
% 0.08/0.25 thf(f18,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($false = ((X1 @ (X0 @ (sK0 @ X0))))) | ($true = ((X1 @ (sK0 @ X0))))) )),
% 0.08/0.25 inference(imp_proxy_clausification,[],[f17])).
% 0.08/0.25 thf(f19,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((X0 @ (sK0 @ X0))) = ((sK0 @ X0)))) )),
% 0.08/0.25 inference(leibniz_equality_elimination,[],[f18])).
% 0.08/0.25 thf(f24,plain,(
% 0.08/0.25 ( ! [X2 : ($o > $o),X0 : ($o > $o)] : (($true = (((^[Y0 : $o]: (~ (X2 @ Y0))) @ (sK0 @ X0)))) | ($false = (((^[Y0 : $o]: (~ (X2 @ Y0))) @ (X0 @ (sK0 @ X0)))))) )),
% 0.08/0.25 inference(primitive_instantiation,[],[f18])).
% 0.08/0.25 thf(f25,plain,(
% 0.08/0.25 ( ! [X2 : ($o > $o),X0 : ($o > $o)] : ((((~ (X2 @ (sK0 @ X0)))) = $true) | (((~ (X2 @ (X0 @ (sK0 @ X0))))) = $false)) )),
% 0.08/0.25 inference(beta-eta_normalization,[],[f24])).
% 0.08/0.25 thf(f26,plain,(
% 0.08/0.25 ( ! [X2 : ($o > $o),X0 : ($o > $o)] : ((((~ (X2 @ (X0 @ (sK0 @ X0))))) = $false) | ($false = ((X2 @ (sK0 @ X0))))) )),
% 0.08/0.25 inference(not_proxy_clausification,[],[f25])).
% 0.08/0.25 thf(f27,plain,(
% 0.08/0.25 ( ! [X2 : ($o > $o),X0 : ($o > $o)] : (($true = ((X2 @ (X0 @ (sK0 @ X0))))) | ($false = ((X2 @ (sK0 @ X0))))) )),
% 0.08/0.25 inference(not_proxy_clausification,[],[f26])).
% 0.08/0.25 thf(f28,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((X0 @ (sK0 @ X0))) = $true) | ($false = ((sK0 @ X0)))) )),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f19])).
% 0.08/0.25 thf(f29,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((X0 @ (sK0 @ X0))) = $false) | (((sK0 @ X0)) = $true)) )),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f19])).
% 0.08/0.25 thf(f57,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o),X1 : ($o > $o)] : (($false = ((X0 @ (sK0 @ X1)))) | ($false = ((sK0 @ X1))) | (((X0 @ $true)) = $true)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f27,f28])).
% 0.08/0.25 thf(f101,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : (($false = ((sK0 @ X0))) | ($false = $true) | ($false = ((sK0 @ X0))) | (((X0 @ $true)) = $true)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f28,f57])).
% 0.08/0.25 thf(f105,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : (($false = ((sK0 @ X0))) | (((X0 @ $true)) = $true) | ($false = $true)) )),
% 0.08/0.25 inference(duplicate_literal_removal,[],[f101])).
% 0.08/0.25 thf(f106,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : (($false = ((sK0 @ X0))) | (((X0 @ $true)) = $true)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f105])).
% 0.08/0.25 thf(f116,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((X0 @ $true)) = $true) | (((X0 @ $false)) = $false) | ($false = $true)) )),
% 0.08/0.25 inference(constrained_superposition,[],[f29,f106])).
% 0.08/0.25 thf(f122,plain,(
% 0.08/0.25 ( ! [X0 : ($o > $o)] : ((((X0 @ $true)) = $true) | (((X0 @ $false)) = $false)) )),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f116])).
% 0.08/0.25 thf(f125,plain,(
% 0.08/0.25 ($false = $true)),
% 0.08/0.25 inference(leibniz_equality_elimination,[],[f122])).
% 0.08/0.25 thf(f132,plain,(
% 0.08/0.25 $false),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f125])).
% 0.08/0.25 % SZS output end Proof for theBenchmark
% 0.08/0.25 % (2873615)------------------------------
% 0.08/0.25 % (2873615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2873615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2873615)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2873615)Termination reason: Refutation
% 0.08/0.25 % (2873615)Time elapsed: 0.002 s
% 0.08/0.25 % (2873615)Peak memory usage: 12 MB
% 0.08/0.25 % (2873615)Instructions burned: 6 (million)
% 0.08/0.25 % (2873610)Success in time 0.021 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------