%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:20:19 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI045^6 : TPTP v9.3.1. Released v9.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n020.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 13:21:05 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
% 0.20/0.29 % (1031280)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (1031288)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1413675780:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.29 % (1031288) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1031280-1031288"...
% 0.20/0.29 % (1031288)...printing done.
% 0.20/0.29 % (1031291)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (1031291)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
% 0.20/0.29 % (1031288)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, entity: $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, god_like: (entity > $o)).
% 0.20/0.29 thf(func_def_1, type, positive_property: ((entity > $o) > $o)).
% 0.20/0.29 thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_6, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_9, type, sK0: ((entity > $o) > (entity > $o) > entity)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ~(positive_property @ (^[X0 : entity] : ((X0 != X0))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',coro1)).
% 0.20/0.29 thf(f2,axiom,(
% 0.20/0.29 ! [X1 : (entity > $o),X0 : (entity > $o)] : (((positive_property @ X0) & ! [X2 : entity] : ((X0 @ X2) => (X1 @ X2))) => (positive_property @ X1))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',coro2)).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 (positive_property @ god_like)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3)).
% 0.20/0.29 thf(f4,conjecture,(
% 0.20/0.29 ? [X0 : entity] : (god_like @ X0)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.20/0.29 thf(f5,negated_conjecture,(
% 0.20/0.29 ~ ? [X0 : entity] : (god_like @ X0)),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : (((positive_property @ X1) & ! [X2 : entity] : ((X1 @ X2) => (X0 @ X2))) => (positive_property @ X0))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ! [X1 : (entity > $o),X0 : (entity > $o)] : ((! [X2 : entity] : ((((X1 @ X2)) = $true) => (((X0 @ X2)) = $true)) & (((positive_property @ X1)) = $true)) => (((positive_property @ X0)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ~(positive_property @ (^[X0 : entity] : ((X0 != X0))))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ~ ($true = ((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))))),
% 0.20/0.29 inference(fool_elimination,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 (positive_property @ god_like)),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 (((positive_property @ god_like)) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ~ ? [X0 : entity] : (god_like @ X0)),
% 0.20/0.29 inference(rectify,[],[f5])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ~ ? [X0 : entity] : (((god_like @ X0)) = $true)),
% 0.20/0.29 inference(fool_elimination,[],[f12])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ($true != ((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))))),
% 0.20/0.29 inference(flattening,[],[f9])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ! [X0 : entity] : (((god_like @ X0)) != $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f13])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ! [X1 : (entity > $o),X0 : (entity > $o)] : ((((positive_property @ X0)) = $true) | (? [X2 : entity] : ((((X0 @ X2)) != $true) & (((X1 @ X2)) = $true)) | (((positive_property @ X1)) != $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f7])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X1 : (entity > $o),X0 : (entity > $o)] : ((((positive_property @ X1)) != $true) | (((positive_property @ X0)) = $true) | ? [X2 : entity] : ((((X0 @ X2)) != $true) & (((X1 @ X2)) = $true)))),
% 0.20/0.29 inference(flattening,[],[f16])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X0)) != $true) | (((positive_property @ X1)) = $true) | ? [X2 : entity] : ((((X1 @ X2)) != $true) & (((X0 @ X2)) = $true)))),
% 0.20/0.29 inference(rectify,[],[f17])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((positive_property @ X0)) != $true) | (((positive_property @ X1)) = $true) | ((((X1 @ (sK0 @ X1 @ X0))) != $true) & (((X0 @ (sK0 @ X1 @ X0))) = $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f18])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ( ! [X0 : entity] : ((((god_like @ X0)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f15])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 (((positive_property @ god_like)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f11])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ($true != ((positive_property @ (^[Y0 : entity]: (~ (Y0 = Y0))))))),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ( ! [X0 : (entity > $o),X1 : (entity > $o)] : ((((X0 @ (sK0 @ X1 @ X0))) = $true) | (((positive_property @ X1)) = $true) | (((positive_property @ X0)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 ($true != ((positive_property @ (^[Y0 : entity]: (~ $true)))))),
% 0.20/0.29 inference(boolean_simplification,[],[f22])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 (((positive_property @ (^[Y0 : entity]: ($false)))) != $true)),
% 0.20/0.29 inference(boolean_simplification,[],[f26])).
% 0.20/0.29 thf(f29,definition,(
% 0.20/0.29 spl1_1 <=> (((positive_property @ (^[Y0 : entity]: ($false)))) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 (((positive_property @ (^[Y0 : entity]: ($false)))) != $true) | spl1_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f29])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ~spl1_1),
% 0.20/0.29 inference(avatar_split_clause,[],[f27,f29])).
% 0.20/0.29 thf(f34,definition,(
% 0.20/0.29 spl1_2 <=> (((positive_property @ god_like)) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.20/0.29 thf(f36,plain,(
% 0.20/0.29 (((positive_property @ god_like)) = $true) | ~spl1_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f34])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 spl1_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f21,f34])).
% 0.20/0.29 thf(f47,definition,(
% 0.20/0.29 spl1_3 <=> ! [X1 : (entity > $o)] : (((positive_property @ X1)) = $true)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 ( ! [X1 : (entity > $o)] : ((((positive_property @ X1)) = $true)) ) | ~spl1_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f47])).
% 0.20/0.29 thf(f105,plain,(
% 0.20/0.29 ( ! [X0 : (entity > $o)] : (($true != $true) | (((positive_property @ X0)) = $true) | (((positive_property @ god_like)) != $true)) )),
% 0.20/0.29 inference(superposition,[],[f20,f23])).
% 0.20/0.29 thf(f108,plain,(
% 0.20/0.29 ( ! [X0 : (entity > $o)] : ((((positive_property @ X0)) = $true) | (((positive_property @ god_like)) != $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f105])).
% 0.20/0.29 thf(f110,plain,(
% 0.20/0.29 ( ! [X0 : (entity > $o)] : ((((positive_property @ X0)) = $true)) ) | ~spl1_2),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f108,f36])).
% 0.20/0.29 thf(f116,plain,(
% 0.20/0.29 spl1_3 | ~spl1_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f110,f34,f47])).
% 0.20/0.29 thf(f119,plain,(
% 0.20/0.29 $false | (spl1_1 | ~spl1_3)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f31,f48])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 spl1_1 | ~spl1_3),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f119])).
% 0.20/0.29 cnf(s1, plain, ~spl1_1, inference(sat_conversion,[],[f32])).
% 0.20/0.29 cnf(s2, plain, spl1_2, inference(sat_conversion,[],[f37])).
% 0.20/0.29 cnf(s8, plain, ~spl1_2 | spl1_3, inference(sat_conversion,[],[f116])).
% 0.20/0.29 cnf(s10, plain, spl1_1 | ~spl1_3, inference(sat_conversion,[],[f120])).
% 0.20/0.29 cnf(s11, plain, spl1_3, inference(rat,[],[s8,s2])).
% 0.20/0.29 cnf(s12, plain, spl1_1, inference(rat,[],[s10,s11])).
% 0.20/0.29 cnf(s16, plain, $false, inference(rat,[],[s1,s12])).
% 0.20/0.29 thf(f121,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s16])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (1031288)------------------------------
% 0.20/0.29 % (1031288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1031288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1031288)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1031288)Termination reason: Refutation
% 0.20/0.29 % (1031288)Time elapsed: 0.003 s
% 0.20/0.29 % (1031288)Peak memory usage: 13 MB
% 0.20/0.29 % (1031288)Instructions burned: 6 (million)
% 0.20/0.29 % (1031280)Success in time 0.035 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------