%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO041^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:46:21 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO041^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n003.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 16:25:59 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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
% 0.22/0.28 % (2699897)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (2699905)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=3286140378: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)
% 0.22/0.28 % (2699905) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2699897-2699905"...
% 0.22/0.28 % (2699908)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (2699908)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
% 0.22/0.28 % (2699905)...printing done.
% 0.22/0.28 % (2699902)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2119164317:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (2699903)lrs+10_16_si=on:nwc=1.5:random_seed=2646471579:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.28 % (2699904)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1993211506:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.28 % (2699905)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, a: $o).
% 0.22/0.28 thf(func_def_1, type, f: ($o > $o)).
% 0.22/0.28 thf(func_def_2, type, g: ($o > $o)).
% 0.22/0.28 thf(func_def_3, type, x: $o).
% 0.22/0.28 thf(func_def_4, type, y: $o).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 ~((((g @ x)) = y) & (x != y) & (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x))),
% 0.22/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',3)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~ ~((((g @ x)) = y) & (x != y) & (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 (((g @ x)) = y) & (x != y) & (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x)),
% 0.22/0.28 inference(flattening,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 (x = ((g @ y)))),
% 0.22/0.28 inference(cnf_transformation,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) = ((g @ (f @ x))))),
% 0.22/0.28 inference(cnf_transformation,[],[f3])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 (x != y)),
% 0.22/0.28 inference(cnf_transformation,[],[f3])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 (y = ((g @ x)))),
% 0.22/0.28 inference(cnf_transformation,[],[f3])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 (y = $true) | (((g @ x)) = $false)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f7])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 (y = $false) | (((g @ x)) = $true)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f7])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) = $true) | (((g @ (f @ x))) = $false)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f5])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) = $false) | (((g @ (f @ x))) = $true)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f5])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 (x = $true) | (((g @ y)) = $false)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f4])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 (x = $false) | (((g @ y)) = $true)),
% 0.22/0.28 inference(iff_proxy_clausification,[],[f4])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 (x = $true) | (y = $true)),
% 0.22/0.28 inference(xor_proxy_clausification,[],[f6])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 (y = $false) | (x = $false)),
% 0.22/0.28 inference(xor_proxy_clausification,[],[f6])).
% 0.22/0.28 thf(f18,definition,(
% 0.22/0.28 spl0_1 <=> (y = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 (y = $false) | ~spl0_1),
% 0.22/0.28 inference(avatar_component_clause,[],[f18])).
% 0.22/0.28 thf(f22,definition,(
% 0.22/0.28 spl0_2 <=> (((g @ x)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 (((g @ x)) != $true) | spl0_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f22])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 spl0_1 | spl0_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f10,f22,f18])).
% 0.22/0.28 thf(f27,definition,(
% 0.22/0.28 spl0_3 <=> (((g @ x)) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.22/0.28 thf(f29,plain,(
% 0.22/0.28 (((g @ x)) = $false) | ~spl0_3),
% 0.22/0.28 inference(avatar_component_clause,[],[f27])).
% 0.22/0.28 thf(f31,definition,(
% 0.22/0.28 spl0_4 <=> (y = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.22/0.28 thf(f33,plain,(
% 0.22/0.28 (y = $true) | ~spl0_4),
% 0.22/0.28 inference(avatar_component_clause,[],[f31])).
% 0.22/0.28 thf(f34,plain,(
% 0.22/0.28 spl0_3 | spl0_4),
% 0.22/0.28 inference(avatar_split_clause,[],[f9,f31,f27])).
% 0.22/0.28 thf(f36,definition,(
% 0.22/0.28 spl0_5 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.22/0.28 thf(f37,plain,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) != $false) | spl0_5),
% 0.22/0.28 inference(avatar_component_clause,[],[f36])).
% 0.22/0.28 thf(f38,plain,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) = $false) | ~spl0_5),
% 0.22/0.28 inference(avatar_component_clause,[],[f36])).
% 0.22/0.28 thf(f40,definition,(
% 0.22/0.28 spl0_6 <=> (((g @ (f @ x))) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.22/0.28 thf(f42,plain,(
% 0.22/0.28 (((g @ (f @ x))) = $true) | ~spl0_6),
% 0.22/0.28 inference(avatar_component_clause,[],[f40])).
% 0.22/0.28 thf(f43,plain,(
% 0.22/0.28 spl0_5 | spl0_6),
% 0.22/0.28 inference(avatar_split_clause,[],[f12,f40,f36])).
% 0.22/0.28 thf(f45,definition,(
% 0.22/0.28 spl0_7 <=> (((g @ (f @ x))) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.22/0.28 thf(f49,definition,(
% 0.22/0.28 spl0_8 <=> (((f @ (f @ (f @ x)))) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.22/0.28 thf(f52,plain,(
% 0.22/0.28 spl0_7 | spl0_8),
% 0.22/0.28 inference(avatar_split_clause,[],[f11,f49,f45])).
% 0.22/0.28 thf(f54,definition,(
% 0.22/0.28 spl0_9 <=> (x = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.22/0.28 thf(f56,plain,(
% 0.22/0.28 (x = $false) | ~spl0_9),
% 0.22/0.28 inference(avatar_component_clause,[],[f54])).
% 0.22/0.28 thf(f58,definition,(
% 0.22/0.28 spl0_10 <=> (((g @ y)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.22/0.28 thf(f61,plain,(
% 0.22/0.28 spl0_9 | spl0_10),
% 0.22/0.28 inference(avatar_split_clause,[],[f14,f58,f54])).
% 0.22/0.28 thf(f63,definition,(
% 0.22/0.28 spl0_11 <=> (x = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.22/0.28 thf(f65,plain,(
% 0.22/0.28 (x = $true) | ~spl0_11),
% 0.22/0.28 inference(avatar_component_clause,[],[f63])).
% 0.22/0.28 thf(f67,definition,(
% 0.22/0.28 spl0_12 <=> (((g @ y)) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 (((g @ y)) != $false) | spl0_12),
% 0.22/0.28 inference(avatar_component_clause,[],[f67])).
% 0.22/0.28 thf(f70,plain,(
% 0.22/0.28 spl0_11 | spl0_12),
% 0.22/0.28 inference(avatar_split_clause,[],[f13,f67,f63])).
% 0.22/0.28 thf(f71,plain,(
% 0.22/0.28 spl0_1 | spl0_9),
% 0.22/0.28 inference(avatar_split_clause,[],[f16,f54,f18])).
% 0.22/0.28 thf(f72,plain,(
% 0.22/0.28 spl0_11 | spl0_4),
% 0.22/0.28 inference(avatar_split_clause,[],[f15,f31,f63])).
% 0.22/0.28 thf(f73,plain,(
% 0.22/0.28 ($false = $true) | (~spl0_9 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f65,f56])).
% 0.22/0.28 thf(f74,plain,(
% 0.22/0.28 $false | (~spl0_9 | ~spl0_11)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f73])).
% 0.22/0.28 thf(f75,plain,(
% 0.22/0.28 ~spl0_9 | ~spl0_11),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f74])).
% 0.22/0.28 thf(f77,plain,(
% 0.22/0.28 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 0.22/0.28 inference(forward_demodulation,[],[f33,f20])).
% 0.22/0.28 thf(f78,plain,(
% 0.22/0.28 $false | (~spl0_1 | ~spl0_4)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.28 thf(f79,plain,(
% 0.22/0.28 ~spl0_1 | ~spl0_4),
% 0.22/0.28 inference(avatar_contradiction_clause,[],[f78])).
% 0.22/0.28 thf(f81,definition,(
% 0.22/0.28 (x != $true) | (((g @ x)) != $true) | (((g @ x)) != $false) | (x = $false)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f84,definition,(
% 0.22/0.28 (x != $true) | (((g @ y)) != $true) | (((g @ y)) != $false) | (x = $false)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f85,plain,(
% 0.22/0.28 ($false != ((g @ $false))) | (~spl0_1 | spl0_12)),
% 0.22/0.28 inference(forward_demodulation,[],[f68,f20])).
% 0.22/0.28 thf(f88,definition,(
% 0.22/0.28 spl0_13 <=> ($false = ((g @ $false)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.22/0.28 thf(f91,plain,(
% 0.22/0.28 ~spl0_13 | ~spl0_1 | spl0_12),
% 0.22/0.28 inference(avatar_split_clause,[],[f85,f67,f18,f88])).
% 0.22/0.28 thf(f95,plain,(
% 0.22/0.28 ($false = ((g @ $true))) | (~spl0_3 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f29,f65])).
% 0.22/0.28 thf(f97,definition,(
% 0.22/0.28 spl0_14 <=> ($false = ((g @ $true)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 0.22/0.28 thf(f99,plain,(
% 0.22/0.28 ($false = ((g @ $true))) | ~spl0_14),
% 0.22/0.28 inference(avatar_component_clause,[],[f97])).
% 0.22/0.28 thf(f100,plain,(
% 0.22/0.28 spl0_14 | ~spl0_3 | ~spl0_11),
% 0.22/0.28 inference(avatar_split_clause,[],[f95,f63,f27,f97])).
% 0.22/0.28 thf(f101,plain,(
% 0.22/0.28 ($true != ((g @ $true))) | (spl0_2 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f23,f65])).
% 0.22/0.28 thf(f103,definition,(
% 0.22/0.28 spl0_15 <=> ($true = ((g @ $true)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
% 0.22/0.28 thf(f106,plain,(
% 0.22/0.28 ~spl0_15 | spl0_2 | ~spl0_11),
% 0.22/0.28 inference(avatar_split_clause,[],[f101,f63,f22,f103])).
% 0.22/0.28 thf(f121,plain,(
% 0.22/0.28 (((f @ (f @ (f @ $true)))) = $false) | (~spl0_5 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f38,f65])).
% 0.22/0.28 thf(f123,definition,(
% 0.22/0.28 spl0_18 <=> (((f @ (f @ (f @ $true)))) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])).
% 0.22/0.28 thf(f125,plain,(
% 0.22/0.28 (((f @ (f @ (f @ $true)))) = $false) | ~spl0_18),
% 0.22/0.28 inference(avatar_component_clause,[],[f123])).
% 0.22/0.28 thf(f126,plain,(
% 0.22/0.28 spl0_18 | ~spl0_5 | ~spl0_11),
% 0.22/0.28 inference(avatar_split_clause,[],[f121,f63,f36,f123])).
% 0.22/0.28 thf(f127,plain,(
% 0.22/0.28 ($false = ((f @ $true))) | ($false = ((f @ (f @ $true)))) | ~spl0_18),
% 0.22/0.28 inference(fool_paramodulation,[],[f125])).
% 0.22/0.28 thf(f130,definition,(
% 0.22/0.28 spl0_19 <=> ($false = ((f @ $true)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])).
% 0.22/0.28 thf(f134,definition,(
% 0.22/0.28 spl0_20 <=> ($false = ((f @ (f @ $true))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition])).
% 0.22/0.28 thf(f136,plain,(
% 0.22/0.28 ($false = ((f @ (f @ $true)))) | ~spl0_20),
% 0.22/0.28 inference(avatar_component_clause,[],[f134])).
% 0.22/0.28 thf(f138,plain,(
% 0.22/0.28 spl0_20 | spl0_19 | ~spl0_18),
% 0.22/0.28 inference(avatar_split_clause,[],[f127,f123,f130,f134])).
% 0.22/0.28 thf(f140,definition,(
% 0.22/0.28 (x != $true) | ($false != ((f @ $true))) | (((g @ (f @ x))) != $false) | ($false = ((g @ $false)))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f145,definition,(
% 0.22/0.28 (((g @ y)) != $true) | (((f @ (f @ (f @ x)))) != $true) | (((f @ (f @ (f @ x)))) != $false) | (((g @ y)) = $false)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f148,plain,(
% 0.22/0.28 ($false = ((f @ $true))) | ($false = ((f @ $true))) | ~spl0_20),
% 0.22/0.28 inference(fool_paramodulation,[],[f136])).
% 0.22/0.28 thf(f150,plain,(
% 0.22/0.28 ($false = ((f @ $true))) | ~spl0_20),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f148])).
% 0.22/0.28 thf(f151,plain,(
% 0.22/0.28 spl0_19 | ~spl0_20),
% 0.22/0.28 inference(avatar_split_clause,[],[f150,f134,f130])).
% 0.22/0.28 thf(f153,definition,(
% 0.22/0.28 spl0_21 <=> (((f @ $false)) = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition])).
% 0.22/0.28 thf(f162,definition,(
% 0.22/0.28 (y != $false) | (((g @ (f @ x))) != $true) | (((g @ (f @ x))) != $false) | (((g @ y)) != $true) | ($true = ((g @ $true)))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f163,plain,(
% 0.22/0.28 (((f @ (f @ (f @ $true)))) != $false) | (spl0_5 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f37,f65])).
% 0.22/0.28 thf(f165,plain,(
% 0.22/0.28 ($true = ((g @ (f @ $true)))) | (~spl0_6 | ~spl0_11)),
% 0.22/0.28 inference(forward_demodulation,[],[f42,f65])).
% 0.22/0.28 thf(f167,plain,(
% 0.22/0.28 ~spl0_18 | spl0_5 | ~spl0_11),
% 0.22/0.28 inference(avatar_split_clause,[],[f163,f63,f36,f123])).
% 0.22/0.28 thf(f170,definition,(
% 0.22/0.28 spl0_22 <=> ($true = ((g @ (f @ $true))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition])).
% 0.22/0.28 thf(f172,plain,(
% 0.22/0.28 ($true = ((g @ (f @ $true)))) | ~spl0_22),
% 0.22/0.28 inference(avatar_component_clause,[],[f170])).
% 0.22/0.28 thf(f173,plain,(
% 0.22/0.28 spl0_22 | ~spl0_6 | ~spl0_11),
% 0.22/0.28 inference(avatar_split_clause,[],[f165,f63,f40,f170])).
% 0.22/0.28 thf(f192,plain,(
% 0.22/0.28 ($true = ((g @ (f @ $false)))) | (~spl0_6 | ~spl0_9)),
% 0.22/0.28 inference(forward_demodulation,[],[f42,f56])).
% 0.22/0.28 thf(f194,definition,(
% 0.22/0.28 spl0_24 <=> ($true = ((g @ (f @ $false))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition])).
% 0.22/0.28 thf(f196,plain,(
% 0.22/0.28 ($true = ((g @ (f @ $false)))) | ~spl0_24),
% 0.22/0.28 inference(avatar_component_clause,[],[f194])).
% 0.22/0.28 thf(f197,plain,(
% 0.22/0.28 spl0_24 | ~spl0_6 | ~spl0_9),
% 0.22/0.28 inference(avatar_split_clause,[],[f192,f54,f40,f194])).
% 0.22/0.28 thf(f198,plain,(
% 0.22/0.28 ($true = ((g @ $true))) | (((f @ $false)) = $false) | ~spl0_24),
% 0.22/0.28 inference(fool_paramodulation,[],[f196])).
% 0.22/0.28 thf(f199,plain,(
% 0.22/0.28 ($false = $true) | (((f @ $false)) = $false) | (~spl0_14 | ~spl0_24)),
% 0.22/0.28 inference(forward_demodulation,[],[f198,f99])).
% 0.22/0.28 thf(f200,plain,(
% 0.22/0.28 (((f @ $false)) = $false) | (~spl0_14 | ~spl0_24)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f199])).
% 0.22/0.28 thf(f201,plain,(
% 0.22/0.28 spl0_21 | ~spl0_14 | ~spl0_24),
% 0.22/0.28 inference(avatar_split_clause,[],[f200,f194,f97,f153])).
% 0.22/0.28 thf(f202,definition,(
% 0.22/0.28 (((f @ (f @ (f @ x)))) != $true) | (((f @ $false)) != $false) | (x != $false) | (x = $true)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f203,definition,(
% 0.22/0.28 ($false != ((f @ $true))) | (((f @ $false)) != $false) | ($false = ((f @ (f @ $true))))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f204,definition,(
% 0.22/0.28 (y != $true) | (((g @ y)) != $false) | ($false = ((g @ $true)))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f215,plain,(
% 0.22/0.28 ($false = ((f @ (f @ (f @ $false))))) | (~spl0_5 | ~spl0_9)),
% 0.22/0.28 inference(forward_demodulation,[],[f38,f56])).
% 0.22/0.28 thf(f228,definition,(
% 0.22/0.28 spl0_27 <=> ($false = ((f @ (f @ (f @ $false)))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition])).
% 0.22/0.28 thf(f230,plain,(
% 0.22/0.28 ($false = ((f @ (f @ (f @ $false))))) | ~spl0_27),
% 0.22/0.28 inference(avatar_component_clause,[],[f228])).
% 0.22/0.28 thf(f231,plain,(
% 0.22/0.28 spl0_27 | ~spl0_5 | ~spl0_9),
% 0.22/0.28 inference(avatar_split_clause,[],[f215,f54,f36,f228])).
% 0.22/0.28 thf(f235,plain,(
% 0.22/0.28 (((f @ $false)) = $false) | ($false = ((f @ (f @ $true)))) | ~spl0_27),
% 0.22/0.28 inference(fool_paramodulation,[],[f230])).
% 0.22/0.28 thf(f237,plain,(
% 0.22/0.28 spl0_21 | spl0_20 | ~spl0_27),
% 0.22/0.28 inference(avatar_split_clause,[],[f235,f228,f134,f153])).
% 0.22/0.28 thf(f244,definition,(
% 0.22/0.28 ($false != ((f @ $true))) | ($false != ((f @ (f @ $true)))) | (x != $false) | (((g @ x)) != $true) | (((g @ (f @ x))) = $true)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f251,definition,(
% 0.22/0.28 (x != $true) | ($false != ((f @ $true))) | ($false != ((f @ (f @ $true)))) | (((f @ (f @ (f @ $true)))) = $false)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f253,definition,(
% 0.22/0.28 (x != $true) | (((f @ (f @ (f @ x)))) != $true) | ($false != ((f @ $true))) | ($false = ((f @ (f @ (f @ $false)))))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f258,definition,(
% 0.22/0.28 (x != $false) | (((g @ (f @ x))) != $false) | (((g @ (f @ x))) != $true) | (x = $true)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f266,definition,(
% 0.22/0.28 (((f @ $false)) != $false) | (x != $false) | (((g @ x)) != $true) | (((g @ (f @ x))) = $true)),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 thf(f282,plain,(
% 0.22/0.28 ($true = ((g @ $true))) | ($false = ((f @ $true))) | ~spl0_22),
% 0.22/0.28 inference(fool_paramodulation,[],[f172])).
% 0.22/0.28 thf(f283,plain,(
% 0.22/0.28 ($false = $true) | ($false = ((f @ $true))) | (~spl0_14 | ~spl0_22)),
% 0.22/0.28 inference(forward_demodulation,[],[f282,f99])).
% 0.22/0.28 thf(f284,plain,(
% 0.22/0.28 ($false = ((f @ $true))) | (~spl0_14 | ~spl0_22)),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f283])).
% 0.22/0.28 thf(f285,plain,(
% 0.22/0.28 spl0_19 | ~spl0_14 | ~spl0_22),
% 0.22/0.28 inference(avatar_split_clause,[],[f284,f170,f97,f130])).
% 0.22/0.28 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f25])).
% 0.22/0.28 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f34])).
% 0.22/0.28 cnf(s3, plain, spl0_5 | spl0_6, inference(sat_conversion,[],[f43])).
% 0.22/0.28 cnf(s4, plain, spl0_7 | spl0_8, inference(sat_conversion,[],[f52])).
% 0.22/0.28 cnf(s5, plain, spl0_9 | spl0_10, inference(sat_conversion,[],[f61])).
% 0.22/0.28 cnf(s6, plain, spl0_11 | spl0_12, inference(sat_conversion,[],[f70])).
% 0.22/0.28 cnf(s7, plain, spl0_1 | spl0_9, inference(sat_conversion,[],[f71])).
% 0.22/0.28 cnf(s8, plain, spl0_4 | spl0_11, inference(sat_conversion,[],[f72])).
% 0.22/0.28 cnf(s9, plain, ~spl0_9 | ~spl0_11, inference(sat_conversion,[],[f75])).
% 0.22/0.28 cnf(s11, plain, ~spl0_1 | ~spl0_4, inference(sat_conversion,[],[f79])).
% 0.22/0.28 cnf(s13, plain, ~spl0_2 | ~spl0_3 | spl0_9 | ~spl0_11, inference(sat_conversion,[],[f81])).
% 0.22/0.28 cnf(s16, plain, spl0_9 | ~spl0_10 | ~spl0_11 | ~spl0_12, inference(sat_conversion,[],[f84])).
% 0.22/0.28 cnf(s17, plain, ~spl0_1 | spl0_12 | ~spl0_13, inference(sat_conversion,[],[f91])).
% 0.22/0.28 cnf(s18, plain, ~spl0_3 | ~spl0_11 | spl0_14, inference(sat_conversion,[],[f100])).
% 0.22/0.28 cnf(s19, plain, spl0_2 | ~spl0_11 | ~spl0_15, inference(sat_conversion,[],[f106])).
% 0.22/0.28 cnf(s22, plain, ~spl0_5 | ~spl0_11 | spl0_18, inference(sat_conversion,[],[f126])).
% 0.22/0.28 cnf(s24, plain, ~spl0_18 | spl0_19 | spl0_20, inference(sat_conversion,[],[f138])).
% 0.22/0.28 cnf(s26, plain, ~spl0_7 | ~spl0_11 | spl0_13 | ~spl0_19, inference(sat_conversion,[],[f140])).
% 0.22/0.28 cnf(s31, plain, ~spl0_5 | ~spl0_8 | ~spl0_10 | spl0_12, inference(sat_conversion,[],[f145])).
% 0.22/0.28 cnf(s32, plain, spl0_19 | ~spl0_20, inference(sat_conversion,[],[f151])).
% 0.22/0.28 cnf(s39, plain, ~spl0_1 | ~spl0_6 | ~spl0_7 | ~spl0_10 | spl0_15, inference(sat_conversion,[],[f162])).
% 0.22/0.28 cnf(s40, plain, spl0_5 | ~spl0_11 | ~spl0_18, inference(sat_conversion,[],[f167])).
% 0.22/0.28 cnf(s42, plain, ~spl0_6 | ~spl0_11 | spl0_22, inference(sat_conversion,[],[f173])).
% 0.22/0.28 cnf(s50, plain, ~spl0_6 | ~spl0_9 | spl0_24, inference(sat_conversion,[],[f197])).
% 0.22/0.28 cnf(s51, plain, ~spl0_14 | spl0_21 | ~spl0_24, inference(sat_conversion,[],[f201])).
% 0.22/0.28 cnf(s52, plain, ~spl0_8 | ~spl0_9 | spl0_11 | ~spl0_21, inference(sat_conversion,[],[f202])).
% 0.22/0.28 cnf(s53, plain, ~spl0_19 | spl0_20 | ~spl0_21, inference(sat_conversion,[],[f203])).
% 0.22/0.28 cnf(s54, plain, ~spl0_4 | ~spl0_12 | spl0_14, inference(sat_conversion,[],[f204])).
% 0.22/0.28 cnf(s65, plain, ~spl0_5 | ~spl0_9 | spl0_27, inference(sat_conversion,[],[f231])).
% 0.22/0.28 cnf(s66, plain, spl0_20 | spl0_21 | ~spl0_27, inference(sat_conversion,[],[f237])).
% 0.22/0.28 cnf(s69, plain, ~spl0_2 | spl0_6 | ~spl0_9 | ~spl0_19 | ~spl0_20, inference(sat_conversion,[],[f244])).
% 0.22/0.28 cnf(s76, plain, ~spl0_11 | spl0_18 | ~spl0_19 | ~spl0_20, inference(sat_conversion,[],[f251])).
% 0.22/0.28 cnf(s78, plain, ~spl0_8 | ~spl0_11 | ~spl0_19 | spl0_27, inference(sat_conversion,[],[f253])).
% 0.22/0.28 cnf(s83, plain, ~spl0_6 | ~spl0_7 | ~spl0_9 | spl0_11, inference(sat_conversion,[],[f258])).
% 0.22/0.28 cnf(s91, plain, ~spl0_2 | spl0_6 | ~spl0_9 | ~spl0_21, inference(sat_conversion,[],[f266])).
% 0.22/0.28 cnf(s100, plain, ~spl0_14 | spl0_19 | ~spl0_22, inference(sat_conversion,[],[f285])).
% 0.22/0.28 cnf(s101, plain, ~spl0_6 | ~spl0_9, inference(rat,[],[s52,s51,s4,s50,s83,s54,s6,s8,s9])).
% 0.22/0.28 cnf(s102, plain, spl0_6 | ~spl0_2 | ~spl0_9, inference(rat,[],[s69,s32,s66,s65,s3,s91])).
% 0.22/0.28 cnf(s103, plain, spl0_1, inference(rat,[],[s102,s101,s1,s7])).
% 0.22/0.28 cnf(s104, plain, ~spl0_4, inference(rat,[],[s11,s103])).
% 0.22/0.28 cnf(s105, plain, spl0_11, inference(rat,[],[s8,s104])).
% 0.22/0.28 cnf(s106, plain, spl0_3, inference(rat,[],[s2,s104])).
% 0.22/0.28 cnf(s107, plain, ~spl0_9, inference(rat,[],[s9,s105])).
% 0.22/0.28 cnf(s108, plain, spl0_14, inference(rat,[],[s18,s105,s106])).
% 0.22/0.28 cnf(s109, plain, ~spl0_2, inference(rat,[],[s13,s105,s107,s106])).
% 0.22/0.28 cnf(s110, plain, spl0_10, inference(rat,[],[s5,s107])).
% 0.22/0.28 cnf(s111, plain, ~spl0_15, inference(rat,[],[s19,s105,s109])).
% 0.22/0.28 cnf(s113, plain, ~spl0_12, inference(rat,[],[s16,s107,s105,s110])).
% 0.22/0.28 cnf(s114, plain, ~spl0_13, inference(rat,[],[s17,s103,s113])).
% 0.22/0.28 cnf(s115, plain, spl0_5, inference(rat,[],[s66,s53,s78,s76,s4,s100,s39,s42,s3,s40,s105,s108,s103,s110,s111])).
% 0.22/0.28 cnf(s116, plain, ~spl0_8, inference(rat,[],[s31,s113,s110,s115])).
% 0.22/0.28 cnf(s117, plain, spl0_18, inference(rat,[],[s22,s105,s115])).
% 0.22/0.28 cnf(s118, plain, spl0_7, inference(rat,[],[s4,s116])).
% 0.22/0.28 cnf(s120, plain, ~spl0_19, inference(rat,[],[s26,s114,s105,s118])).
% 0.22/0.28 cnf(s123, plain, ~spl0_20, inference(rat,[],[s32,s120])).
% 0.22/0.28 cnf(s124, plain, $false, inference(rat,[],[s24,s117,s123,s120])).
% 0.22/0.28 thf(f286,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s124])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (2699905)------------------------------
% 0.22/0.28 % (2699905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (2699905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (2699905)CaDiCaL version: 2.1.3
% 0.22/0.28 % (2699905)Termination reason: Refutation
% 0.22/0.28 % (2699905)Time elapsed: 0.005 s
% 0.22/0.28 % (2699905)Peak memory usage: 13 MB
% 0.22/0.28 % (2699905)Instructions burned: 11 (million)
% 0.22/0.28 % (2699897)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------