%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:48:46 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:25:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25 % (2700136)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (2700151)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3861708118:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.09/0.25 % (2700146)% WARNING: option uhcvi not known.
% 0.09/0.25 % (2700144)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2025606896_3000 on theBenchmark for (3000ds/0Mi)
% 0.09/0.25 % (2700146)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=344903128:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.09/0.25 % (2700147)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1965650665:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.09/0.25 % (2700148)dis+10_1_sil=32000:sp=arity:random_seed=917929742:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.09/0.25 % (2700149)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=130243467:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (2700146)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25
% 0.09/0.25 % (2700146)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % (2700149)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (2700151) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2700136-2700151"...
% 0.09/0.25 % (2700150)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2850572767:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.09/0.25 % (2700151)...printing done.
% 0.09/0.25 % (2700151)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, a: $o).
% 0.09/0.25 thf(func_def_1, type, f: ($o > $o)).
% 0.09/0.25 thf(func_def_2, type, g: ($o > $o)).
% 0.09/0.25 thf(func_def_3, type, x: $o).
% 0.09/0.25 thf(func_def_4, type, y: $o).
% 0.09/0.25 thf(f1,axiom,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x) & (((g @ x)) = y) & (x != y)),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',3)).
% 0.09/0.25 thf(f2,plain,(
% 0.09/0.25 (x != y)),
% 0.09/0.25 inference(cnf_transformation,[],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 (y = ((g @ x)))),
% 0.09/0.25 inference(cnf_transformation,[],[f1])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 (x = ((g @ y)))),
% 0.09/0.25 inference(cnf_transformation,[],[f1])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = ((g @ (f @ x))))),
% 0.09/0.25 inference(cnf_transformation,[],[f1])).
% 0.09/0.25 thf(f7,definition,(
% 0.09/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 (x = $true) | (y = $true)),
% 0.09/0.25 inference(xor_proxy_clausification,[],[f2])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 (x = $false) | (y = $false)),
% 0.09/0.25 inference(xor_proxy_clausification,[],[f2])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 (y = $true) | (((g @ x)) = $false)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f3])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 (y = $false) | (((g @ x)) = $true)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f3])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 (x = $true) | (((g @ y)) = $false)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f4])).
% 0.09/0.25 thf(f13,plain,(
% 0.09/0.25 (x = $false) | (((g @ y)) = $true)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f4])).
% 0.09/0.25 thf(f14,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = $true) | (((g @ (f @ x))) = $false)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f5])).
% 0.09/0.25 thf(f15,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = $false) | (((g @ (f @ x))) = $true)),
% 0.09/0.25 inference(iff_proxy_clausification,[],[f5])).
% 0.09/0.25 thf(f17,definition,(
% 0.09/0.25 spl0_1 <=> (y = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.09/0.25 thf(f19,plain,(
% 0.09/0.25 (y = $false) | ~spl0_1),
% 0.09/0.25 inference(avatar_component_clause,[],[f17])).
% 0.09/0.25 thf(f21,definition,(
% 0.09/0.25 spl0_2 <=> (x = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 (x = $false) | ~spl0_2),
% 0.09/0.25 inference(avatar_component_clause,[],[f21])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 spl0_1 | spl0_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f9,f21,f17])).
% 0.09/0.25 thf(f26,definition,(
% 0.09/0.25 spl0_3 <=> (y = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 (y = $true) | ~spl0_3),
% 0.09/0.25 inference(avatar_component_clause,[],[f26])).
% 0.09/0.25 thf(f30,definition,(
% 0.09/0.25 spl0_4 <=> (x = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 (x = $true) | ~spl0_4),
% 0.09/0.25 inference(avatar_component_clause,[],[f30])).
% 0.09/0.25 thf(f33,plain,(
% 0.09/0.25 spl0_3 | spl0_4),
% 0.09/0.25 inference(avatar_split_clause,[],[f8,f30,f26])).
% 0.09/0.25 thf(f35,definition,(
% 0.09/0.25 spl0_5 <=> (((g @ x)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.09/0.25 thf(f36,plain,(
% 0.09/0.25 (((g @ x)) != $true) | spl0_5),
% 0.09/0.25 inference(avatar_component_clause,[],[f35])).
% 0.09/0.25 thf(f37,plain,(
% 0.09/0.25 (((g @ x)) = $true) | ~spl0_5),
% 0.09/0.25 inference(avatar_component_clause,[],[f35])).
% 0.09/0.25 thf(f38,plain,(
% 0.09/0.25 spl0_5 | spl0_1),
% 0.09/0.25 inference(avatar_split_clause,[],[f11,f17,f35])).
% 0.09/0.25 thf(f40,definition,(
% 0.09/0.25 spl0_6 <=> (((g @ x)) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.09/0.25 thf(f42,plain,(
% 0.09/0.25 (((g @ x)) = $false) | ~spl0_6),
% 0.09/0.25 inference(avatar_component_clause,[],[f40])).
% 0.09/0.25 thf(f43,plain,(
% 0.09/0.25 spl0_6 | spl0_3),
% 0.09/0.25 inference(avatar_split_clause,[],[f10,f26,f40])).
% 0.09/0.25 thf(f45,definition,(
% 0.09/0.25 spl0_7 <=> (((g @ y)) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.09/0.25 thf(f47,plain,(
% 0.09/0.25 (((g @ y)) = $true) | ~spl0_7),
% 0.09/0.25 inference(avatar_component_clause,[],[f45])).
% 0.09/0.25 thf(f48,plain,(
% 0.09/0.25 spl0_7 | spl0_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f13,f21,f45])).
% 0.09/0.25 thf(f50,definition,(
% 0.09/0.25 spl0_8 <=> (((g @ y)) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.09/0.25 thf(f52,plain,(
% 0.09/0.25 (((g @ y)) = $false) | ~spl0_8),
% 0.09/0.25 inference(avatar_component_clause,[],[f50])).
% 0.09/0.25 thf(f53,plain,(
% 0.09/0.25 spl0_8 | spl0_4),
% 0.09/0.25 inference(avatar_split_clause,[],[f12,f30,f50])).
% 0.09/0.25 thf(f55,definition,(
% 0.09/0.25 spl0_9 <=> (((g @ (f @ x))) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.09/0.25 thf(f56,plain,(
% 0.09/0.25 (((g @ (f @ x))) != $true) | spl0_9),
% 0.09/0.25 inference(avatar_component_clause,[],[f55])).
% 0.09/0.25 thf(f57,plain,(
% 0.09/0.25 (((g @ (f @ x))) = $true) | ~spl0_9),
% 0.09/0.25 inference(avatar_component_clause,[],[f55])).
% 0.09/0.25 thf(f59,definition,(
% 0.09/0.25 spl0_10 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.09/0.25 thf(f60,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) != $false) | spl0_10),
% 0.09/0.25 inference(avatar_component_clause,[],[f59])).
% 0.09/0.25 thf(f61,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = $false) | ~spl0_10),
% 0.09/0.25 inference(avatar_component_clause,[],[f59])).
% 0.09/0.25 thf(f62,plain,(
% 0.09/0.25 spl0_9 | spl0_10),
% 0.09/0.25 inference(avatar_split_clause,[],[f15,f59,f55])).
% 0.09/0.25 thf(f64,definition,(
% 0.09/0.25 spl0_11 <=> (((g @ (f @ x))) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.09/0.25 thf(f66,plain,(
% 0.09/0.25 (((g @ (f @ x))) = $false) | ~spl0_11),
% 0.09/0.25 inference(avatar_component_clause,[],[f64])).
% 0.09/0.25 thf(f68,definition,(
% 0.09/0.25 spl0_12 <=> (((f @ (f @ (f @ x)))) = $true)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 0.09/0.25 thf(f70,plain,(
% 0.09/0.25 (((f @ (f @ (f @ x)))) = $true) | ~spl0_12),
% 0.09/0.25 inference(avatar_component_clause,[],[f68])).
% 0.09/0.25 thf(f71,plain,(
% 0.09/0.25 spl0_11 | spl0_12),
% 0.09/0.25 inference(avatar_split_clause,[],[f14,f68,f64])).
% 0.09/0.25 thf(f83,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.09/0.25 inference(constrained_superposition,[],[f32,f23])).
% 0.09/0.25 thf(f87,plain,(
% 0.09/0.25 $false | (~spl0_2 | ~spl0_4)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f83])).
% 0.09/0.25 thf(f88,plain,(
% 0.09/0.25 ~spl0_2 | ~spl0_4),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f87])).
% 0.09/0.25 thf(f93,plain,(
% 0.09/0.25 ($true = ((g @ $false))) | (~spl0_2 | ~spl0_5)),
% 0.09/0.25 inference(constrained_superposition,[],[f37,f23])).
% 0.09/0.25 thf(f103,plain,(
% 0.09/0.25 ($false = ((g @ $true))) | (~spl0_3 | ~spl0_8)),
% 0.09/0.25 inference(constrained_superposition,[],[f52,f28])).
% 0.09/0.25 thf(f121,plain,(
% 0.09/0.25 ($true = ((g @ $true))) | (((f @ x)) = $false) | ~spl0_9),
% 0.09/0.25 inference(constrained_superposition,[],[f57,f7])).
% 0.09/0.25 thf(f123,definition,(
% 0.09/0.25 spl0_13 <=> (((f @ x)) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.09/0.25 thf(f124,plain,(
% 0.09/0.25 (((f @ x)) != $false) | spl0_13),
% 0.09/0.25 inference(avatar_component_clause,[],[f123])).
% 0.09/0.25 thf(f125,plain,(
% 0.09/0.25 (((f @ x)) = $false) | ~spl0_13),
% 0.09/0.25 inference(avatar_component_clause,[],[f123])).
% 0.09/0.25 thf(f127,definition,(
% 0.09/0.25 spl0_14 <=> ($true = ((g @ $true)))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 0.09/0.25 thf(f129,plain,(
% 0.09/0.25 ($true = ((g @ $true))) | ~spl0_14),
% 0.09/0.25 inference(avatar_component_clause,[],[f127])).
% 0.09/0.25 thf(f130,plain,(
% 0.09/0.25 spl0_13 | spl0_14 | ~spl0_9),
% 0.09/0.25 inference(avatar_split_clause,[],[f121,f55,f127,f123])).
% 0.09/0.25 thf(f132,plain,(
% 0.09/0.25 ($false != ((f @ $false))) | (~spl0_2 | spl0_13)),
% 0.09/0.25 inference(constrained_superposition,[],[f124,f23])).
% 0.09/0.25 thf(f138,plain,(
% 0.09/0.25 ($true != $true) | (((g @ (f @ x))) = $false) | spl0_9),
% 0.09/0.25 inference(constrained_superposition,[],[f56,f7])).
% 0.09/0.25 thf(f139,plain,(
% 0.09/0.25 (((g @ (f @ x))) = $false) | spl0_9),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f138])).
% 0.09/0.25 thf(f167,plain,(
% 0.09/0.25 ($false = ((f @ (f @ $true)))) | (((f @ x)) = $false) | ~spl0_10),
% 0.09/0.25 inference(constrained_superposition,[],[f61,f7])).
% 0.09/0.25 thf(f168,plain,(
% 0.09/0.25 ($false = ((f @ $true))) | (((f @ (f @ x))) = $false) | ~spl0_10),
% 0.09/0.25 inference(constrained_superposition,[],[f61,f7])).
% 0.09/0.25 thf(f172,definition,(
% 0.09/0.25 spl0_15 <=> (((f @ (f @ x))) = $false)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
% 0.09/0.25 thf(f173,plain,(
% 0.09/0.25 (((f @ (f @ x))) != $false) | spl0_15),
% 0.09/0.25 inference(avatar_component_clause,[],[f172])).
% 0.09/0.25 thf(f174,plain,(
% 0.09/0.25 (((f @ (f @ x))) = $false) | ~spl0_15),
% 0.09/0.25 inference(avatar_component_clause,[],[f172])).
% 0.09/0.25 thf(f176,definition,(
% 0.09/0.25 spl0_16 <=> ($false = ((f @ $true)))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition])).
% 0.09/0.25 thf(f178,plain,(
% 0.09/0.25 ($false = ((f @ $true))) | ~spl0_16),
% 0.09/0.25 inference(avatar_component_clause,[],[f176])).
% 0.09/0.25 thf(f179,plain,(
% 0.09/0.25 spl0_15 | spl0_16 | ~spl0_10),
% 0.09/0.25 inference(avatar_split_clause,[],[f168,f59,f176,f172])).
% 0.09/0.25 thf(f181,definition,(
% 0.09/0.25 spl0_17 <=> ($false = ((f @ (f @ $true))))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
% 0.09/0.25 thf(f183,plain,(
% 0.09/0.25 ($false = ((f @ (f @ $true)))) | ~spl0_17),
% 0.09/0.25 inference(avatar_component_clause,[],[f181])).
% 0.09/0.25 thf(f184,plain,(
% 0.09/0.25 spl0_13 | spl0_17 | ~spl0_10),
% 0.09/0.25 inference(avatar_split_clause,[],[f167,f59,f181,f123])).
% 0.09/0.25 thf(f186,plain,(
% 0.09/0.25 ($false = ((f @ $false))) | (~spl0_2 | ~spl0_13)),
% 0.09/0.25 inference(constrained_superposition,[],[f125,f23])).
% 0.09/0.25 thf(f188,plain,(
% 0.09/0.25 ($false = ((g @ $false))) | (~spl0_11 | ~spl0_13)),
% 0.09/0.25 inference(constrained_superposition,[],[f66,f125])).
% 0.09/0.25 thf(f196,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_2 | ~spl0_5 | ~spl0_11 | ~spl0_13)),
% 0.09/0.25 inference(constrained_superposition,[],[f188,f93])).
% 0.09/0.25 thf(f203,plain,(
% 0.09/0.25 $false | (~spl0_2 | ~spl0_5 | ~spl0_11 | ~spl0_13)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f196])).
% 0.09/0.25 thf(f204,plain,(
% 0.09/0.25 ~spl0_2 | ~spl0_5 | ~spl0_11 | ~spl0_13),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f203])).
% 0.09/0.25 thf(f211,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_3 | ~spl0_8 | ~spl0_14)),
% 0.09/0.25 inference(constrained_superposition,[],[f129,f103])).
% 0.09/0.25 thf(f222,plain,(
% 0.09/0.25 $false | (~spl0_3 | ~spl0_8 | ~spl0_14)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f211])).
% 0.09/0.25 thf(f223,plain,(
% 0.09/0.25 ~spl0_3 | ~spl0_8 | ~spl0_14),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f222])).
% 0.09/0.25 thf(f232,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.09/0.25 inference(constrained_superposition,[],[f19,f28])).
% 0.09/0.25 thf(f238,plain,(
% 0.09/0.25 $false | (~spl0_1 | ~spl0_3)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f232])).
% 0.09/0.25 thf(f239,plain,(
% 0.09/0.25 ~spl0_1 | ~spl0_3),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f238])).
% 0.09/0.25 thf(f252,plain,(
% 0.09/0.25 ($true != ((g @ $true))) | (~spl0_4 | spl0_5)),
% 0.09/0.25 inference(constrained_superposition,[],[f36,f32])).
% 0.09/0.25 thf(f261,plain,(
% 0.09/0.25 ($true = ((g @ $false))) | (~spl0_1 | ~spl0_7)),
% 0.09/0.25 inference(constrained_superposition,[],[f47,f19])).
% 0.09/0.25 thf(f272,plain,(
% 0.09/0.25 ($false = ((f @ $true))) | (x = $false) | ~spl0_13),
% 0.09/0.25 inference(constrained_superposition,[],[f125,f7])).
% 0.09/0.25 thf(f277,plain,(
% 0.09/0.25 spl0_2 | spl0_16 | ~spl0_13),
% 0.09/0.25 inference(avatar_split_clause,[],[f272,f123,f176,f21])).
% 0.09/0.25 thf(f326,plain,(
% 0.09/0.25 ($false != ((f @ $false))) | (~spl0_13 | spl0_15)),
% 0.09/0.25 inference(constrained_superposition,[],[f173,f125])).
% 0.09/0.25 thf(f332,definition,(
% 0.09/0.25 spl0_19 <=> ($false = ((f @ $false)))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])).
% 0.09/0.25 thf(f333,plain,(
% 0.09/0.25 ($false = ((f @ $false))) | ~spl0_19),
% 0.09/0.25 inference(avatar_component_clause,[],[f332])).
% 0.09/0.25 thf(f336,plain,(
% 0.09/0.25 ~spl0_19 | ~spl0_13 | spl0_15),
% 0.09/0.25 inference(avatar_split_clause,[],[f326,f172,f123,f332])).
% 0.09/0.25 thf(f359,plain,(
% 0.09/0.25 ($false != ((f @ $true))) | (((f @ (f @ x))) = $false) | spl0_10),
% 0.09/0.25 inference(constrained_superposition,[],[f60,f7])).
% 0.09/0.25 thf(f365,plain,(
% 0.09/0.25 spl0_15 | ~spl0_16 | spl0_10),
% 0.09/0.25 inference(avatar_split_clause,[],[f359,f59,f176,f172])).
% 0.09/0.25 thf(f374,plain,(
% 0.09/0.25 spl0_19 | ~spl0_2 | ~spl0_13),
% 0.09/0.25 inference(avatar_split_clause,[],[f186,f123,f21,f332])).
% 0.09/0.25 thf(f400,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_5 | ~spl0_6)),
% 0.09/0.25 inference(constrained_superposition,[],[f37,f42])).
% 0.09/0.25 thf(f404,plain,(
% 0.09/0.25 $false | (~spl0_5 | ~spl0_6)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f400])).
% 0.09/0.25 thf(f405,plain,(
% 0.09/0.25 ~spl0_5 | ~spl0_6),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f404])).
% 0.09/0.25 thf(f406,plain,(
% 0.09/0.25 ~spl0_14 | ~spl0_4 | spl0_5),
% 0.09/0.25 inference(avatar_split_clause,[],[f252,f35,f30,f127])).
% 0.09/0.25 thf(f421,plain,(
% 0.09/0.25 ($false != ((f @ $true))) | (x = $false) | spl0_13),
% 0.09/0.25 inference(constrained_superposition,[],[f124,f7])).
% 0.09/0.25 thf(f463,plain,(
% 0.09/0.25 ($false = ((f @ $true))) | (((f @ x)) = $false) | ~spl0_15),
% 0.09/0.25 inference(constrained_superposition,[],[f174,f7])).
% 0.09/0.25 thf(f469,plain,(
% 0.09/0.25 spl0_13 | spl0_16 | ~spl0_15),
% 0.09/0.25 inference(avatar_split_clause,[],[f463,f172,f176,f123])).
% 0.09/0.25 thf(f471,plain,(
% 0.09/0.25 spl0_2 | ~spl0_16 | spl0_13),
% 0.09/0.25 inference(avatar_split_clause,[],[f421,f123,f176,f21])).
% 0.09/0.25 thf(f509,plain,(
% 0.09/0.25 ( ! [X0 : $o] : (($false = ((f @ X0))) | ($false = X0)) ) | ~spl0_16),
% 0.09/0.25 inference(constrained_superposition,[],[f178,f7])).
% 0.09/0.25 thf(f515,plain,(
% 0.09/0.25 ($false = ((f @ $false))) | (x = $false) | (~spl0_15 | ~spl0_16)),
% 0.09/0.25 inference(constrained_superposition,[],[f174,f509])).
% 0.09/0.25 thf(f524,plain,(
% 0.09/0.25 ($false = ((f @ $false))) | ($true = $false) | (~spl0_16 | ~spl0_17)),
% 0.09/0.25 inference(constrained_superposition,[],[f183,f509])).
% 0.09/0.25 thf(f527,plain,(
% 0.09/0.25 ($false = ((f @ $false))) | (~spl0_16 | ~spl0_17)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f524])).
% 0.09/0.25 thf(f529,plain,(
% 0.09/0.25 spl0_19 | ~spl0_16 | ~spl0_17),
% 0.09/0.25 inference(avatar_split_clause,[],[f527,f181,f176,f332])).
% 0.09/0.25 thf(f530,plain,(
% 0.09/0.25 ~spl0_19 | ~spl0_2 | spl0_13),
% 0.09/0.25 inference(avatar_split_clause,[],[f132,f123,f21,f332])).
% 0.09/0.25 thf(f533,plain,(
% 0.09/0.25 spl0_11 | spl0_9),
% 0.09/0.25 inference(avatar_split_clause,[],[f139,f55,f64])).
% 0.09/0.25 thf(f653,plain,(
% 0.09/0.25 ($true = ((f @ $false))) | (~spl0_12 | ~spl0_15)),
% 0.09/0.25 inference(constrained_superposition,[],[f70,f174])).
% 0.09/0.25 thf(f656,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_10 | ~spl0_12)),
% 0.09/0.25 inference(constrained_superposition,[],[f70,f61])).
% 0.09/0.25 thf(f666,plain,(
% 0.09/0.25 $false | (~spl0_10 | ~spl0_12)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f656])).
% 0.09/0.25 thf(f667,plain,(
% 0.09/0.25 ~spl0_10 | ~spl0_12),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f666])).
% 0.09/0.25 thf(f722,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_1 | ~spl0_7 | ~spl0_11 | ~spl0_13)),
% 0.09/0.25 inference(constrained_superposition,[],[f188,f261])).
% 0.09/0.25 thf(f729,plain,(
% 0.09/0.25 $false | (~spl0_1 | ~spl0_7 | ~spl0_11 | ~spl0_13)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f722])).
% 0.09/0.25 thf(f730,plain,(
% 0.09/0.25 ~spl0_1 | ~spl0_7 | ~spl0_11 | ~spl0_13),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f729])).
% 0.09/0.25 thf(f753,definition,(
% 0.09/0.25 spl0_24 <=> ($true = ((f @ $false)))),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition])).
% 0.09/0.25 thf(f755,plain,(
% 0.09/0.25 ($true = ((f @ $false))) | ~spl0_24),
% 0.09/0.25 inference(avatar_component_clause,[],[f753])).
% 0.09/0.25 thf(f757,plain,(
% 0.09/0.25 spl0_24 | ~spl0_12 | ~spl0_15),
% 0.09/0.25 inference(avatar_split_clause,[],[f653,f172,f68,f753])).
% 0.09/0.25 thf(f758,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_19 | ~spl0_24)),
% 0.09/0.25 inference(constrained_superposition,[],[f755,f333])).
% 0.09/0.25 thf(f759,plain,(
% 0.09/0.25 ($true = $false) | (~spl0_19 | ~spl0_24)),
% 0.09/0.25 inference(constrained_superposition,[],[f333,f755])).
% 0.09/0.25 thf(f760,plain,(
% 0.09/0.25 $false | (~spl0_19 | ~spl0_24)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f759])).
% 0.09/0.25 thf(f761,plain,(
% 0.09/0.25 ~spl0_19 | ~spl0_24),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f760])).
% 0.09/0.25 thf(f762,plain,(
% 0.09/0.25 $false | (~spl0_19 | ~spl0_24)),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f758])).
% 0.09/0.25 thf(f763,plain,(
% 0.09/0.25 ~spl0_19 | ~spl0_24),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f762])).
% 0.09/0.25 thf(f768,plain,(
% 0.09/0.25 spl0_2 | spl0_19 | ~spl0_15 | ~spl0_16),
% 0.09/0.25 inference(avatar_split_clause,[],[f515,f176,f172,f332,f21])).
% 0.09/0.25 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f24])).
% 0.09/0.25 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f33])).
% 0.09/0.25 cnf(s3, plain, spl0_1 | spl0_5, inference(sat_conversion,[],[f38])).
% 0.09/0.25 cnf(s4, plain, spl0_3 | spl0_6, inference(sat_conversion,[],[f43])).
% 0.09/0.25 cnf(s5, plain, spl0_2 | spl0_7, inference(sat_conversion,[],[f48])).
% 0.09/0.25 cnf(s6, plain, spl0_4 | spl0_8, inference(sat_conversion,[],[f53])).
% 0.09/0.25 cnf(s7, plain, spl0_9 | spl0_10, inference(sat_conversion,[],[f62])).
% 0.09/0.25 cnf(s8, plain, spl0_11 | spl0_12, inference(sat_conversion,[],[f71])).
% 0.09/0.25 cnf(s10, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f88])).
% 0.09/0.25 cnf(s11, plain, ~spl0_9 | spl0_13 | spl0_14, inference(sat_conversion,[],[f130])).
% 0.09/0.25 cnf(s12, plain, ~spl0_10 | spl0_15 | spl0_16, inference(sat_conversion,[],[f179])).
% 0.09/0.25 cnf(s13, plain, ~spl0_10 | spl0_13 | spl0_17, inference(sat_conversion,[],[f184])).
% 0.09/0.25 cnf(s16, plain, ~spl0_2 | ~spl0_5 | ~spl0_11 | ~spl0_13, inference(sat_conversion,[],[f204])).
% 0.09/0.25 cnf(s20, plain, ~spl0_3 | ~spl0_8 | ~spl0_14, inference(sat_conversion,[],[f223])).
% 0.09/0.25 cnf(s23, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f239])).
% 0.09/0.25 cnf(s28, plain, spl0_2 | ~spl0_13 | spl0_16, inference(sat_conversion,[],[f277])).
% 0.09/0.25 cnf(s30, plain, ~spl0_13 | spl0_15 | ~spl0_19, inference(sat_conversion,[],[f336])).
% 0.09/0.25 cnf(s32, plain, spl0_10 | spl0_15 | ~spl0_16, inference(sat_conversion,[],[f365])).
% 0.09/0.25 cnf(s35, plain, ~spl0_2 | ~spl0_13 | spl0_19, inference(sat_conversion,[],[f374])).
% 0.09/0.25 cnf(s45, plain, ~spl0_5 | ~spl0_6, inference(sat_conversion,[],[f405])).
% 0.09/0.25 cnf(s46, plain, ~spl0_4 | spl0_5 | ~spl0_14, inference(sat_conversion,[],[f406])).
% 0.09/0.25 cnf(s48, plain, spl0_13 | ~spl0_15 | spl0_16, inference(sat_conversion,[],[f469])).
% 0.09/0.25 cnf(s50, plain, spl0_2 | spl0_13 | ~spl0_16, inference(sat_conversion,[],[f471])).
% 0.09/0.25 cnf(s53, plain, ~spl0_16 | ~spl0_17 | spl0_19, inference(sat_conversion,[],[f529])).
% 0.09/0.25 cnf(s55, plain, ~spl0_2 | spl0_13 | ~spl0_19, inference(sat_conversion,[],[f530])).
% 0.09/0.25 cnf(s59, plain, spl0_9 | spl0_11, inference(sat_conversion,[],[f533])).
% 0.09/0.25 cnf(s65, plain, ~spl0_10 | ~spl0_12, inference(sat_conversion,[],[f667])).
% 0.09/0.25 cnf(s72, plain, ~spl0_1 | ~spl0_7 | ~spl0_11 | ~spl0_13, inference(sat_conversion,[],[f730])).
% 0.09/0.25 cnf(s80, plain, ~spl0_12 | ~spl0_15 | spl0_24, inference(sat_conversion,[],[f757])).
% 0.09/0.25 cnf(s81, plain, ~spl0_19 | ~spl0_24, inference(sat_conversion,[],[f761])).
% 0.09/0.25 cnf(s82, plain, ~spl0_19 | ~spl0_24, inference(sat_conversion,[],[f763])).
% 0.09/0.25 cnf(s87, plain, spl0_2 | ~spl0_15 | ~spl0_16 | spl0_19, inference(sat_conversion,[],[f768])).
% 0.09/0.25 cnf(s91, plain, spl0_9 | spl0_1, inference(rat,[],[s48,s12,s53,s13,s55,s16,s7,s59,s3,s1])).
% 0.09/0.25 cnf(s92, plain, spl0_1, inference(rat,[],[s80,s8,s30,s82,s16,s35,s11,s91,s20,s6,s4,s10,s45,s1,s3])).
% 0.09/0.25 cnf(s93, plain, ~spl0_3, inference(rat,[],[s23,s92])).
% 0.09/0.25 cnf(s94, plain, spl0_6, inference(rat,[],[s4,s93])).
% 0.09/0.25 cnf(s95, plain, spl0_4, inference(rat,[],[s2,s93])).
% 0.09/0.25 cnf(s96, plain, ~spl0_5, inference(rat,[],[s45,s94])).
% 0.09/0.25 cnf(s98, plain, ~spl0_2, inference(rat,[],[s10,s95])).
% 0.09/0.25 cnf(s99, plain, ~spl0_14, inference(rat,[],[s46,s95,s96])).
% 0.09/0.25 cnf(s100, plain, spl0_7, inference(rat,[],[s5,s98])).
% 0.09/0.25 cnf(s102, plain, spl0_9, inference(rat,[],[s48,s12,s50,s72,s7,s59,s98,s92,s100])).
% 0.09/0.25 cnf(s103, plain, spl0_13, inference(rat,[],[s11,s99,s102])).
% 0.09/0.25 cnf(s104, plain, spl0_16, inference(rat,[],[s28,s98,s103])).
% 0.09/0.25 cnf(s105, plain, ~spl0_11, inference(rat,[],[s72,s100,s92,s103])).
% 0.09/0.25 cnf(s107, plain, spl0_12, inference(rat,[],[s8,s105])).
% 0.09/0.25 cnf(s109, plain, ~spl0_10, inference(rat,[],[s65,s107])).
% 0.09/0.25 cnf(s111, plain, spl0_15, inference(rat,[],[s32,s104,s109])).
% 0.09/0.25 cnf(s114, plain, spl0_19, inference(rat,[],[s87,s104,s98,s111])).
% 0.09/0.25 cnf(s115, plain, spl0_24, inference(rat,[],[s80,s107,s111])).
% 0.09/0.25 cnf(s116, plain, $false, inference(rat,[],[s81,s115,s114])).
% 0.09/0.25 thf(f771,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s116])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (2700151)------------------------------
% 0.09/0.25 % (2700151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (2700151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (2700151)CaDiCaL version: 2.1.3
% 0.09/0.25 % (2700151)Termination reason: Refutation
% 0.09/0.25 % (2700151)Time elapsed: 0.011 s
% 0.09/0.25 % (2700151)Peak memory usage: 12 MB
% 0.09/0.25 % (2700151)Instructions burned: 35 (million)
% 0.09/0.25 % (2700136)Success in time 0.026 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------