%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO041^2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 08:48:47 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 : SYO041^2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n010.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 16:24:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (3078613)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (3078624)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2068956403:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.25 % (3078623)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=624577875:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (3078618)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2041957516_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (3078620)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3433450223:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (3078622)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3501235395:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (3078621)dis+10_1_sil=32000:sp=arity:random_seed=2776414246:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (3078622)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (3078619)% WARNING: option uhcvi not known.
% 0.08/0.25 % (3078624) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3078613-3078624"...
% 0.08/0.25 % (3078624)...printing done.
% 0.08/0.25 % (3078619)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3842514268:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (3078619)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (3078619)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (3078624)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, a: $o).
% 0.08/0.25 thf(func_def_1, type, f: ($o > $o)).
% 0.08/0.25 thf(func_def_2, type, g: ($o > $o)).
% 0.08/0.25 thf(func_def_3, type, x: $o).
% 0.08/0.25 thf(func_def_4, type, y: $o).
% 0.08/0.25 thf(f1,conjecture,(
% 0.08/0.25 ~((((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x) & (((g @ x)) = y) & (x != y))),
% 0.08/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',3)).
% 0.08/0.25 thf(f2,negated_conjecture,(
% 0.08/0.25 ~ ~((((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x) & (((g @ x)) = y) & (x != y))),
% 0.08/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.25 thf(f3,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x) & (((g @ x)) = y) & (x != y)),
% 0.08/0.25 inference(flattening,[],[f2])).
% 0.08/0.25 thf(f4,plain,(
% 0.08/0.25 (x != y)),
% 0.08/0.25 inference(cnf_transformation,[],[f3])).
% 0.08/0.25 thf(f5,plain,(
% 0.08/0.25 (y = ((g @ x)))),
% 0.08/0.25 inference(cnf_transformation,[],[f3])).
% 0.08/0.25 thf(f6,plain,(
% 0.08/0.25 (x = ((g @ y)))),
% 0.08/0.25 inference(cnf_transformation,[],[f3])).
% 0.08/0.25 thf(f7,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = ((g @ (f @ x))))),
% 0.08/0.25 inference(cnf_transformation,[],[f3])).
% 0.08/0.25 thf(f9,definition,(
% 0.08/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.25 thf(f10,plain,(
% 0.08/0.25 (x = $true) | (y = $true)),
% 0.08/0.25 inference(xor_proxy_clausification,[],[f4])).
% 0.08/0.25 thf(f11,plain,(
% 0.08/0.25 (x = $false) | (y = $false)),
% 0.08/0.25 inference(xor_proxy_clausification,[],[f4])).
% 0.08/0.25 thf(f12,plain,(
% 0.08/0.25 (y = $true) | (((g @ x)) = $false)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f5])).
% 0.08/0.25 thf(f13,plain,(
% 0.08/0.25 (y = $false) | (((g @ x)) = $true)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f5])).
% 0.08/0.25 thf(f14,plain,(
% 0.08/0.25 (x = $true) | (((g @ y)) = $false)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f6])).
% 0.08/0.25 thf(f15,plain,(
% 0.08/0.25 (x = $false) | (((g @ y)) = $true)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f6])).
% 0.08/0.25 thf(f16,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = $true) | (((g @ (f @ x))) = $false)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f7])).
% 0.08/0.25 thf(f17,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = $false) | (((g @ (f @ x))) = $true)),
% 0.08/0.25 inference(iff_proxy_clausification,[],[f7])).
% 0.08/0.25 thf(f19,definition,(
% 0.08/0.25 spl0_1 <=> (y = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.08/0.25 thf(f21,plain,(
% 0.08/0.25 (y = $false) | ~spl0_1),
% 0.08/0.25 inference(avatar_component_clause,[],[f19])).
% 0.08/0.25 thf(f23,definition,(
% 0.08/0.25 spl0_2 <=> (x = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.08/0.25 thf(f25,plain,(
% 0.08/0.25 (x = $false) | ~spl0_2),
% 0.08/0.25 inference(avatar_component_clause,[],[f23])).
% 0.08/0.25 thf(f26,plain,(
% 0.08/0.25 spl0_1 | spl0_2),
% 0.08/0.25 inference(avatar_split_clause,[],[f11,f23,f19])).
% 0.08/0.25 thf(f28,definition,(
% 0.08/0.25 spl0_3 <=> (y = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.08/0.25 thf(f30,plain,(
% 0.08/0.25 (y = $true) | ~spl0_3),
% 0.08/0.25 inference(avatar_component_clause,[],[f28])).
% 0.08/0.25 thf(f32,definition,(
% 0.08/0.25 spl0_4 <=> (x = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.08/0.25 thf(f34,plain,(
% 0.08/0.25 (x = $true) | ~spl0_4),
% 0.08/0.25 inference(avatar_component_clause,[],[f32])).
% 0.08/0.25 thf(f35,plain,(
% 0.08/0.25 spl0_3 | spl0_4),
% 0.08/0.25 inference(avatar_split_clause,[],[f10,f32,f28])).
% 0.08/0.25 thf(f37,definition,(
% 0.08/0.25 spl0_5 <=> (((g @ x)) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.08/0.25 thf(f38,plain,(
% 0.08/0.25 (((g @ x)) != $true) | spl0_5),
% 0.08/0.25 inference(avatar_component_clause,[],[f37])).
% 0.08/0.25 thf(f39,plain,(
% 0.08/0.25 (((g @ x)) = $true) | ~spl0_5),
% 0.08/0.25 inference(avatar_component_clause,[],[f37])).
% 0.08/0.25 thf(f40,plain,(
% 0.08/0.25 spl0_5 | spl0_1),
% 0.08/0.25 inference(avatar_split_clause,[],[f13,f19,f37])).
% 0.08/0.25 thf(f42,definition,(
% 0.08/0.25 spl0_6 <=> (((g @ x)) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.08/0.25 thf(f44,plain,(
% 0.08/0.25 (((g @ x)) = $false) | ~spl0_6),
% 0.08/0.25 inference(avatar_component_clause,[],[f42])).
% 0.08/0.25 thf(f45,plain,(
% 0.08/0.25 spl0_6 | spl0_3),
% 0.08/0.25 inference(avatar_split_clause,[],[f12,f28,f42])).
% 0.08/0.25 thf(f47,definition,(
% 0.08/0.25 spl0_7 <=> (((g @ y)) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.08/0.25 thf(f48,plain,(
% 0.08/0.25 (((g @ y)) != $true) | spl0_7),
% 0.08/0.25 inference(avatar_component_clause,[],[f47])).
% 0.08/0.25 thf(f49,plain,(
% 0.08/0.25 (((g @ y)) = $true) | ~spl0_7),
% 0.08/0.25 inference(avatar_component_clause,[],[f47])).
% 0.08/0.25 thf(f50,plain,(
% 0.08/0.25 spl0_7 | spl0_2),
% 0.08/0.25 inference(avatar_split_clause,[],[f15,f23,f47])).
% 0.08/0.25 thf(f52,definition,(
% 0.08/0.25 spl0_8 <=> (((g @ y)) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.08/0.25 thf(f54,plain,(
% 0.08/0.25 (((g @ y)) = $false) | ~spl0_8),
% 0.08/0.25 inference(avatar_component_clause,[],[f52])).
% 0.08/0.25 thf(f55,plain,(
% 0.08/0.25 spl0_8 | spl0_4),
% 0.08/0.25 inference(avatar_split_clause,[],[f14,f32,f52])).
% 0.08/0.25 thf(f57,definition,(
% 0.08/0.25 spl0_9 <=> (((g @ (f @ x))) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.08/0.25 thf(f58,plain,(
% 0.08/0.25 (((g @ (f @ x))) != $true) | spl0_9),
% 0.08/0.25 inference(avatar_component_clause,[],[f57])).
% 0.08/0.25 thf(f59,plain,(
% 0.08/0.25 (((g @ (f @ x))) = $true) | ~spl0_9),
% 0.08/0.25 inference(avatar_component_clause,[],[f57])).
% 0.08/0.25 thf(f61,definition,(
% 0.08/0.25 spl0_10 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.08/0.25 thf(f63,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = $false) | ~spl0_10),
% 0.08/0.25 inference(avatar_component_clause,[],[f61])).
% 0.08/0.25 thf(f64,plain,(
% 0.08/0.25 spl0_9 | spl0_10),
% 0.08/0.25 inference(avatar_split_clause,[],[f17,f61,f57])).
% 0.08/0.25 thf(f66,definition,(
% 0.08/0.25 spl0_11 <=> (((g @ (f @ x))) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.08/0.25 thf(f68,plain,(
% 0.08/0.25 (((g @ (f @ x))) = $false) | ~spl0_11),
% 0.08/0.25 inference(avatar_component_clause,[],[f66])).
% 0.08/0.25 thf(f70,definition,(
% 0.08/0.25 spl0_12 <=> (((f @ (f @ (f @ x)))) = $true)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 0.08/0.25 thf(f72,plain,(
% 0.08/0.25 (((f @ (f @ (f @ x)))) = $true) | ~spl0_12),
% 0.08/0.25 inference(avatar_component_clause,[],[f70])).
% 0.08/0.25 thf(f73,plain,(
% 0.08/0.25 spl0_11 | spl0_12),
% 0.08/0.25 inference(avatar_split_clause,[],[f16,f70,f66])).
% 0.08/0.25 thf(f75,plain,(
% 0.08/0.25 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.08/0.25 inference(constrained_superposition,[],[f34,f25])).
% 0.08/0.25 thf(f79,plain,(
% 0.08/0.25 $false | (~spl0_2 | ~spl0_4)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f75])).
% 0.08/0.25 thf(f80,plain,(
% 0.08/0.25 ~spl0_2 | ~spl0_4),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f79])).
% 0.08/0.25 thf(f82,plain,(
% 0.08/0.25 ($true = ((g @ $false))) | (~spl0_2 | ~spl0_5)),
% 0.08/0.25 inference(constrained_superposition,[],[f39,f25])).
% 0.08/0.25 thf(f85,plain,(
% 0.08/0.25 ($true != ((g @ $true))) | (~spl0_3 | spl0_7)),
% 0.08/0.25 inference(constrained_superposition,[],[f48,f30])).
% 0.08/0.25 thf(f92,plain,(
% 0.08/0.25 ($true = $false) | (~spl0_9 | ~spl0_11)),
% 0.08/0.25 inference(constrained_superposition,[],[f68,f59])).
% 0.08/0.25 thf(f96,plain,(
% 0.08/0.25 $false | (~spl0_9 | ~spl0_11)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f92])).
% 0.08/0.25 thf(f97,plain,(
% 0.08/0.25 ~spl0_9 | ~spl0_11),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f96])).
% 0.08/0.25 thf(f161,plain,(
% 0.08/0.25 ($false = ((f @ $true))) | (((f @ (f @ x))) = $false) | ~spl0_10),
% 0.08/0.25 inference(constrained_superposition,[],[f63,f9])).
% 0.08/0.25 thf(f165,definition,(
% 0.08/0.25 spl0_13 <=> (((f @ (f @ x))) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.08/0.25 thf(f166,plain,(
% 0.08/0.25 (((f @ (f @ x))) != $false) | spl0_13),
% 0.08/0.25 inference(avatar_component_clause,[],[f165])).
% 0.08/0.25 thf(f167,plain,(
% 0.08/0.25 (((f @ (f @ x))) = $false) | ~spl0_13),
% 0.08/0.25 inference(avatar_component_clause,[],[f165])).
% 0.08/0.25 thf(f169,definition,(
% 0.08/0.25 spl0_14 <=> ($false = ((f @ $true)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition])).
% 0.08/0.25 thf(f171,plain,(
% 0.08/0.25 ($false = ((f @ $true))) | ~spl0_14),
% 0.08/0.25 inference(avatar_component_clause,[],[f169])).
% 0.08/0.25 thf(f172,plain,(
% 0.08/0.25 spl0_13 | spl0_14 | ~spl0_10),
% 0.08/0.25 inference(avatar_split_clause,[],[f161,f61,f169,f165])).
% 0.08/0.25 thf(f174,definition,(
% 0.08/0.25 spl0_15 <=> (((f @ x)) = $false)),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
% 0.08/0.25 thf(f175,plain,(
% 0.08/0.25 (((f @ x)) != $false) | spl0_15),
% 0.08/0.25 inference(avatar_component_clause,[],[f174])).
% 0.08/0.25 thf(f176,plain,(
% 0.08/0.25 (((f @ x)) = $false) | ~spl0_15),
% 0.08/0.25 inference(avatar_component_clause,[],[f174])).
% 0.08/0.25 thf(f185,plain,(
% 0.08/0.25 ($false != ((f @ $false))) | (~spl0_2 | spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f175,f25])).
% 0.08/0.25 thf(f191,plain,(
% 0.08/0.25 ($true = ((g @ $true))) | (((f @ x)) = $false) | ~spl0_9),
% 0.08/0.25 inference(constrained_superposition,[],[f59,f9])).
% 0.08/0.25 thf(f198,definition,(
% 0.08/0.25 spl0_17 <=> ($true = ((g @ $true)))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
% 0.08/0.25 thf(f201,plain,(
% 0.08/0.25 spl0_15 | spl0_17 | ~spl0_9),
% 0.08/0.25 inference(avatar_split_clause,[],[f191,f57,f198,f174])).
% 0.08/0.25 thf(f203,plain,(
% 0.08/0.25 ($false = ((f @ $true))) | (x = $false) | ~spl0_15),
% 0.08/0.25 inference(constrained_superposition,[],[f176,f9])).
% 0.08/0.25 thf(f204,plain,(
% 0.08/0.25 ($false = ((f @ $false))) | (~spl0_2 | ~spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f176,f25])).
% 0.08/0.25 thf(f214,plain,(
% 0.08/0.25 ($true != ((g @ $false))) | (spl0_9 | ~spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f58,f176])).
% 0.08/0.25 thf(f219,plain,(
% 0.08/0.25 ($true != $true) | (~spl0_2 | ~spl0_5 | spl0_9 | ~spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f214,f82])).
% 0.08/0.25 thf(f220,plain,(
% 0.08/0.25 $false | (~spl0_2 | ~spl0_5 | spl0_9 | ~spl0_15)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f219])).
% 0.08/0.25 thf(f221,plain,(
% 0.08/0.25 ~spl0_2 | ~spl0_5 | spl0_9 | ~spl0_15),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f220])).
% 0.08/0.25 thf(f224,plain,(
% 0.08/0.25 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.08/0.25 inference(constrained_superposition,[],[f21,f30])).
% 0.08/0.25 thf(f230,plain,(
% 0.08/0.25 $false | (~spl0_1 | ~spl0_3)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f224])).
% 0.08/0.25 thf(f231,plain,(
% 0.08/0.25 ~spl0_1 | ~spl0_3),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f230])).
% 0.08/0.25 thf(f234,plain,(
% 0.08/0.25 spl0_2 | spl0_14 | ~spl0_15),
% 0.08/0.25 inference(avatar_split_clause,[],[f203,f174,f169,f23])).
% 0.08/0.25 thf(f236,definition,(
% 0.08/0.25 spl0_18 <=> ($true = ((g @ (f @ $true))))),
% 0.08/0.25 introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])).
% 0.08/0.25 thf(f237,plain,(
% 0.08/0.25 ($true = ((g @ (f @ $true)))) | ~spl0_18),
% 0.08/0.25 inference(avatar_component_clause,[],[f236])).
% 0.08/0.25 thf(f248,plain,(
% 0.08/0.25 ($true != ((g @ $true))) | (~spl0_4 | spl0_5)),
% 0.08/0.25 inference(constrained_superposition,[],[f38,f34])).
% 0.08/0.25 thf(f257,plain,(
% 0.08/0.25 ($true = ((g @ $false))) | (~spl0_1 | ~spl0_7)),
% 0.08/0.25 inference(constrained_superposition,[],[f49,f21])).
% 0.08/0.25 thf(f258,plain,(
% 0.08/0.25 ($true = $false) | (~spl0_7 | ~spl0_8)),
% 0.08/0.25 inference(constrained_superposition,[],[f49,f54])).
% 0.08/0.25 thf(f262,plain,(
% 0.08/0.25 $false | (~spl0_7 | ~spl0_8)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f258])).
% 0.08/0.25 thf(f263,plain,(
% 0.08/0.25 ~spl0_7 | ~spl0_8),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f262])).
% 0.08/0.25 thf(f268,plain,(
% 0.08/0.25 ( ! [X0 : $o] : (($false = ((f @ X0))) | ($false = X0)) ) | ~spl0_14),
% 0.08/0.25 inference(constrained_superposition,[],[f171,f9])).
% 0.08/0.25 thf(f281,plain,(
% 0.08/0.25 ($true != $true) | (~spl0_1 | ~spl0_7 | spl0_9 | ~spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f214,f257])).
% 0.08/0.25 thf(f282,plain,(
% 0.08/0.25 $false | (~spl0_1 | ~spl0_7 | spl0_9 | ~spl0_15)),
% 0.08/0.25 inference(trivial_inequality_removal,[],[f281])).
% 0.08/0.25 thf(f283,plain,(
% 0.08/0.25 ~spl0_1 | ~spl0_7 | spl0_9 | ~spl0_15),
% 0.08/0.25 inference(avatar_contradiction_clause,[],[f282])).
% 0.08/0.25 thf(f299,plain,(
% 0.08/0.25 ($true = ((g @ (f @ $true)))) | (~spl0_4 | ~spl0_9)),
% 0.08/0.25 inference(constrained_superposition,[],[f59,f34])).
% 0.08/0.25 thf(f307,plain,(
% 0.08/0.25 spl0_18 | ~spl0_4 | ~spl0_9),
% 0.08/0.25 inference(avatar_split_clause,[],[f299,f57,f32,f236])).
% 0.08/0.25 thf(f331,plain,(
% 0.08/0.25 ($false != ((f @ $false))) | (spl0_13 | ~spl0_15)),
% 0.08/0.25 inference(constrained_superposition,[],[f166,f176])).
% 0.08/0.25 thf(f350,plain,(
% 0.08/0.25 ($false = ((f @ $false))) | (((f @ x)) = $false) | (~spl0_10 | ~spl0_14)),
% 0.08/0.25 inference(constrained_superposition,[],[f63,f268])).
% 0.08/0.25 thf(f353,plain,(
% 0.08/0.25 ( ! [X0 : $o] : ((((g @ (f @ X0))) = X0) | ($false = X0)) ) | ~spl0_18),
% 0.08/0.26 inference(constrained_superposition,[],[f237,f9])).
% 0.08/0.26 thf(f362,plain,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = ((g @ (f @ X0)))) | ($false = X0) | ($false = X0)) ) | ~spl0_18),
% 0.08/0.26 inference(iff_proxy_clausification,[],[f353])).
% 0.08/0.26 thf(f364,plain,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = ((g @ (f @ X0)))) | ($false = X0)) ) | ~spl0_18),
% 0.08/0.26 inference(duplicate_literal_removal,[],[f362])).
% 0.08/0.26 thf(f412,plain,(
% 0.08/0.26 ($true = $false) | (~spl0_10 | ~spl0_12)),
% 0.08/0.26 inference(constrained_superposition,[],[f72,f63])).
% 0.08/0.26 thf(f413,plain,(
% 0.08/0.26 ($true = ((g @ $true))) | (((f @ (f @ x))) = $false) | (~spl0_12 | ~spl0_18)),
% 0.08/0.26 inference(constrained_superposition,[],[f364,f72])).
% 0.08/0.26 thf(f421,plain,(
% 0.08/0.26 $false | (~spl0_10 | ~spl0_12)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f412])).
% 0.08/0.26 thf(f422,plain,(
% 0.08/0.26 ~spl0_10 | ~spl0_12),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f421])).
% 0.08/0.26 thf(f426,plain,(
% 0.08/0.26 spl0_13 | spl0_17 | ~spl0_12 | ~spl0_18),
% 0.08/0.26 inference(avatar_split_clause,[],[f413,f236,f70,f198,f165])).
% 0.08/0.26 thf(f433,definition,(
% 0.08/0.26 spl0_20 <=> ($false = ((f @ $false)))),
% 0.08/0.26 introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition])).
% 0.08/0.26 thf(f435,plain,(
% 0.08/0.26 ($false = ((f @ $false))) | ~spl0_20),
% 0.08/0.26 inference(avatar_component_clause,[],[f433])).
% 0.08/0.26 thf(f451,plain,(
% 0.08/0.26 ($false = ((f @ $false))) | (x = $false) | (~spl0_13 | ~spl0_14)),
% 0.08/0.26 inference(constrained_superposition,[],[f167,f268])).
% 0.08/0.26 thf(f455,plain,(
% 0.08/0.26 ($true = ((f @ $false))) | (~spl0_12 | ~spl0_13)),
% 0.08/0.26 inference(constrained_superposition,[],[f72,f167])).
% 0.08/0.26 thf(f457,plain,(
% 0.08/0.26 ($true = $false) | (~spl0_12 | ~spl0_13 | ~spl0_20)),
% 0.08/0.26 inference(constrained_superposition,[],[f455,f435])).
% 0.08/0.26 thf(f461,plain,(
% 0.08/0.26 $false | (~spl0_12 | ~spl0_13 | ~spl0_20)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f457])).
% 0.08/0.26 thf(f462,plain,(
% 0.08/0.26 ~spl0_12 | ~spl0_13 | ~spl0_20),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f461])).
% 0.08/0.26 thf(f469,plain,(
% 0.08/0.26 ~spl0_20 | spl0_13 | ~spl0_15),
% 0.08/0.26 inference(avatar_split_clause,[],[f331,f174,f165,f433])).
% 0.08/0.26 thf(f470,plain,(
% 0.08/0.26 spl0_20 | ~spl0_2 | ~spl0_15),
% 0.08/0.26 inference(avatar_split_clause,[],[f204,f174,f23,f433])).
% 0.08/0.26 thf(f495,plain,(
% 0.08/0.26 ($true = $false) | (~spl0_5 | ~spl0_6)),
% 0.08/0.26 inference(constrained_superposition,[],[f39,f44])).
% 0.08/0.26 thf(f499,plain,(
% 0.08/0.26 $false | (~spl0_5 | ~spl0_6)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f495])).
% 0.08/0.26 thf(f500,plain,(
% 0.08/0.26 ~spl0_5 | ~spl0_6),
% 0.08/0.26 inference(avatar_contradiction_clause,[],[f499])).
% 0.08/0.26 thf(f501,plain,(
% 0.08/0.26 ~spl0_17 | ~spl0_4 | spl0_5),
% 0.08/0.26 inference(avatar_split_clause,[],[f248,f37,f32,f198])).
% 0.08/0.26 thf(f520,plain,(
% 0.08/0.26 ($false != ((f @ $true))) | (~spl0_4 | spl0_15)),
% 0.08/0.26 inference(constrained_superposition,[],[f175,f34])).
% 0.08/0.26 thf(f577,plain,(
% 0.08/0.26 ($false = ((f @ $true))) | (((f @ x)) = $false) | ~spl0_13),
% 0.08/0.26 inference(constrained_superposition,[],[f167,f9])).
% 0.08/0.26 thf(f590,plain,(
% 0.08/0.26 spl0_15 | spl0_14 | ~spl0_13),
% 0.08/0.26 inference(avatar_split_clause,[],[f577,f165,f169,f174])).
% 0.08/0.26 thf(f597,plain,(
% 0.08/0.26 spl0_15 | spl0_20 | ~spl0_10 | ~spl0_14),
% 0.08/0.26 inference(avatar_split_clause,[],[f350,f169,f61,f433,f174])).
% 0.08/0.26 thf(f598,plain,(
% 0.08/0.26 spl0_2 | spl0_20 | ~spl0_13 | ~spl0_14),
% 0.08/0.26 inference(avatar_split_clause,[],[f451,f169,f165,f433,f23])).
% 0.08/0.26 thf(f599,plain,(
% 0.08/0.26 ~spl0_14 | ~spl0_4 | spl0_15),
% 0.08/0.26 inference(avatar_split_clause,[],[f520,f174,f32,f169])).
% 0.08/0.26 thf(f605,plain,(
% 0.08/0.26 ~spl0_20 | ~spl0_2 | spl0_15),
% 0.08/0.26 inference(avatar_split_clause,[],[f185,f174,f23,f433])).
% 0.08/0.26 thf(f606,plain,(
% 0.08/0.26 ~spl0_17 | ~spl0_3 | spl0_7),
% 0.08/0.26 inference(avatar_split_clause,[],[f85,f47,f28,f198])).
% 0.08/0.26 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f26])).
% 0.08/0.26 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f35])).
% 0.08/0.26 cnf(s3, plain, spl0_1 | spl0_5, inference(sat_conversion,[],[f40])).
% 0.08/0.26 cnf(s4, plain, spl0_3 | spl0_6, inference(sat_conversion,[],[f45])).
% 0.08/0.26 cnf(s5, plain, spl0_2 | spl0_7, inference(sat_conversion,[],[f50])).
% 0.08/0.26 cnf(s6, plain, spl0_4 | spl0_8, inference(sat_conversion,[],[f55])).
% 0.08/0.26 cnf(s7, plain, spl0_9 | spl0_10, inference(sat_conversion,[],[f64])).
% 0.08/0.26 cnf(s8, plain, spl0_11 | spl0_12, inference(sat_conversion,[],[f73])).
% 0.08/0.26 cnf(s10, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f80])).
% 0.08/0.26 cnf(s12, plain, ~spl0_9 | ~spl0_11, inference(sat_conversion,[],[f97])).
% 0.08/0.26 cnf(s13, plain, ~spl0_10 | spl0_13 | spl0_14, inference(sat_conversion,[],[f172])).
% 0.08/0.26 cnf(s17, plain, ~spl0_9 | spl0_15 | spl0_17, inference(sat_conversion,[],[f201])).
% 0.08/0.26 cnf(s19, plain, ~spl0_2 | ~spl0_5 | spl0_9 | ~spl0_15, inference(sat_conversion,[],[f221])).
% 0.08/0.26 cnf(s21, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f231])).
% 0.08/0.26 cnf(s23, plain, spl0_2 | spl0_14 | ~spl0_15, inference(sat_conversion,[],[f234])).
% 0.08/0.26 cnf(s26, plain, ~spl0_7 | ~spl0_8, inference(sat_conversion,[],[f263])).
% 0.08/0.26 cnf(s27, plain, ~spl0_1 | ~spl0_7 | spl0_9 | ~spl0_15, inference(sat_conversion,[],[f283])).
% 0.08/0.26 cnf(s28, plain, ~spl0_4 | ~spl0_9 | spl0_18, inference(sat_conversion,[],[f307])).
% 0.08/0.26 cnf(s33, plain, ~spl0_10 | ~spl0_12, inference(sat_conversion,[],[f422])).
% 0.08/0.26 cnf(s36, plain, ~spl0_12 | spl0_13 | spl0_17 | ~spl0_18, inference(sat_conversion,[],[f426])).
% 0.08/0.26 cnf(s43, plain, ~spl0_12 | ~spl0_13 | ~spl0_20, inference(sat_conversion,[],[f462])).
% 0.08/0.26 cnf(s45, plain, spl0_13 | ~spl0_15 | ~spl0_20, inference(sat_conversion,[],[f469])).
% 0.08/0.26 cnf(s46, plain, ~spl0_2 | ~spl0_15 | spl0_20, inference(sat_conversion,[],[f470])).
% 0.08/0.26 cnf(s52, plain, ~spl0_5 | ~spl0_6, inference(sat_conversion,[],[f500])).
% 0.08/0.26 cnf(s53, plain, ~spl0_4 | spl0_5 | ~spl0_17, inference(sat_conversion,[],[f501])).
% 0.08/0.26 cnf(s64, plain, ~spl0_13 | spl0_14 | spl0_15, inference(sat_conversion,[],[f590])).
% 0.08/0.26 cnf(s67, plain, ~spl0_10 | ~spl0_14 | spl0_15 | spl0_20, inference(sat_conversion,[],[f597])).
% 0.08/0.26 cnf(s68, plain, spl0_2 | ~spl0_13 | ~spl0_14 | spl0_20, inference(sat_conversion,[],[f598])).
% 0.08/0.26 cnf(s69, plain, ~spl0_4 | ~spl0_14 | spl0_15, inference(sat_conversion,[],[f599])).
% 0.08/0.26 cnf(s71, plain, ~spl0_2 | spl0_15 | ~spl0_20, inference(sat_conversion,[],[f605])).
% 0.08/0.26 cnf(s72, plain, ~spl0_3 | spl0_7 | ~spl0_17, inference(sat_conversion,[],[f606])).
% 0.08/0.26 cnf(s79, plain, spl0_20 | ~spl0_10 | spl0_15, inference(rat,[],[s64,s13,s67])).
% 0.08/0.26 cnf(s80, plain, spl0_9 | spl0_1, inference(rat,[],[s79,s71,s19,s7,s3,s1])).
% 0.08/0.26 cnf(s81, plain, spl0_1, inference(rat,[],[s43,s45,s46,s8,s17,s12,s80,s72,s26,s6,s4,s10,s52,s1,s3])).
% 0.08/0.26 cnf(s82, plain, ~spl0_3, inference(rat,[],[s21,s81])).
% 0.08/0.26 cnf(s83, plain, spl0_6, inference(rat,[],[s4,s82])).
% 0.08/0.26 cnf(s84, plain, spl0_4, inference(rat,[],[s2,s82])).
% 0.08/0.26 cnf(s85, plain, ~spl0_5, inference(rat,[],[s52,s83])).
% 0.08/0.26 cnf(s87, plain, ~spl0_2, inference(rat,[],[s10,s84])).
% 0.08/0.26 cnf(s88, plain, ~spl0_17, inference(rat,[],[s53,s84,s85])).
% 0.08/0.26 cnf(s89, plain, spl0_7, inference(rat,[],[s5,s87])).
% 0.08/0.26 cnf(s91, plain, ~spl0_10, inference(rat,[],[s64,s13,s69,s27,s12,s8,s33,s84,s81,s89])).
% 0.08/0.26 cnf(s92, plain, spl0_9, inference(rat,[],[s7,s91])).
% 0.08/0.26 cnf(s93, plain, ~spl0_11, inference(rat,[],[s12,s92])).
% 0.08/0.26 cnf(s94, plain, spl0_15, inference(rat,[],[s17,s88,s92])).
% 0.08/0.26 cnf(s95, plain, spl0_18, inference(rat,[],[s28,s84,s92])).
% 0.08/0.26 cnf(s96, plain, spl0_12, inference(rat,[],[s8,s93])).
% 0.08/0.26 cnf(s97, plain, spl0_14, inference(rat,[],[s23,s87,s94])).
% 0.08/0.26 cnf(s98, plain, spl0_13, inference(rat,[],[s36,s95,s88,s96])).
% 0.08/0.26 cnf(s99, plain, spl0_20, inference(rat,[],[s68,s98,s87,s97])).
% 0.08/0.26 cnf(s100, plain, $false, inference(rat,[],[s43,s96,s99,s98])).
% 0.08/0.26 thf(f611,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(avatar_sat_refutation,[],[s100])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (3078624)------------------------------
% 0.08/0.26 % (3078624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3078624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3078624)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3078624)Termination reason: Refutation
% 0.08/0.26 % (3078624)Time elapsed: 0.010 s
% 0.08/0.26 % (3078624)Peak memory usage: 13 MB
% 0.08/0.26 % (3078624)Instructions burned: 27 (million)
% 0.08/0.26 % (3078613)Success in time 0.042 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------