%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO500^1 : 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 : n001.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 08:50:20 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO500^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:17:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.28 % (1537207)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (1537213)% WARNING: option uhcvi not known.
% 0.21/0.28 % (1537212)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2550135031_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (1537213)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1994528937:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (1537214)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1840901907:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (1537213)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % Exception at run slice level
% 0.21/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.28 % (1537213)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28 % (1537213) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1537207-1537213"...
% 0.21/0.28 % (1537214) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1537207-1537214"...
% 0.21/0.28 % (1537213)...printing done.
% 0.21/0.28 % (1537213)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, f: ($o > $o)).
% 0.21/0.28 thf(func_def_1, type, x: $o).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 (((f @ (f @ (f @ x)))) = ((f @ x)))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~ (((f @ (f @ (f @ x)))) = ((f @ x)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 (((f @ x)) != ((f @ (f @ (f @ x)))))),
% 0.21/0.28 inference(flattening,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 (((f @ x)) != ((f @ (f @ (f @ x)))))),
% 0.21/0.28 inference(cnf_transformation,[],[f3])).
% 0.21/0.28 thf(f6,definition,(
% 0.21/0.28 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.28 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (((f @ x)) = $true) | (((f @ (f @ (f @ x)))) = $true)),
% 0.21/0.28 inference(xor_proxy_clausification,[],[f4])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (((f @ x)) = $false) | (((f @ (f @ (f @ x)))) = $false)),
% 0.21/0.28 inference(xor_proxy_clausification,[],[f4])).
% 0.21/0.28 thf(f10,definition,(
% 0.21/0.28 spl0_1 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 (((f @ (f @ (f @ x)))) = $false) | ~spl0_1),
% 0.21/0.28 inference(avatar_component_clause,[],[f10])).
% 0.21/0.28 thf(f14,definition,(
% 0.21/0.28 spl0_2 <=> (((f @ x)) = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 (((f @ x)) != $false) | spl0_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f14])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 (((f @ x)) = $false) | ~spl0_2),
% 0.21/0.28 inference(avatar_component_clause,[],[f14])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 spl0_1 | spl0_2),
% 0.21/0.28 inference(avatar_split_clause,[],[f8,f14,f10])).
% 0.21/0.28 thf(f19,definition,(
% 0.21/0.28 spl0_3 <=> (((f @ (f @ (f @ x)))) = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 (((f @ (f @ (f @ x)))) = $true) | ~spl0_3),
% 0.21/0.28 inference(avatar_component_clause,[],[f19])).
% 0.21/0.28 thf(f23,definition,(
% 0.21/0.28 spl0_4 <=> (((f @ x)) = $true)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (((f @ x)) = $true) | ~spl0_4),
% 0.21/0.28 inference(avatar_component_clause,[],[f23])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 spl0_3 | spl0_4),
% 0.21/0.28 inference(avatar_split_clause,[],[f7,f23,f19])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ($true = ((f @ (f @ $false)))) | (~spl0_2 | ~spl0_3)),
% 0.21/0.28 inference(forward_demodulation,[],[f21,f16])).
% 0.21/0.28 thf(f39,definition,(
% 0.21/0.28 spl0_5 <=> (x = $false)),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.21/0.28 thf(f40,plain,(
% 0.21/0.28 (x != $false) | spl0_5),
% 0.21/0.28 inference(avatar_component_clause,[],[f39])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 (x = $false) | ~spl0_5),
% 0.21/0.28 inference(avatar_component_clause,[],[f39])).
% 0.21/0.28 thf(f43,definition,(
% 0.21/0.28 spl0_6 <=> ($false = ((f @ $true)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.21/0.28 thf(f44,plain,(
% 0.21/0.28 ($false != ((f @ $true))) | spl0_6),
% 0.21/0.28 inference(avatar_component_clause,[],[f43])).
% 0.21/0.28 thf(f45,plain,(
% 0.21/0.28 ($false = ((f @ $true))) | ~spl0_6),
% 0.21/0.28 inference(avatar_component_clause,[],[f43])).
% 0.21/0.28 thf(f47,plain,(
% 0.21/0.28 ($false != ((f @ $true))) | (x = $false) | spl0_2),
% 0.21/0.28 inference(constrained_superposition,[],[f15,f6])).
% 0.21/0.28 thf(f55,plain,(
% 0.21/0.28 ($false = ((f @ $true))) | (((f @ (f @ x))) = $false) | ~spl0_1),
% 0.21/0.28 inference(constrained_superposition,[],[f12,f6])).
% 0.21/0.28 thf(f60,plain,(
% 0.21/0.28 (((f @ (f @ x))) = $false) | (~spl0_1 | spl0_6)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f55,f44])).
% 0.21/0.28 thf(f67,plain,(
% 0.21/0.28 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.21/0.28 inference(forward_demodulation,[],[f21,f12])).
% 0.21/0.28 thf(f68,plain,(
% 0.21/0.28 $false | (~spl0_1 | ~spl0_3)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f67])).
% 0.21/0.28 thf(f69,plain,(
% 0.21/0.28 ~spl0_1 | ~spl0_3),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f68])).
% 0.21/0.28 thf(f73,plain,(
% 0.21/0.28 ($false = ((f @ (f @ $true)))) | (~spl0_1 | ~spl0_4)),
% 0.21/0.28 inference(constrained_superposition,[],[f12,f25])).
% 0.21/0.28 thf(f85,plain,(
% 0.21/0.28 ($false = ((f @ $true))) | (~spl0_1 | ~spl0_4 | spl0_6)),
% 0.21/0.28 inference(forward_demodulation,[],[f60,f25])).
% 0.21/0.28 thf(f86,plain,(
% 0.21/0.28 $false | (~spl0_1 | ~spl0_4 | spl0_6)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f85,f44])).
% 0.21/0.28 thf(f87,plain,(
% 0.21/0.28 ~spl0_1 | ~spl0_4 | spl0_6),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f86])).
% 0.21/0.28 thf(f90,plain,(
% 0.21/0.28 ($false = ((f @ $false))) | (~spl0_2 | ~spl0_5)),
% 0.21/0.28 inference(forward_demodulation,[],[f16,f41])).
% 0.21/0.28 thf(f95,plain,(
% 0.21/0.28 ($true = ((f @ $false))) | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 0.21/0.28 inference(forward_demodulation,[],[f27,f90])).
% 0.21/0.28 thf(f96,plain,(
% 0.21/0.28 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 0.21/0.28 inference(forward_demodulation,[],[f95,f90])).
% 0.21/0.28 thf(f97,plain,(
% 0.21/0.28 $false | (~spl0_2 | ~spl0_3 | ~spl0_5)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f96])).
% 0.21/0.28 thf(f98,plain,(
% 0.21/0.28 ~spl0_2 | ~spl0_3 | ~spl0_5),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f97])).
% 0.21/0.28 thf(f101,plain,(
% 0.21/0.28 ($false = ((f @ $true))) | (x = $false) | ~spl0_2),
% 0.21/0.28 inference(constrained_superposition,[],[f16,f6])).
% 0.21/0.28 thf(f104,plain,(
% 0.21/0.28 ($false = ((f @ $true))) | (~spl0_2 | spl0_5)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f101,f40])).
% 0.21/0.28 thf(f105,plain,(
% 0.21/0.28 spl0_6 | ~spl0_2 | spl0_5),
% 0.21/0.28 inference(avatar_split_clause,[],[f104,f39,f14,f43])).
% 0.21/0.28 thf(f110,plain,(
% 0.21/0.28 ($true = ((f @ $true))) | ($false = ((f @ $false))) | (~spl0_2 | ~spl0_3)),
% 0.21/0.28 inference(constrained_superposition,[],[f27,f6])).
% 0.21/0.28 thf(f111,plain,(
% 0.21/0.28 ($true = $false) | ($false = ((f @ $false))) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.28 inference(forward_demodulation,[],[f110,f45])).
% 0.21/0.28 thf(f112,plain,(
% 0.21/0.28 ($false = ((f @ $false))) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f111])).
% 0.21/0.28 thf(f115,plain,(
% 0.21/0.28 ($true = ((f @ $false))) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.28 inference(constrained_superposition,[],[f27,f112])).
% 0.21/0.28 thf(f117,plain,(
% 0.21/0.28 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.28 inference(forward_demodulation,[],[f115,f112])).
% 0.21/0.28 thf(f118,plain,(
% 0.21/0.28 $false | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f117])).
% 0.21/0.28 thf(f119,plain,(
% 0.21/0.28 ~spl0_2 | ~spl0_3 | ~spl0_6),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f118])).
% 0.21/0.28 thf(f123,plain,(
% 0.21/0.28 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.21/0.28 inference(forward_demodulation,[],[f25,f16])).
% 0.21/0.28 thf(f124,plain,(
% 0.21/0.28 $false | (~spl0_2 | ~spl0_4)),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f123])).
% 0.21/0.28 thf(f125,plain,(
% 0.21/0.28 ~spl0_2 | ~spl0_4),
% 0.21/0.28 inference(avatar_contradiction_clause,[],[f124])).
% 0.21/0.28 thf(f133,plain,(
% 0.21/0.28 ($false = ((f @ $false))) | (~spl0_1 | ~spl0_4 | ~spl0_6)),
% 0.21/0.28 inference(forward_demodulation,[],[f73,f45])).
% 0.21/0.28 thf(f134,plain,(
% 0.21/0.28 (x = $false) | (spl0_2 | ~spl0_6)),
% 0.21/0.28 inference(forward_subsumption_resolution,[],[f47,f45])).
% 0.21/0.28 thf(f141,definition,(
% 0.21/0.28 spl0_10 <=> ($false = ((f @ $false)))),
% 0.21/0.28 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.21/0.28 thf(f146,plain,(
% 0.21/0.28 spl0_10 | ~spl0_1 | ~spl0_4 | ~spl0_6),
% 0.21/0.28 inference(avatar_split_clause,[],[f133,f43,f23,f10,f141])).
% 0.21/0.28 thf(f147,plain,(
% 0.21/0.28 spl0_5 | spl0_2 | ~spl0_6),
% 0.21/0.28 inference(avatar_split_clause,[],[f134,f43,f14,f39])).
% 0.21/0.28 thf(f150,plain,(
% 0.21/0.28 ($false != ((f @ $false))) | (spl0_2 | ~spl0_5)),
% 0.21/0.28 inference(forward_demodulation,[],[f15,f41])).
% 0.21/0.28 thf(f151,plain,(
% 0.21/0.28 ~spl0_10 | spl0_2 | ~spl0_5),
% 0.21/0.28 inference(avatar_split_clause,[],[f150,f39,f14,f141])).
% 0.21/0.28 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f17])).
% 0.21/0.28 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f26])).
% 0.21/0.28 cnf(s6, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f69])).
% 0.21/0.28 cnf(s8, plain, ~spl0_1 | ~spl0_4 | spl0_6, inference(sat_conversion,[],[f87])).
% 0.21/0.28 cnf(s9, plain, ~spl0_2 | ~spl0_3 | ~spl0_5, inference(sat_conversion,[],[f98])).
% 0.21/0.28 cnf(s11, plain, ~spl0_2 | spl0_5 | spl0_6, inference(sat_conversion,[],[f105])).
% 0.21/0.28 cnf(s12, plain, ~spl0_2 | ~spl0_3 | ~spl0_6, inference(sat_conversion,[],[f119])).
% 0.21/0.28 cnf(s13, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f125])).
% 0.21/0.28 cnf(s18, plain, ~spl0_1 | ~spl0_4 | ~spl0_6 | spl0_10, inference(sat_conversion,[],[f146])).
% 0.21/0.28 cnf(s19, plain, spl0_2 | spl0_5 | ~spl0_6, inference(sat_conversion,[],[f147])).
% 0.21/0.28 cnf(s20, plain, spl0_2 | ~spl0_5 | ~spl0_10, inference(sat_conversion,[],[f151])).
% 0.21/0.28 cnf(s21, plain, ~spl0_3 | ~spl0_2, inference(rat,[],[s11,s9,s12])).
% 0.21/0.28 cnf(s22, plain, ~spl0_2, inference(rat,[],[s21,s2,s13])).
% 0.21/0.28 cnf(s23, plain, spl0_1, inference(rat,[],[s1,s22])).
% 0.21/0.28 cnf(s24, plain, ~spl0_3, inference(rat,[],[s6,s23])).
% 0.21/0.28 cnf(s25, plain, spl0_4, inference(rat,[],[s2,s24])).
% 0.21/0.28 cnf(s26, plain, spl0_6, inference(rat,[],[s8,s23,s25])).
% 0.21/0.28 cnf(s27, plain, spl0_10, inference(rat,[],[s18,s25,s23,s26])).
% 0.21/0.28 cnf(s28, plain, spl0_5, inference(rat,[],[s19,s22,s26])).
% 0.21/0.28 cnf(s29, plain, $false, inference(rat,[],[s20,s22,s27,s28])).
% 0.21/0.28 thf(f152,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(avatar_sat_refutation,[],[s29])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (1537213)------------------------------
% 0.21/0.28 % (1537213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1537213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1537213)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1537213)Termination reason: Refutation
% 0.21/0.28 % (1537213)Time elapsed: 0.005 s
% 0.21/0.28 % (1537213)Peak memory usage: 13 MB
% 0.21/0.28 % (1537213)Instructions burned: 6 (million)
% 0.21/0.28 % (1537207)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------