%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:49:43 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO311^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n003.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 16:46:44 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.30 % (2732932)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (2732937)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=799666900_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (2732938)% WARNING: option uhcvi not known.
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (2732938)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2943063878:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (2732939)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2080031244:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (2732938)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (2732938)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.30 % (2732939) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2732932-2732939"...
% 0.21/0.30 % (2732938) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2732932-2732938"...
% 0.21/0.30 % (2732939)...printing done.
% 0.21/0.30 % (2732938)...printing done.
% 0.21/0.30 % (2732939)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_3, type, vIMP: ($o > $o > $o)).
% 0.21/0.30 thf(func_def_4, type, sK0: ($o > $o)).
% 0.21/0.30 thf(func_def_5, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.30 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.21/0.30 thf(func_def_12, type, vAND: ($o > $o > $o)).
% 0.21/0.30 thf(f1,conjecture,(
% 0.21/0.30 ! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & ~(X0 @ $false @ $false) & (X0 @ $true @ $true))),
% 0.21/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cOMEGA_EXAMPLE2)).
% 0.21/0.30 thf(f2,negated_conjecture,(
% 0.21/0.30 ~(! [X1 : ($o > $o)] : ((X1 @ $true) <=> (X1 @ $true => $true)) & ? [X0 : ($o > $o > $o)] : (~(X0 @ $true @ $false) & ~(X0 @ $false @ $true) & ~(X0 @ $false @ $false) & (X0 @ $true @ $true)))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.30 thf(f3,plain,(
% 0.21/0.30 ~(! [X0 : ($o > $o)] : ((X0 @ $true) <=> (X0 @ $true => $true)) & ? [X1 : ($o > $o > $o)] : (~(X1 @ $true @ $false) & ~(X1 @ $false @ $true) & ~(X1 @ $false @ $false) & (X1 @ $true @ $true)))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f4,plain,(
% 0.21/0.30 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : (~ ($true = ((X1 @ $true @ $false))) & ~ ($true = ((X1 @ $false @ $true))) & ~ ($true = ((X1 @ $false @ $false))) & ($true = ((X1 @ $true @ $true)))))),
% 0.21/0.30 inference(fool_elimination,[],[f3])).
% 0.21/0.30 thf(f5,plain,(
% 0.21/0.30 ~(! [X0 : ($o > $o)] : (((X0 @ $true)) = ((X0 @ ($true => $true)))) & ? [X1 : ($o > $o > $o)] : (($true != ((X1 @ $true @ $false))) & ($true != ((X1 @ $false @ $true))) & ($true != ((X1 @ $false @ $false))) & ($true = ((X1 @ $true @ $true)))))),
% 0.21/0.30 inference(flattening,[],[f4])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ? [X0 : ($o > $o)] : (((X0 @ $true)) != ((X0 @ ($true => $true)))) | ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))))),
% 0.21/0.30 inference(ennf_transformation,[],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 (((sK0 @ $true)) != ((sK0 @ ($true => $true)))) | ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : ((((sK0 @ $true)) != ((sK0 @ ($true => $true)))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f7])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true = ((sK0 @ ($true => $true))))) )),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f8])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($false = ((sK0 @ ($true => $true))))) )),
% 0.21/0.30 inference(xor_proxy_clausification,[],[f8])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($false = ((sK0 @ $true)))) )),
% 0.21/0.30 inference(boolean_simplification,[],[f12])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($false = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f13])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true = ((sK0 @ $true)))) )),
% 0.21/0.30 inference(boolean_simplification,[],[f11])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true = ((sK0 @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f15])).
% 0.21/0.30 thf(f30,definition,(
% 0.21/0.30 spl1_5 <=> ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true != ((X1 @ $true @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true = ((X1 @ $false @ $true))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.21/0.30 thf(f31,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true != ((X1 @ $true @ $true))) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $false))) | ($true = ((X1 @ $false @ $true)))) ) | ~spl1_5),
% 0.21/0.30 inference(avatar_component_clause,[],[f30])).
% 0.21/0.30 thf(f33,definition,(
% 0.21/0.30 spl1_6 <=> ($false = ((sK0 @ $true)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition])).
% 0.21/0.30 thf(f35,plain,(
% 0.21/0.30 ($false = ((sK0 @ $true))) | ~spl1_6),
% 0.21/0.30 inference(avatar_component_clause,[],[f33])).
% 0.21/0.30 thf(f36,plain,(
% 0.21/0.30 spl1_5 | spl1_6),
% 0.21/0.30 inference(avatar_split_clause,[],[f14,f33,f30])).
% 0.21/0.30 thf(f196,plain,(
% 0.21/0.30 ($true != (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $true @ $true))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $true @ $false))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $false @ $false))) | ($true = (((^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ $false @ $true))) | ~spl1_5),
% 0.21/0.30 inference(primitive_instantiation,[],[f31])).
% 0.21/0.30 thf(f218,plain,(
% 0.21/0.30 ($true != (($true & $true))) | ($true = (($true & $false))) | ($true = (($false & $false))) | ($true = (($false & $true))) | ~spl1_5),
% 0.21/0.30 inference(beta-eta_normalization,[],[f196])).
% 0.21/0.30 thf(f219,plain,(
% 0.21/0.30 ($true = $false) | ($true = (($true & $false))) | ($true = (($false & $false))) | ($true = (($false & $true))) | ($true = $false) | ~spl1_5),
% 0.21/0.30 inference(and_proxy_clausification,[],[f218])).
% 0.21/0.30 thf(f220,plain,(
% 0.21/0.30 ($true = $false) | ($true = $false) | ($true = (($false & $false))) | ($true = (($false & $true))) | ($true = $false) | ~spl1_5),
% 0.21/0.30 inference(and_proxy_clausification,[],[f219])).
% 0.21/0.30 thf(f232,plain,(
% 0.21/0.30 ($true = $false) | ($true = $false) | ($true = $false) | ($true = (($false & $true))) | ($true = $false) | ~spl1_5),
% 0.21/0.30 inference(and_proxy_clausification,[],[f220])).
% 0.21/0.30 thf(f241,plain,(
% 0.21/0.30 ($true = $false) | ($true = $false) | ($true = $false) | ($true = $false) | ($true = $false) | ~spl1_5),
% 0.21/0.30 inference(and_proxy_clausification,[],[f232])).
% 0.21/0.30 thf(f242,plain,(
% 0.21/0.30 ($true = $false) | ~spl1_5),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f241])).
% 0.21/0.30 thf(f243,plain,(
% 0.21/0.30 $false | ~spl1_5),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f242])).
% 0.21/0.30 thf(f244,plain,(
% 0.21/0.30 ~spl1_5),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f243])).
% 0.21/0.30 thf(f277,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true = $false) | ($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) ) | ~spl1_6),
% 0.21/0.30 inference(forward_demodulation,[],[f16,f35])).
% 0.21/0.30 thf(f278,plain,(
% 0.21/0.30 ( ! [X1 : ($o > $o > $o)] : (($true = ((X1 @ $true @ $false))) | ($true = ((X1 @ $false @ $true))) | ($true = ((X1 @ $false @ $false))) | ($true != ((X1 @ $true @ $true)))) ) | ~spl1_6),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f277])).
% 0.21/0.30 thf(f279,plain,(
% 0.21/0.30 spl1_5 | ~spl1_6),
% 0.21/0.30 inference(avatar_split_clause,[],[f278,f33,f30])).
% 0.21/0.30 cnf(s7, plain, spl1_5 | spl1_6, inference(sat_conversion,[],[f36])).
% 0.21/0.30 cnf(s48, plain, ~spl1_5, inference(sat_conversion,[],[f244])).
% 0.21/0.30 cnf(s54, plain, spl1_5 | ~spl1_6, inference(sat_conversion,[],[f279])).
% 0.21/0.30 cnf(s55, plain, ~spl1_6, inference(rat,[],[s54,s48])).
% 0.21/0.30 cnf(s56, plain, $false, inference(rat,[],[s7,s55,s48])).
% 0.21/0.30 thf(f280,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s56])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (2732939)------------------------------
% 0.21/0.30 % (2732939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2732939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2732939)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2732939)Termination reason: Refutation
% 0.21/0.30 % (2732939)Time elapsed: 0.005 s
% 0.21/0.30 % (2732939)Peak memory usage: 12 MB
% 0.21/0.30 % (2732939)Instructions burned: 7 (million)
% 0.21/0.30 % (2732932)Success in time 0.049 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------