%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO276^5 : 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 : n002.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 08:49:39 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO276^5 : 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 : n002.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 16:45:23 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
% 0.20/0.29 % (1532866)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1532877)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=50685541_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (1532878)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1532878)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1511899263:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1532879)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1873217650:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1532880)dis+10_1_sil=32000:sp=arity:random_seed=1266634641:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1532882)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3234148726:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (1532878)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (1532881)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3638376159:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1532878)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (1532883)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2642075349:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (1532881)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (1532887)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3713332762:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (1532880) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532880"...
% 0.20/0.29 % (1532878) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532878"...
% 0.20/0.29 % (1532882) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532882"...
% 0.20/0.29 % (1532881) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532881"...
% 0.20/0.29 % (1532879) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532879"...
% 0.20/0.29 % (1532880)...printing done.
% 0.20/0.29 % (1532878)...printing done.
% 0.20/0.29 % (1532882)...printing done.
% 0.20/0.29 % (1532883) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1532866-1532883"...
% 0.20/0.29 % (1532881)...printing done.
% 0.20/0.29 % (1532880)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_1, type, cP: ($i > $o)).
% 0.20/0.29 thf(func_def_3, type, s: ($i > $i)).
% 0.20/0.29 thf(func_def_8, type, sK0: (($i > $i > $o) > $i)).
% 0.20/0.29 thf(func_def_9, type, sK1: (($i > $i > $o) > $i)).
% 0.20/0.29 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ((cP @ n) & ! [X0 : ($i > $i > $o)] : ((! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2))) & (X0 @ cO @ cO)) => (X0 @ n @ m))) => (cP @ m)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_SV_I2)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~(((cP @ n) & ! [X0 : ($i > $i > $o)] : ((! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2))) & (X0 @ cO @ cO)) => (X0 @ n @ m))) => (cP @ m))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~(((cP @ n) & ! [X0 : ($i > $i > $o)] : ((! [X1 : $i,X2 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2))) & (X0 @ cO @ cO)) => (X0 @ n @ m))) => (cP @ m))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~(((((cP @ n)) = $true) & ! [X0 : ($i > $i > $o)] : ((! [X1 : $i,X2 : $i] : ((((X0 @ X1 @ X2)) = $true) => (((X0 @ (s @ X1) @ (s @ X2))) = $true)) & (((X0 @ cO @ cO)) = $true)) => (((X0 @ n @ m)) = $true))) => (((cP @ m)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 (((cP @ m)) != $true) & ((((cP @ n)) = $true) & ! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | (? [X1 : $i,X2 : $i] : ((((X0 @ (s @ X1) @ (s @ X2))) != $true) & (((X0 @ X1 @ X2)) = $true)) | (((X0 @ cO @ cO)) != $true))))),
% 0.20/0.29 inference(ennf_transformation,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 (((cP @ m)) != $true) & (((cP @ n)) = $true) & ! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | ? [X1 : $i,X2 : $i] : ((((X0 @ (s @ X1) @ (s @ X2))) != $true) & (((X0 @ X1 @ X2)) = $true)) | (((X0 @ cO @ cO)) != $true))),
% 0.20/0.29 inference(flattening,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 (((cP @ m)) != $true) & (((cP @ n)) = $true) & ! [X0 : ($i > $i > $o)] : ((((X0 @ n @ m)) = $true) | (($true != ((X0 @ (s @ (sK0 @ X0)) @ (s @ (sK1 @ X0))))) & ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0))))) | (((X0 @ cO @ cO)) != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $i > $o)] : ((((X0 @ cO @ cO)) != $true) | ($true = ((X0 @ (sK0 @ X0) @ (sK1 @ X0)))) | (((X0 @ n @ m)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ( ! [X0 : ($i > $i > $o)] : (($true != ((X0 @ (s @ (sK0 @ X0)) @ (s @ (sK1 @ X0))))) | (((X0 @ n @ m)) = $true) | (((X0 @ cO @ cO)) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 (((cP @ n)) = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 (((cP @ m)) != $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f7])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ cO @ cO))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))))) | ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))) @ n @ m)))),
% 0.20/0.29 inference(primitive_instantiation,[],[f8])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ($true != ((cO = cO))) | ($true = (((sK0 @ =) = (sK1 @ =)))) | ($true = ((n = m)))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f14])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 (cO != cO) | ($true = (((sK0 @ =) = (sK1 @ =)))) | ($true = ((n = m)))),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f41])).
% 0.20/0.29 thf(f43,plain,(
% 0.20/0.29 (cO != cO) | (((sK1 @ =)) = ((sK0 @ =))) | ($true = ((n = m)))),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f42])).
% 0.20/0.29 thf(f44,plain,(
% 0.20/0.29 (cO != cO) | (((sK1 @ =)) = ((sK0 @ =))) | (n = m)),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f43])).
% 0.20/0.29 thf(f45,plain,(
% 0.20/0.29 (((sK1 @ =)) = ((sK0 @ =))) | (n = m)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f44])).
% 0.20/0.29 thf(f47,definition,(
% 0.20/0.29 spl2_1 <=> (n = m)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.20/0.29 thf(f49,plain,(
% 0.20/0.29 (n = m) | ~spl2_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f47])).
% 0.20/0.29 thf(f51,definition,(
% 0.20/0.29 spl2_2 <=> (((sK1 @ =)) = ((sK0 @ =)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 (((sK1 @ =)) = ((sK0 @ =))) | ~spl2_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f51])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 spl2_1 | spl2_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f45,f51,f47])).
% 0.20/0.29 thf(f80,plain,(
% 0.20/0.29 ($true != (((s @ (sK0 @ =)) = (s @ (sK0 @ =))))) | ($true = ((n = m))) | ($true != ((cO = cO))) | ~spl2_2),
% 0.20/0.29 inference(constrained_superposition,[],[f9,f53])).
% 0.20/0.29 thf(f92,plain,(
% 0.20/0.29 (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | ($true = ((n = m))) | ($true != ((cO = cO))) | ~spl2_2),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f80])).
% 0.20/0.29 thf(f93,plain,(
% 0.20/0.29 (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | (n = m) | ($true != ((cO = cO))) | ~spl2_2),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f92])).
% 0.20/0.29 thf(f94,plain,(
% 0.20/0.29 (((s @ (sK0 @ =))) != ((s @ (sK0 @ =)))) | (n = m) | (cO != cO) | ~spl2_2),
% 0.20/0.29 inference(equality_proxy_clausification,[],[f93])).
% 0.20/0.29 thf(f95,plain,(
% 0.20/0.29 (n = m) | ~spl2_2),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f94])).
% 0.20/0.29 thf(f116,plain,(
% 0.20/0.29 spl2_1 | ~spl2_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f95,f51,f47])).
% 0.20/0.29 thf(f119,plain,(
% 0.20/0.29 (((cP @ m)) = $true) | ~spl2_1),
% 0.20/0.29 inference(constrained_superposition,[],[f10,f49])).
% 0.20/0.29 thf(f120,plain,(
% 0.20/0.29 $false | ~spl2_1),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f119,f11])).
% 0.20/0.29 thf(f121,plain,(
% 0.20/0.29 ~spl2_1),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f120])).
% 0.20/0.29 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f54])).
% 0.20/0.29 cnf(s2, plain, spl2_1 | ~spl2_2, inference(sat_conversion,[],[f116])).
% 0.20/0.29 cnf(s4, plain, ~spl2_1, inference(sat_conversion,[],[f121])).
% 0.20/0.29 cnf(s5, plain, ~spl2_2, inference(rat,[],[s2,s4])).
% 0.20/0.29 cnf(s6, plain, $false, inference(rat,[],[s1,s5,s4])).
% 0.20/0.29 thf(f122,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s6])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (1532880)------------------------------
% 0.20/0.29 % (1532880)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1532880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1532880)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1532880)Termination reason: Refutation
% 0.20/0.29 % (1532880)Time elapsed: 0.005 s
% 0.20/0.29 % (1532880)Peak memory usage: 12 MB
% 0.20/0.29 % (1532880)Instructions burned: 7 (million)
% 0.20/0.29 % (1532866)Success in time 0.046 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------