%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO222^5 : 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 : n008.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 08:49:33 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO222^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:40:40 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.10/0.26 % (3395565)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (3395576)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1088234065:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.10/0.26 % (3395576)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (3395572)% WARNING: option uhcvi not known.
% 0.10/0.26 % (3395573)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1606528887:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.10/0.26 % (3395571)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1425279982_3000 on theBenchmark for (3000ds/0Mi)
% 0.10/0.26 % (3395572)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1727682874:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.10/0.26 % (3395575)dis+10_1_sil=32000:sp=arity:random_seed=3272754839:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.10/0.26 % (3395578)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2799406907:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.10/0.26 % Exception at run slice level
% 0.10/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.10/0.26 % (3395572)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.26 % (3395577)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3904681751:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.10/0.26 % (3395572)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.26 % (3395578) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3395565-3395578"...
% 0.10/0.26 % (3395578)...printing done.
% 0.10/0.26 % (3395573) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3395565-3395573"...
% 0.10/0.26 % (3395578)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% 0.10/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.10/0.26 thf(func_def_0, type, f: ($i > $i)).
% 0.10/0.26 thf(func_def_2, type, cP: ($i > $o)).
% 0.10/0.26 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 0.10/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.10/0.26 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.10/0.26 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.10/0.26 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.10/0.26 thf(f1,conjecture,(
% 0.10/0.26 ? [X0 : ($i > $o)] : (((! [X1 : $i,X2 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2)) & (cP @ a)) => ? [X3 : $i] : (X0 @ X3)) & ! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)))),
% 0.10/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM115A)).
% 0.10/0.26 thf(f2,negated_conjecture,(
% 0.10/0.26 ~ ? [X0 : ($i > $o)] : (((! [X1 : $i,X2 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2)) & (cP @ a)) => ? [X3 : $i] : (X0 @ X3)) & ! [X1 : $i] : ((X0 @ (f @ X1)) => (cP @ X1)))),
% 0.10/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.10/0.26 thf(f3,plain,(
% 0.10/0.26 ~ ? [X0 : ($i > $o)] : (((! [X1 : $i,X2 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2)) & (cP @ a)) => ? [X3 : $i] : (X0 @ X3)) & ! [X4 : $i] : ((X0 @ (f @ X4)) => (cP @ X4)))),
% 0.10/0.26 inference(rectify,[],[f2])).
% 0.10/0.26 thf(f4,plain,(
% 0.10/0.26 ~ ? [X0 : ($i > $o)] : (((! [X1 : $i,X2 : $i] : ((((f @ X1)) = ((f @ X2))) => (X1 = X2)) & (((cP @ a)) = $true)) => ? [X3 : $i] : (((X0 @ X3)) = $true)) & ! [X4 : $i] : ((((X0 @ (f @ X4))) = $true) => (((cP @ X4)) = $true)))),
% 0.10/0.26 inference(fool_elimination,[],[f3])).
% 0.10/0.26 thf(f5,plain,(
% 0.10/0.26 ! [X0 : ($i > $o)] : ((! [X3 : $i] : (((X0 @ X3)) != $true) & (! [X1 : $i,X2 : $i] : ((X1 = X2) | (((f @ X1)) != ((f @ X2)))) & (((cP @ a)) = $true))) | ? [X4 : $i] : ((((cP @ X4)) != $true) & (((X0 @ (f @ X4))) = $true)))),
% 0.10/0.26 inference(ennf_transformation,[],[f4])).
% 0.10/0.26 thf(f6,plain,(
% 0.10/0.26 ! [X0 : ($i > $o)] : ((! [X3 : $i] : (((X0 @ X3)) != $true) & ! [X1 : $i,X2 : $i] : ((X1 = X2) | (((f @ X1)) != ((f @ X2)))) & (((cP @ a)) = $true)) | ? [X4 : $i] : ((((cP @ X4)) != $true) & (((X0 @ (f @ X4))) = $true)))),
% 0.10/0.26 inference(flattening,[],[f5])).
% 0.10/0.26 thf(f7,plain,(
% 0.10/0.26 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ($true != ((X0 @ X1))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X2)) != ((f @ X3)))) & (((cP @ a)) = $true)) | ? [X4 : $i] : ((((cP @ X4)) != $true) & (((X0 @ (f @ X4))) = $true)))),
% 0.10/0.26 inference(rectify,[],[f6])).
% 0.10/0.26 thf(f8,plain,(
% 0.10/0.26 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ($true != ((X0 @ X1))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X2)) != ((f @ X3)))) & (((cP @ a)) = $true)) | (($true != ((cP @ (sK0 @ X0)))) & ($true = ((X0 @ (f @ (sK0 @ X0)))))))),
% 0.10/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0)],[f7])).
% 0.10/0.26 thf(f9,plain,(
% 0.10/0.26 ( ! [X0 : ($i > $o)] : ((((cP @ a)) = $true) | ($true = ((X0 @ (f @ (sK0 @ X0)))))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f8])).
% 0.10/0.26 thf(f11,plain,(
% 0.10/0.26 ( ! [X2 : $i,X3 : $i,X0 : ($i > $o)] : ((X2 = X3) | (((f @ X2)) != ((f @ X3))) | ($true = ((X0 @ (f @ (sK0 @ X0)))))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f8])).
% 0.10/0.26 thf(f13,plain,(
% 0.10/0.26 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ X1))) | ($true = ((X0 @ (f @ (sK0 @ X0)))))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f8])).
% 0.10/0.26 thf(f14,plain,(
% 0.10/0.26 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((cP @ (sK0 @ X0)))) | ($true != ((X0 @ X1)))) )),
% 0.10/0.26 inference(cnf_transformation,[],[f8])).
% 0.10/0.26 thf(f18,definition,(
% 0.10/0.26 spl1_1 <=> ! [X0 : ($i > $o)] : ($true = ((X0 @ (f @ (sK0 @ X0)))))),
% 0.10/0.26 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.10/0.26 thf(f19,plain,(
% 0.10/0.26 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (f @ (sK0 @ X0)))))) ) | ~spl1_1),
% 0.10/0.26 inference(avatar_component_clause,[],[f18])).
% 0.10/0.26 thf(f21,definition,(
% 0.10/0.26 spl1_2 <=> (((cP @ a)) = $true)),
% 0.10/0.26 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.10/0.26 thf(f23,plain,(
% 0.10/0.26 (((cP @ a)) = $true) | ~spl1_2),
% 0.10/0.26 inference(avatar_component_clause,[],[f21])).
% 0.10/0.26 thf(f24,plain,(
% 0.10/0.26 spl1_1 | spl1_2),
% 0.10/0.26 inference(avatar_split_clause,[],[f9,f21,f18])).
% 0.10/0.26 thf(f30,definition,(
% 0.10/0.26 spl1_4 <=> ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X2)) != ((f @ X3))))),
% 0.10/0.26 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 0.10/0.26 thf(f31,plain,(
% 0.10/0.26 ( ! [X2 : $i,X3 : $i] : ((((f @ X2)) != ((f @ X3))) | (X2 = X3)) ) | ~spl1_4),
% 0.10/0.26 inference(avatar_component_clause,[],[f30])).
% 0.10/0.26 thf(f32,plain,(
% 0.10/0.26 spl1_1 | spl1_4),
% 0.10/0.26 inference(avatar_split_clause,[],[f11,f30,f18])).
% 0.10/0.26 thf(f35,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((f @ (sK0 @ (= @ X0)))) = X0)) )),
% 0.10/0.26 inference(leibniz_equality_elimination,[],[f13])).
% 0.10/0.26 thf(f69,plain,(
% 0.10/0.26 ( ! [X0 : $i,X1 : $i] : ((((f @ X1)) != X0) | (((sK0 @ (= @ X0))) = X1)) ) | ~spl1_4),
% 0.10/0.26 inference(constrained_superposition,[],[f31,f35])).
% 0.10/0.26 thf(f71,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((sK0 @ (= @ (f @ X0)))) = X0)) ) | ~spl1_4),
% 0.10/0.26 inference(equality_resolution,[],[f69])).
% 0.10/0.26 thf(f72,plain,(
% 0.10/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cP @ X0))) | ($true != (((f @ X0) = X1)))) ) | ~spl1_4),
% 0.10/0.26 inference(constrained_superposition,[],[f14,f71])).
% 0.10/0.26 thf(f73,plain,(
% 0.10/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cP @ X0))) | (((f @ X0)) != X1)) ) | ~spl1_4),
% 0.10/0.26 inference(equality_proxy_clausification,[],[f72])).
% 0.10/0.26 thf(f74,plain,(
% 0.10/0.26 ( ! [X0 : $i] : (($true != $true) | (((f @ a)) != X0)) ) | (~spl1_2 | ~spl1_4)),
% 0.10/0.26 inference(constrained_superposition,[],[f73,f23])).
% 0.10/0.26 thf(f77,plain,(
% 0.10/0.26 ( ! [X0 : $i] : ((((f @ a)) != X0)) ) | (~spl1_2 | ~spl1_4)),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f74])).
% 0.10/0.26 thf(f78,plain,(
% 0.10/0.26 $false | (~spl1_2 | ~spl1_4)),
% 0.10/0.26 inference(equality_resolution,[],[f77])).
% 0.10/0.26 thf(f79,plain,(
% 0.10/0.26 ~spl1_2 | ~spl1_4),
% 0.10/0.26 inference(avatar_contradiction_clause,[],[f78])).
% 0.10/0.26 thf(f82,plain,(
% 0.10/0.26 ($true = (((^[Y0 : $i]: ($false)) @ (f @ (sK0 @ (^[Y0 : $i]: ($false))))))) | ~spl1_1),
% 0.10/0.26 inference(primitive_instantiation,[],[f19])).
% 0.10/0.26 thf(f94,plain,(
% 0.10/0.26 ($true = $false) | ~spl1_1),
% 0.10/0.26 inference(beta-eta_normalization,[],[f82])).
% 0.10/0.26 thf(f95,plain,(
% 0.10/0.26 $false | ~spl1_1),
% 0.10/0.26 inference(trivial_inequality_removal,[],[f94])).
% 0.10/0.26 thf(f96,plain,(
% 0.10/0.26 ~spl1_1),
% 0.10/0.26 inference(avatar_contradiction_clause,[],[f95])).
% 0.10/0.26 cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f24])).
% 0.10/0.26 cnf(s3, plain, spl1_1 | spl1_4, inference(sat_conversion,[],[f32])).
% 0.10/0.26 cnf(s7, plain, ~spl1_2 | ~spl1_4, inference(sat_conversion,[],[f79])).
% 0.10/0.26 cnf(s9, plain, ~spl1_1, inference(sat_conversion,[],[f96])).
% 0.10/0.26 cnf(s11, plain, spl1_4, inference(rat,[],[s3,s9])).
% 0.10/0.26 cnf(s12, plain, ~spl1_2, inference(rat,[],[s7,s11])).
% 0.10/0.26 cnf(s14, plain, $false, inference(rat,[],[s1,s12,s9])).
% 0.10/0.26 thf(f98,plain,(
% 0.10/0.26 $false),
% 0.10/0.26 inference(avatar_sat_refutation,[],[s14])).
% 0.10/0.26 % SZS output end Proof for theBenchmark
% 0.10/0.26 % (3395578)------------------------------
% 0.10/0.26 % (3395578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3395578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3395578)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3395578)Termination reason: Refutation
% 0.10/0.26 % (3395578)Time elapsed: 0.005 s
% 0.10/0.26 % (3395578)Peak memory usage: 13 MB
% 0.10/0.26 % (3395578)Instructions burned: 6 (million)
% 0.10/0.26 % (3395565)Success in time 0.029 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------