%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO317^5 : 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 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO317^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:46:59 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.31 % (2733632)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (2733638)% WARNING: option uhcvi not known.
% 0.20/0.31 % (2733638)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=526444293:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (2733638)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2733638)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (2733637)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=110740499_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (2733639)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3599681781:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (2733640)dis+10_1_sil=32000:sp=arity:random_seed=3589729729:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (2733642)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=425918317:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2733643)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=198089620:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (2733641)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1439783064:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (2733641)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (2733657)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2851579569:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (2733639) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2733632-2733639"...
% 0.20/0.31 % (2733664)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2640332040:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (2733643) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2733632-2733643"...
% 0.20/0.31 % (2733639)...printing done.
% 0.20/0.31 % (2733643)...printing done.
% 0.20/0.31 % (2733639)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, cP: ($i > $o)).
% 0.20/0.31 thf(func_def_1, type, f: ($i > $i)).
% 0.20/0.31 thf(func_def_2, type, cEQ: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.20/0.31 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.31 thf(f1,conjecture,(
% 0.20/0.31 (! [X1 : $i,X2 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2)) & (cP @ a) & ! [X0 : $i,X1 : $i] : (((cP @ X0) & (cEQ @ X0 @ X1)) => (cP @ X1)) & ! [X0 : $i] : (cEQ @ X0 @ X0)) => ? [X3 : ($i > $o)] : (? [X2 : $i] : (X3 @ X2) & ! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0)))),
% 0.20/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM304)).
% 0.20/0.31 thf(f2,negated_conjecture,(
% 0.20/0.31 ~((! [X1 : $i,X2 : $i] : ((cEQ @ (f @ X1) @ (f @ X2)) => (cEQ @ X1 @ X2)) & (cP @ a) & ! [X0 : $i,X1 : $i] : (((cP @ X0) & (cEQ @ X0 @ X1)) => (cP @ X1)) & ! [X0 : $i] : (cEQ @ X0 @ X0)) => ? [X3 : ($i > $o)] : (? [X2 : $i] : (X3 @ X2) & ! [X0 : $i] : ((X3 @ (f @ X0)) => (cP @ X0))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.31 thf(f3,plain,(
% 0.20/0.31 ~((! [X0 : $i,X1 : $i] : ((cEQ @ (f @ X0) @ (f @ X1)) => (cEQ @ X0 @ X1)) & (cP @ a) & ! [X2 : $i,X3 : $i] : (((cP @ X2) & (cEQ @ X2 @ X3)) => (cP @ X3)) & ! [X4 : $i] : (cEQ @ X4 @ X4)) => ? [X5 : ($i > $o)] : (? [X6 : $i] : (X5 @ X6) & ! [X7 : $i] : ((X5 @ (f @ X7)) => (cP @ X7))))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f4,plain,(
% 0.20/0.31 ~((! [X0 : $i,X1 : $i] : ((((cEQ @ (f @ X0) @ (f @ X1))) = $true) => (((cEQ @ X0 @ X1)) = $true)) & (((cP @ a)) = $true) & ! [X2 : $i,X3 : $i] : (((((cP @ X2)) = $true) & (((cEQ @ X2 @ X3)) = $true)) => (((cP @ X3)) = $true)) & ! [X4 : $i] : (((cEQ @ X4 @ X4)) = $true)) => ? [X5 : ($i > $o)] : (? [X6 : $i] : (((X5 @ X6)) = $true) & ! [X7 : $i] : ((((X5 @ (f @ X7))) = $true) => (((cP @ X7)) = $true))))),
% 0.20/0.31 inference(fool_elimination,[],[f3])).
% 0.20/0.31 thf(f5,plain,(
% 0.20/0.31 ! [X5 : ($i > $o)] : (! [X6 : $i] : (((X5 @ X6)) != $true) | ? [X7 : $i] : ((((cP @ X7)) != $true) & (((X5 @ (f @ X7))) = $true))) & (! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ X1)) = $true) | (((cEQ @ (f @ X0) @ (f @ X1))) != $true)) & (((cP @ a)) = $true) & ! [X2 : $i,X3 : $i] : ((((cP @ X3)) = $true) | ((((cP @ X2)) != $true) | (((cEQ @ X2 @ X3)) != $true))) & ! [X4 : $i] : (((cEQ @ X4 @ X4)) = $true))),
% 0.20/0.31 inference(ennf_transformation,[],[f4])).
% 0.20/0.31 thf(f6,plain,(
% 0.20/0.31 ! [X5 : ($i > $o)] : (! [X6 : $i] : (((X5 @ X6)) != $true) | ? [X7 : $i] : ((((cP @ X7)) != $true) & (((X5 @ (f @ X7))) = $true))) & ! [X0 : $i,X1 : $i] : ((((cEQ @ X0 @ X1)) = $true) | (((cEQ @ (f @ X0) @ (f @ X1))) != $true)) & (((cP @ a)) = $true) & ! [X2 : $i,X3 : $i] : ((((cP @ X3)) = $true) | (((cP @ X2)) != $true) | (((cEQ @ X2 @ X3)) != $true)) & ! [X4 : $i] : (((cEQ @ X4 @ X4)) = $true)),
% 0.20/0.31 inference(flattening,[],[f5])).
% 0.20/0.31 thf(f7,plain,(
% 0.20/0.31 ! [X0 : ($i > $o)] : (! [X1 : $i] : ($true != ((X0 @ X1))) | ? [X2 : $i] : ((((cP @ X2)) != $true) & ($true = ((X0 @ (f @ X2)))))) & ! [X3 : $i,X4 : $i] : (($true = ((cEQ @ X3 @ X4))) | ($true != ((cEQ @ (f @ X3) @ (f @ X4))))) & (((cP @ a)) = $true) & ! [X5 : $i,X6 : $i] : (($true = ((cP @ X6))) | ($true != ((cP @ X5))) | ($true != ((cEQ @ X5 @ X6)))) & ! [X7 : $i] : ($true = ((cEQ @ X7 @ X7)))),
% 0.20/0.31 inference(rectify,[],[f6])).
% 0.20/0.31 thf(f8,plain,(
% 0.20/0.31 ! [X0 : ($i > $o)] : (! [X1 : $i] : ($true != ((X0 @ X1))) | (($true != ((cP @ (sK0 @ X0)))) & ($true = ((X0 @ (f @ (sK0 @ X0))))))) & ! [X3 : $i,X4 : $i] : (($true = ((cEQ @ X3 @ X4))) | ($true != ((cEQ @ (f @ X3) @ (f @ X4))))) & (((cP @ a)) = $true) & ! [X5 : $i,X6 : $i] : (($true = ((cP @ X6))) | ($true != ((cP @ X5))) | ($true != ((cEQ @ X5 @ X6)))) & ! [X7 : $i] : ($true = ((cEQ @ X7 @ X7)))),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f7])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 ( ! [X7 : $i] : (($true = ((cEQ @ X7 @ X7)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f10,plain,(
% 0.20/0.31 ( ! [X6 : $i,X5 : $i] : (($true != ((cEQ @ X5 @ X6))) | ($true != ((cP @ X5))) | ($true = ((cP @ X6)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f11,plain,(
% 0.20/0.31 (((cP @ a)) = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 ( ! [X3 : $i,X4 : $i] : (($true != ((cEQ @ (f @ X3) @ (f @ X4)))) | ($true = ((cEQ @ X3 @ X4)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ X1))) | ($true = ((X0 @ (f @ (sK0 @ X0)))))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f14,plain,(
% 0.20/0.31 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((cP @ (sK0 @ X0)))) | ($true != ((X0 @ X1)))) )),
% 0.20/0.31 inference(cnf_transformation,[],[f8])).
% 0.20/0.31 thf(f39,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((f @ (sK0 @ (= @ X0)))) = X0)) )),
% 0.20/0.31 inference(leibniz_equality_elimination,[],[f13])).
% 0.20/0.31 thf(f129,plain,(
% 0.20/0.31 ( ! [X0 : $i,X1 : $i] : (($true != ((cEQ @ (f @ X1) @ X0))) | ($true = ((cEQ @ X1 @ (sK0 @ (= @ X0)))))) )),
% 0.20/0.31 inference(constrained_superposition,[],[f12,f39])).
% 0.20/0.31 thf(f771,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | ($true = ((cEQ @ X0 @ (sK0 @ (= @ (f @ X0))))))) )),
% 0.20/0.31 inference(constrained_superposition,[],[f129,f9])).
% 0.20/0.31 thf(f792,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true = ((cEQ @ X0 @ (sK0 @ (= @ (f @ X0))))))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f771])).
% 0.20/0.31 thf(f896,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) != $true) | ($true = ((cP @ (sK0 @ (= @ (f @ X0))))))) )),
% 0.20/0.31 inference(constrained_superposition,[],[f10,f792])).
% 0.20/0.31 thf(f920,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((cP @ X0)) != $true) | ($true = ((cP @ (sK0 @ (= @ (f @ X0))))))) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f896])).
% 0.20/0.31 thf(f930,plain,(
% 0.20/0.31 ($true != $true) | ($true = ((cP @ (sK0 @ (= @ (f @ a))))))),
% 0.20/0.31 inference(constrained_superposition,[],[f920,f11])).
% 0.20/0.31 thf(f943,plain,(
% 0.20/0.31 ($true = ((cP @ (sK0 @ (= @ (f @ a))))))),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f930])).
% 0.20/0.31 thf(f992,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | ($true != (((f @ a) = X0)))) )),
% 0.20/0.31 inference(constrained_superposition,[],[f14,f943])).
% 0.20/0.31 thf(f1016,plain,(
% 0.20/0.31 ( ! [X0 : $i] : (($true != $true) | (((f @ a)) != X0)) )),
% 0.20/0.31 inference(equality_proxy_clausification,[],[f992])).
% 0.20/0.31 thf(f1017,plain,(
% 0.20/0.31 ( ! [X0 : $i] : ((((f @ a)) != X0)) )),
% 0.20/0.31 inference(trivial_inequality_removal,[],[f1016])).
% 0.20/0.31 thf(f1025,plain,(
% 0.20/0.31 $false),
% 0.20/0.31 inference(equality_resolution,[],[f1017])).
% 0.20/0.31 % SZS output end Proof for theBenchmark
% 0.20/0.31 % (2733639)------------------------------
% 0.20/0.31 % (2733639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (2733639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (2733639)CaDiCaL version: 2.1.3
% 0.20/0.31 % (2733639)Termination reason: Refutation
% 0.20/0.31 % (2733639)Time elapsed: 0.039 s
% 0.20/0.31 % (2733639)Peak memory usage: 12 MB
% 0.20/0.31 % (2733639)Instructions burned: 71 (million)
% 0.20/0.31 % (2733632)Success in time 0.077 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------