%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO102^5 : 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 : n018.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 08:48:58 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO102^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:36:17 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 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
% 0.21/0.26 % (301742)Will run a generic schedule for satisfiability detection.
% 0.21/0.26 % (301754)% WARNING: option uhcvi not known.
% 0.21/0.26 % (301754)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4037517995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.26 % (301754)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.26 % (301754)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.26 % (301754) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-301742-301754"...
% 0.21/0.26 % (301754)...printing done.
% 0.21/0.26 % (301753)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3260184122_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.26 % (301755)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1559048692:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.26 % (301757)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1745038337:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.26 % Exception at run slice level
% 0.21/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.26 % (301756)dis+10_1_sil=32000:sp=arity:random_seed=903340273:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.26 % (301754)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% 0.21/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.26 thf(func_def_0, type, cP: ($i > $i > $o)).
% 0.21/0.26 thf(f1,conjecture,(
% 0.21/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X2 @ X1) & (cP @ X0 @ X1)) => (cP @ X0 @ X2)) & ! [X0 : $i] : (cP @ X0 @ X0)) => ! [X3 : $i,X4 : $i,X5 : $i] : (((cP @ X4 @ X5) & (cP @ X3 @ X4)) => (cP @ X3 @ X5))),
% 0.21/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM101)).
% 0.21/0.26 thf(f2,negated_conjecture,(
% 0.21/0.26 ~((! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X2 @ X1) & (cP @ X0 @ X1)) => (cP @ X0 @ X2)) & ! [X0 : $i] : (cP @ X0 @ X0)) => ! [X3 : $i,X4 : $i,X5 : $i] : (((cP @ X4 @ X5) & (cP @ X3 @ X4)) => (cP @ X3 @ X5)))),
% 0.21/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.26 thf(f3,plain,(
% 0.21/0.26 ~((! [X0 : $i,X1 : $i,X2 : $i] : (((cP @ X2 @ X1) & (cP @ X0 @ X1)) => (cP @ X0 @ X2)) & ! [X3 : $i] : (cP @ X3 @ X3)) => ! [X4 : $i,X5 : $i,X6 : $i] : (((cP @ X5 @ X6) & (cP @ X4 @ X5)) => (cP @ X4 @ X6)))),
% 0.21/0.26 inference(rectify,[],[f2])).
% 0.21/0.26 thf(f4,plain,(
% 0.21/0.26 ~((! [X0 : $i,X1 : $i,X2 : $i] : (((((cP @ X2 @ X1)) = $true) & (((cP @ X0 @ X1)) = $true)) => (((cP @ X0 @ X2)) = $true)) & ! [X3 : $i] : (((cP @ X3 @ X3)) = $true)) => ! [X4 : $i,X5 : $i,X6 : $i] : (((((cP @ X5 @ X6)) = $true) & (((cP @ X4 @ X5)) = $true)) => (((cP @ X4 @ X6)) = $true)))),
% 0.21/0.26 inference(fool_elimination,[],[f3])).
% 0.21/0.26 thf(f5,plain,(
% 0.21/0.26 ? [X4 : $i,X5 : $i,X6 : $i] : ((((cP @ X4 @ X6)) != $true) & ((((cP @ X5 @ X6)) = $true) & (((cP @ X4 @ X5)) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((cP @ X0 @ X2)) = $true) | ((((cP @ X2 @ X1)) != $true) | (((cP @ X0 @ X1)) != $true))) & ! [X3 : $i] : (((cP @ X3 @ X3)) = $true))),
% 0.21/0.26 inference(ennf_transformation,[],[f4])).
% 0.21/0.26 thf(f6,plain,(
% 0.21/0.26 ? [X4 : $i,X5 : $i,X6 : $i] : ((((cP @ X4 @ X6)) != $true) & (((cP @ X5 @ X6)) = $true) & (((cP @ X4 @ X5)) = $true)) & ! [X0 : $i,X1 : $i,X2 : $i] : ((((cP @ X0 @ X2)) = $true) | (((cP @ X2 @ X1)) != $true) | (((cP @ X0 @ X1)) != $true)) & ! [X3 : $i] : (((cP @ X3 @ X3)) = $true)),
% 0.21/0.26 inference(flattening,[],[f5])).
% 0.21/0.26 thf(f7,plain,(
% 0.21/0.26 ? [X0 : $i,X1 : $i,X2 : $i] : ((((cP @ X0 @ X2)) != $true) & ($true = ((cP @ X1 @ X2))) & (((cP @ X0 @ X1)) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : ((((cP @ X3 @ X5)) = $true) | ($true != ((cP @ X5 @ X4))) | (((cP @ X3 @ X4)) != $true)) & ! [X6 : $i] : ($true = ((cP @ X6 @ X6)))),
% 0.21/0.26 inference(rectify,[],[f6])).
% 0.21/0.26 thf(f8,plain,(
% 0.21/0.26 (($true != ((cP @ sK0 @ sK2))) & ($true = ((cP @ sK1 @ sK2))) & ($true = ((cP @ sK0 @ sK1)))) & ! [X3 : $i,X4 : $i,X5 : $i] : ((((cP @ X3 @ X5)) = $true) | ($true != ((cP @ X5 @ X4))) | (((cP @ X3 @ X4)) != $true)) & ! [X6 : $i] : ($true = ((cP @ X6 @ X6)))),
% 0.21/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7])).
% 0.21/0.26 thf(f9,plain,(
% 0.21/0.26 ( ! [X6 : $i] : (($true = ((cP @ X6 @ X6)))) )),
% 0.21/0.26 inference(cnf_transformation,[],[f8])).
% 0.21/0.26 thf(f10,plain,(
% 0.21/0.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((cP @ X5 @ X4))) | (((cP @ X3 @ X5)) = $true) | (((cP @ X3 @ X4)) != $true)) )),
% 0.21/0.26 inference(cnf_transformation,[],[f8])).
% 0.21/0.26 thf(f11,plain,(
% 0.21/0.26 ($true = ((cP @ sK0 @ sK1)))),
% 0.21/0.26 inference(cnf_transformation,[],[f8])).
% 0.21/0.26 thf(f12,plain,(
% 0.21/0.26 ($true = ((cP @ sK1 @ sK2)))),
% 0.21/0.26 inference(cnf_transformation,[],[f8])).
% 0.21/0.26 thf(f13,plain,(
% 0.21/0.26 ($true != ((cP @ sK0 @ sK2)))),
% 0.21/0.26 inference(cnf_transformation,[],[f8])).
% 0.21/0.26 thf(f15,definition,(
% 0.21/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.21/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.21/0.26 thf(f18,plain,(
% 0.21/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cP @ X0 @ sK1))) | ($true != ((cP @ X0 @ sK2)))) )),
% 0.21/0.26 inference(constrained_superposition,[],[f10,f12])).
% 0.21/0.26 thf(f19,plain,(
% 0.21/0.26 ( ! [X0 : $i] : (($true != ((cP @ X0 @ sK2))) | ($true = ((cP @ X0 @ sK1)))) )),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f18])).
% 0.21/0.26 thf(f23,plain,(
% 0.21/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((cP @ X2 @ X0))) | (((cP @ X2 @ X1)) != $true) | (((cP @ X0 @ X1)) = $false)) )),
% 0.21/0.26 inference(constrained_superposition,[],[f10,f15])).
% 0.21/0.26 thf(f27,plain,(
% 0.21/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((cP @ X2 @ X1)) != $true) | ($true = ((cP @ X2 @ X0))) | (((cP @ X0 @ X1)) = $false)) )),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f23])).
% 0.21/0.26 thf(f36,plain,(
% 0.21/0.26 ($true != $true) | ($true = ((cP @ sK2 @ sK1)))),
% 0.21/0.26 inference(constrained_superposition,[],[f19,f9])).
% 0.21/0.26 thf(f42,plain,(
% 0.21/0.26 ($true = ((cP @ sK2 @ sK1)))),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f36])).
% 0.21/0.26 thf(f50,plain,(
% 0.21/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cP @ sK0 @ X0))) | ($false = ((cP @ X0 @ sK1)))) )),
% 0.21/0.26 inference(constrained_superposition,[],[f27,f11])).
% 0.21/0.26 thf(f56,plain,(
% 0.21/0.26 ( ! [X0 : $i] : (($true = ((cP @ sK0 @ X0))) | ($false = ((cP @ X0 @ sK1)))) )),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f50])).
% 0.21/0.26 thf(f133,plain,(
% 0.21/0.26 ($true = $false) | ($true = ((cP @ sK0 @ sK2)))),
% 0.21/0.26 inference(constrained_superposition,[],[f42,f56])).
% 0.21/0.26 thf(f134,plain,(
% 0.21/0.26 ($true = ((cP @ sK0 @ sK2)))),
% 0.21/0.26 inference(trivial_inequality_removal,[],[f133])).
% 0.21/0.26 thf(f143,plain,(
% 0.21/0.26 $false),
% 0.21/0.26 inference(forward_subsumption_resolution,[],[f134,f13])).
% 0.21/0.26 % SZS output end Proof for theBenchmark
% 0.21/0.26 % (301754)------------------------------
% 0.21/0.26 % (301754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (301754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (301754)CaDiCaL version: 2.1.3
% 0.21/0.26 % (301754)Termination reason: Refutation
% 0.21/0.26 % (301754)Time elapsed: 0.003 s
% 0.21/0.26 % (301754)Peak memory usage: 12 MB
% 0.21/0.26 % (301754)Instructions burned: 9 (million)
% 0.21/0.26 % (301742)Success in time 0.032 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------