%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET046^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:23:33 AM UTC 2026
% Result : Theorem 0.07s 0.28s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET046^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:36:54 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.28 % (3157666)Will run a generic schedule for satisfiability detection.
% 0.07/0.28 % (3157685)% WARNING: option uhcvi not known.
% 0.07/0.28 % (3157690)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=537255539:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.28 % (3157690) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3157666-3157690"...
% 0.07/0.28 % (3157684)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1565677859_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.28 % (3157685)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2478424801:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.28 % (3157687)dis+10_1_sil=32000:sp=arity:random_seed=3901448409:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.28 % (3157688)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2775942583:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.28 % (3157685)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.28 % (3157690)...printing done.
% 0.07/0.28 % Exception at run slice level% (3157688)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.28 % (3157685)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.28
% 0.07/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.28 % (3157690)Refutation found. Thanks to Tanya!
% 0.07/0.28 % SZS status Theorem for theBenchmark
% 0.07/0.28 % SZS output start Proof for theBenchmark
% 0.07/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.28 thf(func_def_0, type, cF: ($i > $i > $o)).
% 0.07/0.28 thf(func_def_5, type, sK1: ($i > $i)).
% 0.07/0.28 thf(f1,conjecture,(
% 0.07/0.28 ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2))))),
% 0.07/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL42)).
% 0.07/0.28 thf(f2,negated_conjecture,(
% 0.07/0.28 ~ ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2))))),
% 0.07/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.28 thf(f3,plain,(
% 0.07/0.28 ~ ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((cF @ X2 @ X1) & (cF @ X1 @ X2)) => (cF @ X1 @ X0)) & ((cF @ X1 @ X0) => ~ ? [X3 : $i] : ((cF @ X3 @ X1) & (cF @ X1 @ X3))))),
% 0.07/0.28 inference(rectify,[],[f2])).
% 0.07/0.28 thf(f4,plain,(
% 0.07/0.28 ~ ~ ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((((cF @ X2 @ X1)) = $true) & (((cF @ X1 @ X2)) = $true)) => (((cF @ X1 @ X0)) = $true)) & ((((cF @ X1 @ X0)) = $true) => ~ ? [X3 : $i] : ((((cF @ X3 @ X1)) = $true) & (((cF @ X1 @ X3)) = $true))))),
% 0.07/0.28 inference(fool_elimination,[],[f3])).
% 0.07/0.28 thf(f5,plain,(
% 0.07/0.28 ? [X0 : $i] : ! [X1 : $i] : ((~ ? [X2 : $i] : ((((cF @ X2 @ X1)) = $true) & (((cF @ X1 @ X2)) = $true)) => (((cF @ X1 @ X0)) = $true)) & ((((cF @ X1 @ X0)) = $true) => ~ ? [X3 : $i] : ((((cF @ X3 @ X1)) = $true) & (((cF @ X1 @ X3)) = $true))))),
% 0.07/0.28 inference(flattening,[],[f4])).
% 0.07/0.28 thf(f6,plain,(
% 0.07/0.28 ? [X0 : $i] : ! [X1 : $i] : (((((cF @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((cF @ X2 @ X1)) = $true) & (((cF @ X1 @ X2)) = $true))) & (! [X3 : $i] : ((((cF @ X3 @ X1)) != $true) | (((cF @ X1 @ X3)) != $true)) | (((cF @ X1 @ X0)) != $true)))),
% 0.07/0.28 inference(ennf_transformation,[],[f5])).
% 0.07/0.28 thf(f7,plain,(
% 0.07/0.28 ! [X1 : $i] : ((($true = ((cF @ X1 @ sK0))) | (($true = ((cF @ (sK1 @ X1) @ X1))) & ($true = ((cF @ X1 @ (sK1 @ X1)))))) & (! [X3 : $i] : ((((cF @ X3 @ X1)) != $true) | (((cF @ X1 @ X3)) != $true)) | ($true != ((cF @ X1 @ sK0)))))),
% 0.07/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X2,sK1 @ X1)],[f6])).
% 0.07/0.28 thf(f8,plain,(
% 0.07/0.28 ( ! [X3 : $i,X1 : $i] : (($true != ((cF @ X1 @ sK0))) | (((cF @ X1 @ X3)) != $true) | (((cF @ X3 @ X1)) != $true)) )),
% 0.07/0.28 inference(cnf_transformation,[],[f7])).
% 0.07/0.28 thf(f9,plain,(
% 0.07/0.28 ( ! [X1 : $i] : (($true = ((cF @ X1 @ (sK1 @ X1)))) | ($true = ((cF @ X1 @ sK0)))) )),
% 0.07/0.28 inference(cnf_transformation,[],[f7])).
% 0.07/0.28 thf(f10,plain,(
% 0.07/0.28 ( ! [X1 : $i] : (($true = ((cF @ (sK1 @ X1) @ X1))) | ($true = ((cF @ X1 @ sK0)))) )),
% 0.07/0.28 inference(cnf_transformation,[],[f7])).
% 0.07/0.28 thf(f13,plain,(
% 0.07/0.28 ( ! [X0 : $i] : (($true != $true) | ($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0)))) | ($true = ((cF @ sK0 @ sK0)))) )),
% 0.07/0.28 inference(constrained_superposition,[],[f8,f10])).
% 0.07/0.28 thf(f14,plain,(
% 0.07/0.28 ( ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0)))) | ($true = ((cF @ sK0 @ sK0)))) )),
% 0.07/0.28 inference(trivial_inequality_removal,[],[f13])).
% 0.07/0.28 thf(f16,definition,(
% 0.07/0.28 spl2_1 <=> ($true = ((cF @ sK0 @ sK0)))),
% 0.07/0.28 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.07/0.28 thf(f18,plain,(
% 0.07/0.28 ($true = ((cF @ sK0 @ sK0))) | ~spl2_1),
% 0.07/0.28 inference(avatar_component_clause,[],[f16])).
% 0.07/0.28 thf(f20,definition,(
% 0.07/0.28 spl2_2 <=> ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0)))))),
% 0.07/0.28 introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.07/0.28 thf(f21,plain,(
% 0.07/0.28 ( ! [X0 : $i] : (($true != ((cF @ (sK1 @ sK0) @ X0))) | ($true != ((cF @ X0 @ (sK1 @ sK0))))) ) | ~spl2_2),
% 0.07/0.28 inference(avatar_component_clause,[],[f20])).
% 0.07/0.28 thf(f22,plain,(
% 0.07/0.28 spl2_1 | spl2_2),
% 0.07/0.28 inference(avatar_split_clause,[],[f14,f20,f16])).
% 0.07/0.28 thf(f24,plain,(
% 0.07/0.28 ($true != $true) | ($true != ((cF @ sK0 @ (sK1 @ sK0)))) | ($true = ((cF @ sK0 @ sK0))) | ~spl2_2),
% 0.07/0.28 inference(constrained_superposition,[],[f21,f10])).
% 0.07/0.28 thf(f25,plain,(
% 0.07/0.28 ($true != ((cF @ sK0 @ (sK1 @ sK0)))) | ($true = ((cF @ sK0 @ sK0))) | ~spl2_2),
% 0.07/0.28 inference(trivial_inequality_removal,[],[f24])).
% 0.07/0.28 thf(f28,definition,(
% 0.07/0.28 spl2_3 <=> ($true = ((cF @ sK0 @ (sK1 @ sK0))))),
% 0.07/0.28 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.07/0.28 thf(f30,plain,(
% 0.07/0.28 ($true != ((cF @ sK0 @ (sK1 @ sK0)))) | spl2_3),
% 0.07/0.28 inference(avatar_component_clause,[],[f28])).
% 0.07/0.28 thf(f31,plain,(
% 0.07/0.28 spl2_1 | ~spl2_3 | ~spl2_2),
% 0.07/0.28 inference(avatar_split_clause,[],[f25,f20,f28,f16])).
% 0.07/0.28 thf(f41,plain,(
% 0.07/0.28 ($true != $true) | ($true = ((cF @ sK0 @ sK0))) | spl2_3),
% 0.07/0.28 inference(constrained_superposition,[],[f30,f9])).
% 0.07/0.28 thf(f42,plain,(
% 0.07/0.28 ($true = ((cF @ sK0 @ sK0))) | spl2_3),
% 0.07/0.28 inference(trivial_inequality_removal,[],[f41])).
% 0.07/0.28 thf(f43,plain,(
% 0.07/0.28 spl2_1 | spl2_3),
% 0.07/0.28 inference(avatar_split_clause,[],[f42,f28,f16])).
% 0.07/0.28 thf(f44,plain,(
% 0.07/0.28 ( ! [X0 : $i] : (($true != $true) | ($true != ((cF @ sK0 @ X0))) | ($true != ((cF @ X0 @ sK0)))) ) | ~spl2_1),
% 0.07/0.28 inference(constrained_superposition,[],[f8,f18])).
% 0.07/0.28 thf(f45,plain,(
% 0.07/0.28 ( ! [X0 : $i] : (($true != ((cF @ sK0 @ X0))) | ($true != ((cF @ X0 @ sK0)))) ) | ~spl2_1),
% 0.07/0.28 inference(trivial_inequality_removal,[],[f44])).
% 0.07/0.28 thf(f56,plain,(
% 0.07/0.28 ($true != $true) | ($true != $true) | ~spl2_1),
% 0.07/0.28 inference(constrained_superposition,[],[f45,f18])).
% 0.07/0.28 thf(f57,plain,(
% 0.07/0.28 ($true != $true) | ~spl2_1),
% 0.07/0.28 inference(duplicate_literal_removal,[],[f56])).
% 0.07/0.28 thf(f58,plain,(
% 0.07/0.28 $false | ~spl2_1),
% 0.07/0.28 inference(trivial_inequality_removal,[],[f57])).
% 0.07/0.28 thf(f59,plain,(
% 0.07/0.28 ~spl2_1),
% 0.07/0.28 inference(avatar_contradiction_clause,[],[f58])).
% 0.07/0.28 cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f22])).
% 0.07/0.28 cnf(s2, plain, spl2_1 | ~spl2_2 | ~spl2_3, inference(sat_conversion,[],[f31])).
% 0.07/0.28 cnf(s4, plain, spl2_1 | spl2_3, inference(sat_conversion,[],[f43])).
% 0.07/0.28 cnf(s6, plain, ~spl2_1, inference(sat_conversion,[],[f59])).
% 0.07/0.28 cnf(s7, plain, spl2_3, inference(rat,[],[s4,s6])).
% 0.07/0.28 cnf(s8, plain, ~spl2_2, inference(rat,[],[s2,s7,s6])).
% 0.07/0.28 cnf(s9, plain, $false, inference(rat,[],[s1,s8,s6])).
% 0.07/0.28 thf(f61,plain,(
% 0.07/0.28 $false),
% 0.07/0.28 inference(avatar_sat_refutation,[],[s9])).
% 0.07/0.28 % SZS output end Proof for theBenchmark
% 0.07/0.28 % (3157690)------------------------------
% 0.07/0.28 % (3157690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.28 % (3157690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.28 % (3157690)CaDiCaL version: 2.1.3
% 0.07/0.28 % (3157690)Termination reason: Refutation
% 0.07/0.28 % (3157690)Time elapsed: 0.003 s
% 0.07/0.28 % (3157690)Peak memory usage: 12 MB
% 0.07/0.28 % (3157690)Instructions burned: 4 (million)
% 0.07/0.28 % (3157666)Success in time 0.055 s
% 0.07/0.28 % Vampire exiting
%------------------------------------------------------------------------------