%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV185^5 : 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 08:39:07 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV185^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n008.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 15:20:09 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.26 % (3291438)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (3291446)dis+10_1_sil=32000:sp=arity:random_seed=2604379543:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.26 % (3291444)% WARNING: option uhcvi not known.
% 0.07/0.26 % (3291444)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1209837440:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.26 % (3291443)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1813239770_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.26 % (3291444)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % (3291447)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3574332122:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.26 % (3291448)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4030847482:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.26 % (3291444)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.26 % (3291449)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=607345050:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.26 % Exception at run slice level
% 0.07/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.26 % (3291447)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.26 % (3291449) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3291438-3291449"...
% 0.07/0.26 % (3291449)...printing done.
% 0.07/0.26 % (3291449)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Theorem for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% 0.07/0.26 thf(type_def_5, type, b: $tType).
% 0.07/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.26 thf(func_def_3, type, sK0: ((b > $o) > b > $o)).
% 0.07/0.26 thf(func_def_4, type, sK1: ((b > $o) > $o)).
% 0.07/0.26 thf(func_def_5, type, sK2: (b > $o)).
% 0.07/0.26 thf(func_def_6, type, sK3: b).
% 0.07/0.26 thf(func_def_7, type, sK4: (b > $o)).
% 0.07/0.26 thf(func_def_8, type, sK5: ((b > $o) > (b > $o) > b)).
% 0.07/0.26 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.07/0.26 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.26 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.26 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.26 thf(f1,conjecture,(
% 0.07/0.26 ! [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (! [X2 : (b > $o)] : ((X1 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X2 : b] : ((X3 @ X2) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X2)))) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X4))))),
% 0.07/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM564_pme)).
% 0.07/0.26 thf(f2,negated_conjecture,(
% 0.07/0.26 ~ ! [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (! [X2 : (b > $o)] : ((X1 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X2 : b] : ((X3 @ X2) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X2)))) => ! [X6 : (b > $o)] : ((X1 @ X6) => (X6 @ X4))))),
% 0.07/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.26 thf(f3,plain,(
% 0.07/0.26 ~ ! [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (! [X2 : (b > $o)] : ((X1 @ X2) => ! [X3 : (b > $o),X4 : b] : (((X0 @ X3 @ X4) & ! [X5 : b] : ((X3 @ X5) => (X2 @ X5))) => (X2 @ X4))) => ! [X6 : (b > $o),X7 : b] : (((X0 @ X6 @ X7) & ! [X8 : b] : ((X6 @ X8) => ! [X9 : (b > $o)] : ((X1 @ X9) => (X9 @ X8)))) => ! [X10 : (b > $o)] : ((X1 @ X10) => (X10 @ X7))))),
% 0.07/0.26 inference(rectify,[],[f2])).
% 0.07/0.26 thf(f4,plain,(
% 0.07/0.26 ~ ! [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (! [X2 : (b > $o)] : ((((X1 @ X2)) = $true) => ! [X3 : (b > $o),X4 : b] : (((((X0 @ X3 @ X4)) = $true) & ! [X5 : b] : ((((X3 @ X5)) = $true) => (((X2 @ X5)) = $true))) => (((X2 @ X4)) = $true))) => ! [X6 : (b > $o),X7 : b] : (((((X0 @ X6 @ X7)) = $true) & ! [X8 : b] : ((((X6 @ X8)) = $true) => ! [X9 : (b > $o)] : ((((X1 @ X9)) = $true) => (((X9 @ X8)) = $true)))) => ! [X10 : (b > $o)] : ((((X1 @ X10)) = $true) => (((X10 @ X7)) = $true))))),
% 0.07/0.26 inference(fool_elimination,[],[f3])).
% 0.07/0.26 thf(f5,plain,(
% 0.07/0.26 ? [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (? [X6 : (b > $o),X7 : b] : (? [X10 : (b > $o)] : ((((X10 @ X7)) != $true) & (((X1 @ X10)) = $true)) & ((((X0 @ X6 @ X7)) = $true) & ! [X8 : b] : (! [X9 : (b > $o)] : ((((X9 @ X8)) = $true) | (((X1 @ X9)) != $true)) | (((X6 @ X8)) != $true)))) & ! [X2 : (b > $o)] : (! [X3 : (b > $o),X4 : b] : ((((X2 @ X4)) = $true) | ((((X0 @ X3 @ X4)) != $true) | ? [X5 : b] : ((((X2 @ X5)) != $true) & (((X3 @ X5)) = $true)))) | (((X1 @ X2)) != $true)))),
% 0.07/0.26 inference(ennf_transformation,[],[f4])).
% 0.07/0.26 thf(f6,plain,(
% 0.07/0.26 ? [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (? [X6 : (b > $o),X7 : b] : (? [X10 : (b > $o)] : ((((X10 @ X7)) != $true) & (((X1 @ X10)) = $true)) & (((X0 @ X6 @ X7)) = $true) & ! [X8 : b] : (! [X9 : (b > $o)] : ((((X9 @ X8)) = $true) | (((X1 @ X9)) != $true)) | (((X6 @ X8)) != $true))) & ! [X2 : (b > $o)] : (! [X3 : (b > $o),X4 : b] : ((((X2 @ X4)) = $true) | (((X0 @ X3 @ X4)) != $true) | ? [X5 : b] : ((((X2 @ X5)) != $true) & (((X3 @ X5)) = $true))) | (((X1 @ X2)) != $true)))),
% 0.07/0.26 inference(flattening,[],[f5])).
% 0.07/0.26 thf(f7,plain,(
% 0.07/0.26 ? [X0 : ((b > $o) > b > $o),X1 : ((b > $o) > $o)] : (? [X2 : (b > $o),X3 : b] : (? [X4 : (b > $o)] : (($true != ((X4 @ X3))) & ($true = ((X1 @ X4)))) & ($true = ((X0 @ X2 @ X3))) & ! [X5 : b] : (! [X6 : (b > $o)] : (($true = ((X6 @ X5))) | (((X1 @ X6)) != $true)) | (((X2 @ X5)) != $true))) & ! [X7 : (b > $o)] : (! [X8 : (b > $o),X9 : b] : (($true = ((X7 @ X9))) | ($true != ((X0 @ X8 @ X9))) | ? [X10 : b] : (($true != ((X7 @ X10))) & ($true = ((X8 @ X10))))) | ($true != ((X1 @ X7)))))),
% 0.07/0.26 inference(rectify,[],[f6])).
% 0.07/0.26 thf(f8,plain,(
% 0.07/0.26 ((($true != ((sK4 @ sK3))) & ($true = ((sK1 @ sK4)))) & ($true = ((sK0 @ sK2 @ sK3))) & ! [X5 : b] : (! [X6 : (b > $o)] : (($true = ((X6 @ X5))) | ($true != ((sK1 @ X6)))) | ($true != ((sK2 @ X5))))) & ! [X7 : (b > $o)] : (! [X8 : (b > $o),X9 : b] : (($true = ((X7 @ X9))) | ($true != ((sK0 @ X8 @ X9))) | (($true != ((X7 @ (sK5 @ X8 @ X7)))) & ($true = ((X8 @ (sK5 @ X8 @ X7)))))) | ($true != ((sK1 @ X7))))),
% 0.07/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X10,sK5 @ X8 @ X7)],[f7])).
% 0.07/0.26 thf(f9,plain,(
% 0.07/0.26 ( ! [X8 : (b > $o),X9 : b,X7 : (b > $o)] : (($true != ((sK1 @ X7))) | ($true != ((sK0 @ X8 @ X9))) | ($true = ((X8 @ (sK5 @ X8 @ X7)))) | ($true = ((X7 @ X9)))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f10,plain,(
% 0.07/0.26 ( ! [X8 : (b > $o),X9 : b,X7 : (b > $o)] : (($true != ((sK1 @ X7))) | ($true != ((sK0 @ X8 @ X9))) | ($true != ((X7 @ (sK5 @ X8 @ X7)))) | ($true = ((X7 @ X9)))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f11,plain,(
% 0.07/0.26 ( ! [X6 : (b > $o),X5 : b] : (($true != ((sK1 @ X6))) | ($true = ((X6 @ X5))) | ($true != ((sK2 @ X5)))) )),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f12,plain,(
% 0.07/0.26 ($true = ((sK0 @ sK2 @ sK3)))),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f13,plain,(
% 0.07/0.26 ($true = ((sK1 @ sK4)))),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f14,plain,(
% 0.07/0.26 ($true != ((sK4 @ sK3)))),
% 0.07/0.26 inference(cnf_transformation,[],[f8])).
% 0.07/0.26 thf(f17,plain,(
% 0.07/0.26 ( ! [X0 : b] : (($true != $true) | ($true = ((sK4 @ X0))) | ($true != ((sK2 @ X0)))) )),
% 0.07/0.26 inference(constrained_superposition,[],[f11,f13])).
% 0.07/0.26 thf(f18,plain,(
% 0.07/0.26 ( ! [X0 : b] : (($true != ((sK2 @ X0))) | ($true = ((sK4 @ X0)))) )),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f17])).
% 0.07/0.26 thf(f19,plain,(
% 0.07/0.26 ( ! [X0 : (b > $o),X1 : b] : (($true != $true) | ($true != ((sK0 @ X0 @ X1))) | ($true = ((X0 @ (sK5 @ X0 @ sK4)))) | ($true = ((sK4 @ X1)))) )),
% 0.07/0.26 inference(constrained_superposition,[],[f9,f13])).
% 0.07/0.26 thf(f20,plain,(
% 0.07/0.26 ( ! [X0 : (b > $o),X1 : b] : (($true != ((sK0 @ X0 @ X1))) | ($true = ((X0 @ (sK5 @ X0 @ sK4)))) | ($true = ((sK4 @ X1)))) )),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.07/0.26 thf(f21,plain,(
% 0.07/0.26 ($true != $true) | ($true = ((sK2 @ (sK5 @ sK2 @ sK4)))) | ($true = ((sK4 @ sK3)))),
% 0.07/0.26 inference(constrained_superposition,[],[f20,f12])).
% 0.07/0.26 thf(f22,plain,(
% 0.07/0.26 ($true = ((sK2 @ (sK5 @ sK2 @ sK4)))) | ($true = ((sK4 @ sK3)))),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f21])).
% 0.07/0.26 thf(f24,definition,(
% 0.07/0.26 spl6_1 <=> ($true = ((sK4 @ sK3)))),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.07/0.26 thf(f26,plain,(
% 0.07/0.26 ($true = ((sK4 @ sK3))) | ~spl6_1),
% 0.07/0.26 inference(avatar_component_clause,[],[f24])).
% 0.07/0.26 thf(f28,definition,(
% 0.07/0.26 spl6_2 <=> ($true = ((sK2 @ (sK5 @ sK2 @ sK4))))),
% 0.07/0.26 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.07/0.26 thf(f30,plain,(
% 0.07/0.26 ($true = ((sK2 @ (sK5 @ sK2 @ sK4)))) | ~spl6_2),
% 0.07/0.26 inference(avatar_component_clause,[],[f28])).
% 0.07/0.26 thf(f31,plain,(
% 0.07/0.26 spl6_1 | spl6_2),
% 0.07/0.26 inference(avatar_split_clause,[],[f22,f28,f24])).
% 0.07/0.26 thf(f32,plain,(
% 0.07/0.26 ($true != $true) | ($true = ((sK4 @ (sK5 @ sK2 @ sK4)))) | ~spl6_2),
% 0.07/0.26 inference(constrained_superposition,[],[f18,f30])).
% 0.07/0.26 thf(f33,plain,(
% 0.07/0.26 ($true = ((sK4 @ (sK5 @ sK2 @ sK4)))) | ~spl6_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f32])).
% 0.07/0.26 thf(f35,plain,(
% 0.07/0.26 ( ! [X0 : (b > $o),X1 : b] : (($true != $true) | ($true != ((sK0 @ X0 @ X1))) | ($true != ((sK4 @ (sK5 @ X0 @ sK4)))) | ($true = ((sK4 @ X1)))) )),
% 0.07/0.26 inference(constrained_superposition,[],[f10,f13])).
% 0.07/0.26 thf(f36,plain,(
% 0.07/0.26 ( ! [X0 : (b > $o),X1 : b] : (($true != ((sK4 @ (sK5 @ X0 @ sK4)))) | ($true != ((sK0 @ X0 @ X1))) | ($true = ((sK4 @ X1)))) )),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f35])).
% 0.07/0.26 thf(f37,plain,(
% 0.07/0.26 ( ! [X0 : b] : (($true != $true) | ($true != ((sK0 @ sK2 @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl6_2),
% 0.07/0.26 inference(constrained_superposition,[],[f36,f33])).
% 0.07/0.26 thf(f38,plain,(
% 0.07/0.26 ( ! [X0 : b] : (($true != ((sK0 @ sK2 @ X0))) | ($true = ((sK4 @ X0)))) ) | ~spl6_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f37])).
% 0.07/0.26 thf(f39,plain,(
% 0.07/0.26 ($true != $true) | ($true = ((sK4 @ sK3))) | ~spl6_2),
% 0.07/0.26 inference(constrained_superposition,[],[f38,f12])).
% 0.07/0.26 thf(f40,plain,(
% 0.07/0.26 ($true = ((sK4 @ sK3))) | ~spl6_2),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f39])).
% 0.07/0.26 thf(f41,plain,(
% 0.07/0.26 spl6_1 | ~spl6_2),
% 0.07/0.26 inference(avatar_split_clause,[],[f40,f28,f24])).
% 0.07/0.26 thf(f42,plain,(
% 0.07/0.26 ($true != $true) | ~spl6_1),
% 0.07/0.26 inference(constrained_superposition,[],[f14,f26])).
% 0.07/0.26 thf(f43,plain,(
% 0.07/0.26 $false | ~spl6_1),
% 0.07/0.26 inference(trivial_inequality_removal,[],[f42])).
% 0.07/0.26 thf(f44,plain,(
% 0.07/0.26 ~spl6_1),
% 0.07/0.26 inference(avatar_contradiction_clause,[],[f43])).
% 0.07/0.26 cnf(s1, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f31])).
% 0.07/0.26 cnf(s2, plain, spl6_1 | ~spl6_2, inference(sat_conversion,[],[f41])).
% 0.07/0.26 cnf(s3, plain, ~spl6_1, inference(sat_conversion,[],[f44])).
% 0.07/0.26 cnf(s4, plain, ~spl6_2, inference(rat,[],[s2,s3])).
% 0.07/0.26 cnf(s5, plain, $false, inference(rat,[],[s1,s4,s3])).
% 0.07/0.26 thf(f45,plain,(
% 0.07/0.26 $false),
% 0.07/0.26 inference(avatar_sat_refutation,[],[s5])).
% 0.07/0.26 % SZS output end Proof for theBenchmark
% 0.07/0.26 % (3291449)------------------------------
% 0.07/0.26 % (3291449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (3291449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (3291449)CaDiCaL version: 2.1.3
% 0.07/0.26 % (3291449)Termination reason: Refutation
% 0.07/0.26 % (3291449)Time elapsed: 0.004 s
% 0.07/0.26 % (3291449)Peak memory usage: 13 MB
% 0.07/0.26 % (3291449)Instructions burned: 5 (million)
% 0.07/0.26 % (3291438)Success in time 0.045 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------