%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV120^5 : 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 08:39:01 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV120^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.19 % Computer : n008.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 15:12:39 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.22 Running first-order model finding
% 0.12/0.22 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
% 0.12/0.28 % (3282981)Will run a generic schedule for satisfiability detection.
% 0.12/0.28 % (3282990)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3695539467:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.28 % (3282990)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.28 % (3282987)% WARNING: option uhcvi not known.
% 0.12/0.28 % (3282987)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=883059382:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.28 % (3282989)dis+10_1_sil=32000:sp=arity:random_seed=1402389255:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.28 % (3282987)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.12/0.28 % (3282991)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1866047202:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.28 % (3282987)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.12/0.28 % (3282992)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4055297789:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.28 % (3282988)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3211005496:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.28 % (3282986)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3246455634_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.28 % (3282992) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3282981-3282992"...
% 0.12/0.28 % Exception at run slice level
% 0.12/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.28 % (3282992)...printing done.
% 0.12/0.28 % (3282992)Refutation found. Thanks to Tanya!
% 0.12/0.28 % SZS status Theorem for theBenchmark
% 0.12/0.28 % SZS output start Proof for theBenchmark
% 0.12/0.28 thf(type_def_5, type, a: $tType).
% 0.12/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.28 thf(func_def_3, type, sK0: ((a > a > $o) > $o)).
% 0.12/0.28 thf(func_def_4, type, sK1: a).
% 0.12/0.28 thf(func_def_5, type, sK2: a).
% 0.12/0.28 thf(func_def_6, type, sK3: a).
% 0.12/0.28 thf(func_def_7, type, sK4: (a > a > $o)).
% 0.12/0.28 thf(func_def_8, type, sK5: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_9, type, sK6: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_10, type, sK7: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_11, type, sK8: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_12, type, sK9: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_13, type, sK10: ((a > a > $o) > a)).
% 0.12/0.28 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.12/0.28 thf(f1,conjecture,(
% 0.12/0.28 ! [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)) & ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2))) => ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X3)))),
% 0.12/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM70_pme)).
% 0.12/0.28 thf(f2,negated_conjecture,(
% 0.12/0.28 ~ ! [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)) & ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X2))) => ! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X1 @ X3)))),
% 0.12/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.12/0.28 thf(f3,plain,(
% 0.12/0.28 ~ ! [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > a > $o)] : (((X0 @ X4) & ! [X5 : a,X6 : a,X7 : a] : (((X4 @ X6 @ X7) & (X4 @ X5 @ X6)) => (X4 @ X5 @ X7))) => (X4 @ X2 @ X3)) & ! [X8 : (a > a > $o)] : (((X0 @ X8) & ! [X9 : a,X10 : a,X11 : a] : (((X8 @ X10 @ X11) & (X8 @ X9 @ X10)) => (X8 @ X9 @ X11))) => (X8 @ X1 @ X2))) => ! [X12 : (a > a > $o)] : (((X0 @ X12) & ! [X13 : a,X14 : a,X15 : a] : (((X12 @ X14 @ X15) & (X12 @ X13 @ X14)) => (X12 @ X13 @ X15))) => (X12 @ X1 @ X3)))),
% 0.12/0.28 inference(rectify,[],[f2])).
% 0.12/0.28 thf(f4,plain,(
% 0.12/0.28 ~ ! [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > a > $o)] : (((((X0 @ X4)) = $true) & ! [X5 : a,X6 : a,X7 : a] : (((((X4 @ X6 @ X7)) = $true) & (((X4 @ X5 @ X6)) = $true)) => (((X4 @ X5 @ X7)) = $true))) => (((X4 @ X2 @ X3)) = $true)) & ! [X8 : (a > a > $o)] : (((((X0 @ X8)) = $true) & ! [X9 : a,X10 : a,X11 : a] : (((((X8 @ X10 @ X11)) = $true) & (((X8 @ X9 @ X10)) = $true)) => (((X8 @ X9 @ X11)) = $true))) => (((X8 @ X1 @ X2)) = $true))) => ! [X12 : (a > a > $o)] : (((((X0 @ X12)) = $true) & ! [X13 : a,X14 : a,X15 : a] : (((((X12 @ X14 @ X15)) = $true) & (((X12 @ X13 @ X14)) = $true)) => (((X12 @ X13 @ X15)) = $true))) => (((X12 @ X1 @ X3)) = $true)))),
% 0.12/0.28 inference(fool_elimination,[],[f3])).
% 0.12/0.28 thf(f5,plain,(
% 0.12/0.28 ? [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : (? [X12 : (a > a > $o)] : ((((X12 @ X1 @ X3)) != $true) & ((((X0 @ X12)) = $true) & ! [X13 : a,X14 : a,X15 : a] : ((((X12 @ X13 @ X15)) = $true) | ((((X12 @ X14 @ X15)) != $true) | (((X12 @ X13 @ X14)) != $true))))) & (! [X4 : (a > a > $o)] : ((((X4 @ X2 @ X3)) = $true) | ((((X0 @ X4)) != $true) | ? [X5 : a,X6 : a,X7 : a] : ((((X4 @ X5 @ X7)) != $true) & ((((X4 @ X6 @ X7)) = $true) & (((X4 @ X5 @ X6)) = $true))))) & ! [X8 : (a > a > $o)] : ((((X8 @ X1 @ X2)) = $true) | ((((X0 @ X8)) != $true) | ? [X9 : a,X10 : a,X11 : a] : ((((X8 @ X9 @ X11)) != $true) & ((((X8 @ X10 @ X11)) = $true) & (((X8 @ X9 @ X10)) = $true)))))))),
% 0.12/0.28 inference(ennf_transformation,[],[f4])).
% 0.12/0.28 thf(f6,plain,(
% 0.12/0.28 ? [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : (? [X12 : (a > a > $o)] : ((((X12 @ X1 @ X3)) != $true) & (((X0 @ X12)) = $true) & ! [X13 : a,X14 : a,X15 : a] : ((((X12 @ X13 @ X15)) = $true) | (((X12 @ X14 @ X15)) != $true) | (((X12 @ X13 @ X14)) != $true))) & ! [X4 : (a > a > $o)] : ((((X4 @ X2 @ X3)) = $true) | (((X0 @ X4)) != $true) | ? [X5 : a,X6 : a,X7 : a] : ((((X4 @ X5 @ X7)) != $true) & (((X4 @ X6 @ X7)) = $true) & (((X4 @ X5 @ X6)) = $true))) & ! [X8 : (a > a > $o)] : ((((X8 @ X1 @ X2)) = $true) | (((X0 @ X8)) != $true) | ? [X9 : a,X10 : a,X11 : a] : ((((X8 @ X9 @ X11)) != $true) & (((X8 @ X10 @ X11)) = $true) & (((X8 @ X9 @ X10)) = $true))))),
% 0.12/0.28 inference(flattening,[],[f5])).
% 0.12/0.28 thf(f7,plain,(
% 0.12/0.28 ? [X0 : ((a > a > $o) > $o),X1 : a,X2 : a,X3 : a] : (? [X4 : (a > a > $o)] : ((((X4 @ X1 @ X3)) != $true) & (((X0 @ X4)) = $true) & ! [X5 : a,X6 : a,X7 : a] : ((((X4 @ X5 @ X7)) = $true) | (((X4 @ X6 @ X7)) != $true) | (((X4 @ X5 @ X6)) != $true))) & ! [X8 : (a > a > $o)] : (($true = ((X8 @ X2 @ X3))) | (((X0 @ X8)) != $true) | ? [X9 : a,X10 : a,X11 : a] : ((((X8 @ X9 @ X11)) != $true) & (((X8 @ X10 @ X11)) = $true) & (((X8 @ X9 @ X10)) = $true))) & ! [X12 : (a > a > $o)] : (($true = ((X12 @ X1 @ X2))) | (((X0 @ X12)) != $true) | ? [X13 : a,X14 : a,X15 : a] : ((((X12 @ X13 @ X15)) != $true) & (((X12 @ X14 @ X15)) = $true) & (((X12 @ X13 @ X14)) = $true))))),
% 0.12/0.28 inference(rectify,[],[f6])).
% 0.12/0.28 thf(f8,plain,(
% 0.12/0.28 (($true != ((sK4 @ sK1 @ sK3))) & ($true = ((sK0 @ sK4))) & ! [X5 : a,X6 : a,X7 : a] : (($true = ((sK4 @ X5 @ X7))) | ($true != ((sK4 @ X6 @ X7))) | ($true != ((sK4 @ X5 @ X6))))) & ! [X8 : (a > a > $o)] : (($true = ((X8 @ sK2 @ sK3))) | ($true != ((sK0 @ X8))) | (($true != ((X8 @ (sK5 @ X8) @ (sK7 @ X8)))) & ($true = ((X8 @ (sK6 @ X8) @ (sK7 @ X8)))) & ($true = ((X8 @ (sK5 @ X8) @ (sK6 @ X8)))))) & ! [X12 : (a > a > $o)] : (($true = ((X12 @ sK1 @ sK2))) | ($true != ((sK0 @ X12))) | (($true != ((X12 @ (sK8 @ X12) @ (sK10 @ X12)))) & ($true = ((X12 @ (sK9 @ X12) @ (sK10 @ X12)))) & ($true = ((X12 @ (sK8 @ X12) @ (sK9 @ X12))))))),
% 0.12/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12),skolemize(X15,sK10 @ X12)],[f7])).
% 0.12/0.28 thf(f9,plain,(
% 0.12/0.28 ( ! [X12 : (a > a > $o)] : (($true != ((sK0 @ X12))) | ($true = ((X12 @ sK1 @ sK2))) | ($true = ((X12 @ (sK8 @ X12) @ (sK9 @ X12))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f10,plain,(
% 0.12/0.28 ( ! [X12 : (a > a > $o)] : (($true != ((sK0 @ X12))) | ($true = ((X12 @ sK1 @ sK2))) | ($true = ((X12 @ (sK9 @ X12) @ (sK10 @ X12))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f11,plain,(
% 0.12/0.28 ( ! [X12 : (a > a > $o)] : (($true != ((sK0 @ X12))) | ($true = ((X12 @ sK1 @ sK2))) | ($true != ((X12 @ (sK8 @ X12) @ (sK10 @ X12))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f12,plain,(
% 0.12/0.28 ( ! [X8 : (a > a > $o)] : (($true != ((sK0 @ X8))) | ($true = ((X8 @ sK2 @ sK3))) | ($true = ((X8 @ (sK5 @ X8) @ (sK6 @ X8))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f13,plain,(
% 0.12/0.28 ( ! [X8 : (a > a > $o)] : (($true != ((sK0 @ X8))) | ($true = ((X8 @ sK2 @ sK3))) | ($true = ((X8 @ (sK6 @ X8) @ (sK7 @ X8))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f14,plain,(
% 0.12/0.28 ( ! [X8 : (a > a > $o)] : (($true != ((sK0 @ X8))) | ($true = ((X8 @ sK2 @ sK3))) | ($true != ((X8 @ (sK5 @ X8) @ (sK7 @ X8))))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f15,plain,(
% 0.12/0.28 ( ! [X6 : a,X7 : a,X5 : a] : (($true != ((sK4 @ X6 @ X7))) | ($true = ((sK4 @ X5 @ X7))) | ($true != ((sK4 @ X5 @ X6)))) )),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f16,plain,(
% 0.12/0.28 ($true = ((sK0 @ sK4)))),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f17,plain,(
% 0.12/0.28 ($true != ((sK4 @ sK1 @ sK3)))),
% 0.12/0.28 inference(cnf_transformation,[],[f8])).
% 0.12/0.28 thf(f20,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK1 @ sK2))) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f9,f16])).
% 0.12/0.28 thf(f21,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK1 @ sK2))) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f20])).
% 0.12/0.28 thf(f23,definition,(
% 0.12/0.28 spl11_1 <=> ($true = ((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition])).
% 0.12/0.28 thf(f25,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK8 @ sK4) @ (sK9 @ sK4)))) | ~spl11_1),
% 0.12/0.28 inference(avatar_component_clause,[],[f23])).
% 0.12/0.28 thf(f27,definition,(
% 0.12/0.28 spl11_2 <=> ($true = ((sK4 @ sK1 @ sK2)))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition])).
% 0.12/0.28 thf(f29,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK1 @ sK2))) | ~spl11_2),
% 0.12/0.28 inference(avatar_component_clause,[],[f27])).
% 0.12/0.28 thf(f30,plain,(
% 0.12/0.28 spl11_1 | spl11_2),
% 0.12/0.28 inference(avatar_split_clause,[],[f21,f27,f23])).
% 0.12/0.28 thf(f33,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK1 @ sK2))) | ($true = ((sK4 @ (sK9 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f10,f16])).
% 0.12/0.28 thf(f34,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK1 @ sK2))) | ($true = ((sK4 @ (sK9 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f33])).
% 0.12/0.28 thf(f35,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK1 @ sK2))) | ($true != ((sK4 @ (sK8 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f11,f16])).
% 0.12/0.28 thf(f36,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK1 @ sK2))) | ($true != ((sK4 @ (sK8 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f35])).
% 0.12/0.28 thf(f37,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f12,f16])).
% 0.12/0.28 thf(f38,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f37])).
% 0.12/0.28 thf(f40,definition,(
% 0.12/0.28 spl11_3 <=> ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition])).
% 0.12/0.28 thf(f42,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ~spl11_3),
% 0.12/0.28 inference(avatar_component_clause,[],[f40])).
% 0.12/0.28 thf(f44,definition,(
% 0.12/0.28 spl11_4 <=> ($true = ((sK4 @ sK2 @ sK3)))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])).
% 0.12/0.28 thf(f46,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK2 @ sK3))) | ~spl11_4),
% 0.12/0.28 inference(avatar_component_clause,[],[f44])).
% 0.12/0.28 thf(f47,plain,(
% 0.12/0.28 spl11_3 | spl11_4),
% 0.12/0.28 inference(avatar_split_clause,[],[f38,f44,f40])).
% 0.12/0.28 thf(f50,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK4 @ (sK6 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f13,f16])).
% 0.12/0.28 thf(f51,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK2 @ sK3))) | ($true = ((sK4 @ (sK6 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f50])).
% 0.12/0.28 thf(f53,definition,(
% 0.12/0.28 spl11_5 <=> ($true = ((sK4 @ (sK6 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition])).
% 0.12/0.28 thf(f55,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK6 @ sK4) @ (sK7 @ sK4)))) | ~spl11_5),
% 0.12/0.28 inference(avatar_component_clause,[],[f53])).
% 0.12/0.28 thf(f56,plain,(
% 0.12/0.28 spl11_5 | spl11_4),
% 0.12/0.28 inference(avatar_split_clause,[],[f51,f44,f53])).
% 0.12/0.28 thf(f57,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != $true) | ($true = ((sK4 @ X0 @ sK3))) | ($true != ((sK4 @ X0 @ sK2)))) ) | ~spl11_4),
% 0.12/0.28 inference(constrained_superposition,[],[f15,f46])).
% 0.12/0.28 thf(f58,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ sK2))) | ($true = ((sK4 @ X0 @ sK3)))) ) | ~spl11_4),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f57])).
% 0.12/0.28 thf(f59,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK1 @ sK3))) | (~spl11_2 | ~spl11_4)),
% 0.12/0.28 inference(constrained_superposition,[],[f58,f29])).
% 0.12/0.28 thf(f60,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK1 @ sK3))) | (~spl11_2 | ~spl11_4)),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f59])).
% 0.12/0.28 thf(f62,plain,(
% 0.12/0.28 ($true != $true) | (~spl11_2 | ~spl11_4)),
% 0.12/0.28 inference(constrained_superposition,[],[f17,f60])).
% 0.12/0.28 thf(f63,plain,(
% 0.12/0.28 $false | (~spl11_2 | ~spl11_4)),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f62])).
% 0.12/0.28 thf(f64,plain,(
% 0.12/0.28 ~spl11_2 | ~spl11_4),
% 0.12/0.28 inference(avatar_contradiction_clause,[],[f63])).
% 0.12/0.28 thf(f66,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ sK2 @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 inference(constrained_superposition,[],[f14,f16])).
% 0.12/0.28 thf(f67,plain,(
% 0.12/0.28 ($true = ((sK4 @ sK2 @ sK3))) | ($true != ((sK4 @ (sK5 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f66])).
% 0.12/0.28 thf(f69,definition,(
% 0.12/0.28 spl11_6 <=> ($true = ((sK4 @ (sK5 @ sK4) @ (sK7 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition])).
% 0.12/0.28 thf(f72,plain,(
% 0.12/0.28 ~spl11_6 | spl11_4),
% 0.12/0.28 inference(avatar_split_clause,[],[f67,f44,f69])).
% 0.12/0.28 thf(f73,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != $true) | ($true = ((sK4 @ X0 @ (sK7 @ sK4)))) | ($true != ((sK4 @ X0 @ (sK6 @ sK4))))) ) | ~spl11_5),
% 0.12/0.28 inference(constrained_superposition,[],[f15,f55])).
% 0.12/0.28 thf(f74,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK6 @ sK4)))) | ($true = ((sK4 @ X0 @ (sK7 @ sK4))))) ) | ~spl11_5),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f73])).
% 0.12/0.28 thf(f75,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ (sK5 @ sK4) @ (sK7 @ sK4)))) | (~spl11_3 | ~spl11_5)),
% 0.12/0.28 inference(constrained_superposition,[],[f74,f42])).
% 0.12/0.28 thf(f76,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK5 @ sK4) @ (sK7 @ sK4)))) | (~spl11_3 | ~spl11_5)),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f75])).
% 0.12/0.28 thf(f77,plain,(
% 0.12/0.28 spl11_6 | ~spl11_3 | ~spl11_5),
% 0.12/0.28 inference(avatar_split_clause,[],[f76,f53,f40,f69])).
% 0.12/0.28 thf(f79,definition,(
% 0.12/0.28 spl11_7 <=> ($true = ((sK4 @ (sK9 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition])).
% 0.12/0.28 thf(f81,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK9 @ sK4) @ (sK10 @ sK4)))) | ~spl11_7),
% 0.12/0.28 inference(avatar_component_clause,[],[f79])).
% 0.12/0.28 thf(f82,plain,(
% 0.12/0.28 spl11_7 | spl11_2),
% 0.12/0.28 inference(avatar_split_clause,[],[f34,f27,f79])).
% 0.12/0.28 thf(f84,definition,(
% 0.12/0.28 spl11_8 <=> ($true = ((sK4 @ (sK8 @ sK4) @ (sK10 @ sK4))))),
% 0.12/0.28 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 0.12/0.28 thf(f87,plain,(
% 0.12/0.28 ~spl11_8 | spl11_2),
% 0.12/0.28 inference(avatar_split_clause,[],[f36,f27,f84])).
% 0.12/0.28 thf(f92,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != $true) | ($true = ((sK4 @ X0 @ (sK10 @ sK4)))) | ($true != ((sK4 @ X0 @ (sK9 @ sK4))))) ) | ~spl11_7),
% 0.12/0.28 inference(constrained_superposition,[],[f15,f81])).
% 0.12/0.28 thf(f93,plain,(
% 0.12/0.28 ( ! [X0 : a] : (($true != ((sK4 @ X0 @ (sK9 @ sK4)))) | ($true = ((sK4 @ X0 @ (sK10 @ sK4))))) ) | ~spl11_7),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f92])).
% 0.12/0.28 thf(f94,plain,(
% 0.12/0.28 ($true != $true) | ($true = ((sK4 @ (sK8 @ sK4) @ (sK10 @ sK4)))) | (~spl11_1 | ~spl11_7)),
% 0.12/0.28 inference(constrained_superposition,[],[f93,f25])).
% 0.12/0.28 thf(f95,plain,(
% 0.12/0.28 ($true = ((sK4 @ (sK8 @ sK4) @ (sK10 @ sK4)))) | (~spl11_1 | ~spl11_7)),
% 0.12/0.28 inference(trivial_inequality_removal,[],[f94])).
% 0.12/0.28 thf(f96,plain,(
% 0.12/0.28 spl11_8 | ~spl11_1 | ~spl11_7),
% 0.12/0.28 inference(avatar_split_clause,[],[f95,f79,f23,f84])).
% 0.12/0.28 cnf(s1, plain, spl11_1 | spl11_2, inference(sat_conversion,[],[f30])).
% 0.12/0.28 cnf(s2, plain, spl11_3 | spl11_4, inference(sat_conversion,[],[f47])).
% 0.12/0.28 cnf(s3, plain, spl11_4 | spl11_5, inference(sat_conversion,[],[f56])).
% 0.12/0.28 cnf(s4, plain, ~spl11_2 | ~spl11_4, inference(sat_conversion,[],[f64])).
% 0.12/0.28 cnf(s5, plain, spl11_4 | ~spl11_6, inference(sat_conversion,[],[f72])).
% 0.12/0.28 cnf(s6, plain, ~spl11_3 | ~spl11_5 | spl11_6, inference(sat_conversion,[],[f77])).
% 0.12/0.28 cnf(s7, plain, spl11_2 | spl11_7, inference(sat_conversion,[],[f82])).
% 0.12/0.28 cnf(s8, plain, spl11_2 | ~spl11_8, inference(sat_conversion,[],[f87])).
% 0.12/0.28 cnf(s9, plain, ~spl11_1 | ~spl11_7 | spl11_8, inference(sat_conversion,[],[f96])).
% 0.12/0.28 cnf(s10, plain, spl11_4, inference(rat,[],[s6,s2,s3,s5])).
% 0.12/0.28 cnf(s11, plain, ~spl11_2, inference(rat,[],[s4,s10])).
% 0.12/0.28 cnf(s12, plain, ~spl11_8, inference(rat,[],[s8,s11])).
% 0.12/0.28 cnf(s13, plain, spl11_7, inference(rat,[],[s7,s11])).
% 0.12/0.28 cnf(s14, plain, spl11_1, inference(rat,[],[s1,s11])).
% 0.12/0.28 cnf(s15, plain, $false, inference(rat,[],[s9,s12,s14,s13])).
% 0.12/0.28 thf(f97,plain,(
% 0.12/0.28 $false),
% 0.12/0.28 inference(avatar_sat_refutation,[],[s15])).
% 0.12/0.28 % SZS output end Proof for theBenchmark
% 0.12/0.28 % (3282992)------------------------------
% 0.12/0.28 % (3282992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.28 % (3282992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.28 % (3282992)CaDiCaL version: 2.1.3
% 0.12/0.28 % (3282992)Termination reason: Refutation
% 0.12/0.28 % (3282992)Time elapsed: 0.007 s
% 0.12/0.28 % (3282992)Peak memory usage: 13 MB
% 0.12/0.28 % (3282992)Instructions burned: 11 (million)
% 0.12/0.28 % (3282981)Success in time 0.049 s
% 0.12/0.28 % Vampire exiting
%------------------------------------------------------------------------------