%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV191^5 : 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 : n017.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 08:39:08 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV191^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:15:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.20/0.29 % (453102)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (453123)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3407603065:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (453122)% WARNING: option uhcvi not known.
% 0.20/0.29 % (453122)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3629992006:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (453121)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3354678034_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (453125)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3460781682:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (453124)dis+10_1_sil=32000:sp=arity:random_seed=183805198:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (453122)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (453126)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2523561034:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (453127)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=958790241:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (453125)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (453122)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (453127) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-453102-453127"...
% 0.20/0.29 % (453127)...printing done.
% 0.20/0.29 % (453127)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, a: $tType).
% 0.20/0.29 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, cP: (a > a > a)).
% 0.20/0.29 thf(func_def_1, type, c0: a).
% 0.20/0.29 thf(func_def_5, type, sP0: (a > a > a > (a > a > a > $o) > $o)).
% 0.20/0.29 thf(func_def_6, type, sK1: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_7, type, sK2: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_8, type, sK3: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_9, type, sK4: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_10, type, sK5: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_11, type, sK6: (a > a > a > (a > a > a > $o) > a)).
% 0.20/0.29 thf(func_def_12, type, sK7: (a > a > a > $o)).
% 0.20/0.29 thf(func_def_13, type, sK8: (a > a > a > $o)).
% 0.20/0.29 thf(func_def_14, type, sK9: a).
% 0.20/0.29 thf(func_def_15, type, sK10: a).
% 0.20/0.29 thf(func_def_16, type, sK11: a).
% 0.20/0.29 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4)) & $true & $true) => ! [X2 : a,X3 : a,X4 : a] : ((? [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : ((X0 @ X6 @ X8 @ X10) & (X0 @ X5 @ X7 @ X9) & (X4 = ((cP @ X9 @ X10))) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6)))) | ((X2 = X4) & (X3 = c0)) | ((X3 = X4) & (X2 = c0))) => (? [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : ((X1 @ X6 @ X8 @ X10) & (X1 @ X5 @ X7 @ X9) & (X4 = ((cP @ X9 @ X10))) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6)))) | ((X2 = X4) & (X3 = c0)) | ((X3 = X4) & (X2 = c0))))) & ! [X0 : (a > a > a > $o)] : ($true => $true)),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_JOINFN_MONOTONE_pme)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4)) & $true & $true) => ! [X2 : a,X3 : a,X4 : a] : ((? [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : ((X0 @ X6 @ X8 @ X10) & (X0 @ X5 @ X7 @ X9) & (X4 = ((cP @ X9 @ X10))) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6)))) | ((X2 = X4) & (X3 = c0)) | ((X3 = X4) & (X2 = c0))) => (? [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : ((X1 @ X6 @ X8 @ X10) & (X1 @ X5 @ X7 @ X9) & (X4 = ((cP @ X9 @ X10))) & (X3 = ((cP @ X7 @ X8))) & (X2 = ((cP @ X5 @ X6)))) | ((X2 = X4) & (X3 = c0)) | ((X3 = X4) & (X2 = c0))))) & ! [X0 : (a > a > a > $o)] : ($true => $true))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : ((! [X2 : a,X3 : a,X4 : a] : ((X0 @ X2 @ X3 @ X4) => (X1 @ X2 @ X3 @ X4)) & $true & $true) => ! [X5 : a,X6 : a,X7 : a] : ((? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((X0 @ X9 @ X11 @ X13) & (X0 @ X8 @ X10 @ X12) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5))) => (? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((X1 @ X15 @ X17 @ X19) & (X1 @ X14 @ X16 @ X18) & (((cP @ X18 @ X19)) = X7) & (((cP @ X16 @ X17)) = X6) & (((cP @ X14 @ X15)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5))))) & ($true => $true))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~(! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : ((! [X2 : a,X3 : a,X4 : a] : ((((X0 @ X2 @ X3 @ X4)) = $true) => (((X1 @ X2 @ X3 @ X4)) = $true)) & $true & $true) => ! [X5 : a,X6 : a,X7 : a] : ((? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5))) => (? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X1 @ X15 @ X17 @ X19)) = $true) & (((X1 @ X14 @ X16 @ X18)) = $true) & (((cP @ X18 @ X19)) = X7) & (((cP @ X16 @ X17)) = X6) & (((cP @ X14 @ X15)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5))))) & ($true => $true))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ~ ! [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (! [X2 : a,X3 : a,X4 : a] : ((((X0 @ X2 @ X3 @ X4)) = $true) => (((X1 @ X2 @ X3 @ X4)) = $true)) => ! [X5 : a,X6 : a,X7 : a] : ((? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5))) => (? [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X1 @ X15 @ X17 @ X19)) = $true) & (((X1 @ X14 @ X16 @ X18)) = $true) & (((cP @ X18 @ X19)) = X7) & (((cP @ X16 @ X17)) = X6) & (((cP @ X14 @ X15)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5)))))),
% 0.20/0.29 inference(true_and_false_elimination,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (? [X5 : a,X6 : a,X7 : a] : ((! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X1 @ X15 @ X17 @ X19)) != $true) | (((X1 @ X14 @ X16 @ X18)) != $true) | (((cP @ X18 @ X19)) != X7) | (((cP @ X16 @ X17)) != X6) | (((cP @ X14 @ X15)) != X5)) & ((X5 != X7) | (c0 != X6)) & ((X6 != X7) | (c0 != X5))) & (? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5)))) & ! [X2 : a,X3 : a,X4 : a] : ((((X1 @ X2 @ X3 @ X4)) = $true) | (((X0 @ X2 @ X3 @ X4)) != $true)))),
% 0.20/0.29 inference(ennf_transformation,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (? [X5 : a,X6 : a,X7 : a] : (! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X1 @ X15 @ X17 @ X19)) != $true) | (((X1 @ X14 @ X16 @ X18)) != $true) | (((cP @ X18 @ X19)) != X7) | (((cP @ X16 @ X17)) != X6) | (((cP @ X14 @ X15)) != X5)) & ((X5 != X7) | (c0 != X6)) & ((X6 != X7) | (c0 != X5)) & (? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5)))) & ! [X2 : a,X3 : a,X4 : a] : ((((X1 @ X2 @ X3 @ X4)) = $true) | (((X0 @ X2 @ X3 @ X4)) != $true)))),
% 0.20/0.29 inference(flattening,[],[f6])).
% 0.20/0.29 thf(f8,definition,(
% 0.20/0.29 ! [X0 : (a > a > a > $o),X7 : a,X6 : a,X5 : a] : (? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ~ ($true = ((sP0 @ X5 @ X6 @ X7 @ X0))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (? [X5 : a,X6 : a,X7 : a] : (! [X14 : a,X15 : a,X16 : a,X17 : a,X18 : a,X19 : a] : ((((X1 @ X15 @ X17 @ X19)) != $true) | (((X1 @ X14 @ X16 @ X18)) != $true) | (((cP @ X18 @ X19)) != X7) | (((cP @ X16 @ X17)) != X6) | (((cP @ X14 @ X15)) != X5)) & ((X5 != X7) | (c0 != X6)) & ((X6 != X7) | (c0 != X5)) & (($true = ((sP0 @ X5 @ X6 @ X7 @ X0))) | ((X5 = X7) & (c0 = X6)) | ((X6 = X7) & (c0 = X5)))) & ! [X2 : a,X3 : a,X4 : a] : ((((X1 @ X2 @ X3 @ X4)) = $true) | (((X0 @ X2 @ X3 @ X4)) != $true)))),
% 0.20/0.29 inference(definition_folding,[],[f7,f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ! [X0 : (a > a > a > $o),X7 : a,X6 : a,X5 : a] : (? [X8 : a,X9 : a,X10 : a,X11 : a,X12 : a,X13 : a] : ((((X0 @ X9 @ X11 @ X13)) = $true) & (((X0 @ X8 @ X10 @ X12)) = $true) & (((cP @ X12 @ X13)) = X7) & (((cP @ X10 @ X11)) = X6) & (((cP @ X8 @ X9)) = X5)) | ($true != ((sP0 @ X5 @ X6 @ X7 @ X0))))),
% 0.20/0.29 inference(nnf_transformation,[],[f8])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ! [X0 : (a > a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X4 : a,X5 : a,X6 : a,X7 : a,X8 : a,X9 : a] : ((((X0 @ X5 @ X7 @ X9)) = $true) & ($true = ((X0 @ X4 @ X6 @ X8))) & (((cP @ X8 @ X9)) = X1) & (((cP @ X6 @ X7)) = X2) & (((cP @ X4 @ X5)) = X3)) | ($true != ((sP0 @ X3 @ X2 @ X1 @ X0))))),
% 0.20/0.29 inference(rectify,[],[f10])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ! [X0 : (a > a > a > $o),X1 : a,X2 : a,X3 : a] : ((($true = ((X0 @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0) @ (sK6 @ X3 @ X2 @ X1 @ X0)))) & ($true = ((X0 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0)))) & (((cP @ (sK5 @ X3 @ X2 @ X1 @ X0) @ (sK6 @ X3 @ X2 @ X1 @ X0))) = X1) & (((cP @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0))) = X2) & (((cP @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = X3)) | ($true != ((sP0 @ X3 @ X2 @ X1 @ X0))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP,vAPP,vAPP,vAPP]),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0),skolemize(X9,sK6 @ X3 @ X2 @ X1 @ X0)],[f11])).
% 0.20/0.29 thf(f13,plain,(
% 0.20/0.29 ? [X0 : (a > a > a > $o),X1 : (a > a > a > $o)] : (? [X2 : a,X3 : a,X4 : a] : (! [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : ((((X1 @ X6 @ X8 @ X10)) != $true) | (((X1 @ X5 @ X7 @ X9)) != $true) | (((cP @ X9 @ X10)) != X4) | (((cP @ X7 @ X8)) != X3) | (((cP @ X5 @ X6)) != X2)) & ((X2 != X4) | (c0 != X3)) & ((X3 != X4) | (c0 != X2)) & (($true = ((sP0 @ X2 @ X3 @ X4 @ X0))) | ((X2 = X4) & (c0 = X3)) | ((X3 = X4) & (c0 = X2)))) & ! [X11 : a,X12 : a,X13 : a] : (($true = ((X1 @ X11 @ X12 @ X13))) | ($true != ((X0 @ X11 @ X12 @ X13)))))),
% 0.20/0.29 inference(rectify,[],[f9])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 (! [X5 : a,X6 : a,X7 : a,X8 : a,X9 : a,X10 : a] : (($true != ((sK8 @ X6 @ X8 @ X10))) | ($true != ((sK8 @ X5 @ X7 @ X9))) | (((cP @ X9 @ X10)) != sK11) | (((cP @ X7 @ X8)) != sK10) | (((cP @ X5 @ X6)) != sK9)) & ((sK9 != sK11) | (c0 != sK10)) & ((sK10 != sK11) | (c0 != sK9)) & (($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | ((sK9 = sK11) & (c0 = sK10)) | ((sK10 = sK11) & (c0 = sK9)))) & ! [X11 : a,X12 : a,X13 : a] : (($true = ((sK8 @ X11 @ X12 @ X13))) | ($true != ((sK7 @ X11 @ X12 @ X13))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11)],[f13])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : (a > a > a > $o),X1 : a] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | (((cP @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK2 @ X3 @ X2 @ X1 @ X0))) = X3)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : (a > a > a > $o),X1 : a] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | (((cP @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0))) = X2)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : (a > a > a > $o),X1 : a] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | (((cP @ (sK5 @ X3 @ X2 @ X1 @ X0) @ (sK6 @ X3 @ X2 @ X1 @ X0))) = X1)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : (a > a > a > $o),X1 : a] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | ($true = ((X0 @ (sK1 @ X3 @ X2 @ X1 @ X0) @ (sK3 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X3 @ X2 @ X1 @ X0))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : (a > a > a > $o),X1 : a] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | ($true = ((X0 @ (sK2 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X3 @ X2 @ X1 @ X0) @ (sK6 @ X3 @ X2 @ X1 @ X0))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f12])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ( ! [X11 : a,X12 : a,X13 : a] : (($true != ((sK7 @ X11 @ X12 @ X13))) | ($true = ((sK8 @ X11 @ X12 @ X13)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | (c0 = sK10) | (c0 = sK9)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | (c0 = sK10) | (sK10 = sK11)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | (sK9 = sK11) | (c0 = sK9)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | (sK9 = sK11) | (sK10 = sK11)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 (sK10 != sK11) | (c0 != sK9)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 (sK9 != sK11) | (c0 != sK10)),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 ( ! [X10 : a,X8 : a,X6 : a,X9 : a,X7 : a,X5 : a] : ((((cP @ X9 @ X10)) != sK11) | ($true != ((sK8 @ X5 @ X7 @ X9))) | ($true != ((sK8 @ X6 @ X8 @ X10))) | (((cP @ X7 @ X8)) != sK10) | (((cP @ X5 @ X6)) != sK9)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f14])).
% 0.20/0.29 thf(f29,definition,(
% 0.20/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.29 thf(f31,definition,(
% 0.20/0.29 spl12_1 <=> (c0 = sK9)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition])).
% 0.20/0.29 thf(f35,definition,(
% 0.20/0.29 spl12_2 <=> (c0 = sK10)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition])).
% 0.20/0.29 thf(f39,definition,(
% 0.20/0.29 spl12_3 <=> ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ($true = ((sP0 @ sK9 @ sK10 @ sK11 @ sK7))) | ~spl12_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f39])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 spl12_1 | spl12_2 | spl12_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f21,f39,f35,f31])).
% 0.20/0.29 thf(f44,definition,(
% 0.20/0.29 spl12_4 <=> (sK10 = sK11)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition])).
% 0.20/0.29 thf(f47,plain,(
% 0.20/0.29 spl12_4 | spl12_2 | spl12_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f22,f39,f35,f44])).
% 0.20/0.29 thf(f49,definition,(
% 0.20/0.29 spl12_5 <=> (sK9 = sK11)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 spl12_1 | spl12_5 | spl12_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f23,f39,f49,f31])).
% 0.20/0.29 thf(f53,plain,(
% 0.20/0.29 spl12_4 | spl12_5 | spl12_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f24,f39,f49,f44])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ~spl12_1 | ~spl12_4),
% 0.20/0.29 inference(avatar_split_clause,[],[f25,f44,f31])).
% 0.20/0.29 thf(f55,plain,(
% 0.20/0.29 ~spl12_2 | ~spl12_5),
% 0.20/0.29 inference(avatar_split_clause,[],[f26,f49,f35])).
% 0.20/0.29 thf(f58,plain,(
% 0.20/0.29 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | ($true = ((sK8 @ X0 @ X1 @ X2))) | ($false = ((sK7 @ X0 @ X1 @ X2)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f20,f29])).
% 0.20/0.29 thf(f60,plain,(
% 0.20/0.29 ( ! [X2 : a,X0 : a,X1 : a] : (($true = ((sK8 @ X0 @ X1 @ X2))) | ($false = ((sK7 @ X0 @ X1 @ X2)))) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.29 thf(f65,plain,(
% 0.20/0.29 ($true != $true) | (sK9 = ((cP @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f15,f41])).
% 0.20/0.29 thf(f68,plain,(
% 0.20/0.29 (sK9 = ((cP @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f65])).
% 0.20/0.29 thf(f70,plain,(
% 0.20/0.29 ($true != $true) | (sK10 = ((cP @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f16,f41])).
% 0.20/0.29 thf(f73,plain,(
% 0.20/0.29 (sK10 = ((cP @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f70])).
% 0.20/0.29 thf(f75,plain,(
% 0.20/0.29 ($true != $true) | (sK11 = ((cP @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f17,f41])).
% 0.20/0.29 thf(f78,plain,(
% 0.20/0.29 (sK11 = ((cP @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.29 thf(f79,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((sK11 != sK11) | ($true != ((sK8 @ X0 @ X1 @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ($true != ((sK8 @ X2 @ X3 @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | (sK10 != ((cP @ X1 @ X3))) | (sK9 != ((cP @ X0 @ X2)))) ) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f27,f78])).
% 0.20/0.29 thf(f80,plain,(
% 0.20/0.29 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((sK10 != ((cP @ X1 @ X3))) | ($true != ((sK8 @ X2 @ X3 @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ($true != ((sK8 @ X0 @ X1 @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | (sK9 != ((cP @ X0 @ X2)))) ) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.29 thf(f82,plain,(
% 0.20/0.29 ( ! [X0 : a,X1 : a] : ((sK10 != sK10) | ($true != ((sK8 @ X0 @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ($true != ((sK8 @ X1 @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | (sK9 != ((cP @ X1 @ X0)))) ) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f80,f73])).
% 0.20/0.29 thf(f84,plain,(
% 0.20/0.29 ( ! [X0 : a,X1 : a] : (($true != ((sK8 @ X1 @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ($true != ((sK8 @ X0 @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | (sK9 != ((cP @ X1 @ X0)))) ) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f82])).
% 0.20/0.29 thf(f93,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK7 @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f18,f41])).
% 0.20/0.29 thf(f96,plain,(
% 0.20/0.29 ($true = ((sK7 @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f93])).
% 0.20/0.29 thf(f97,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK8 @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f20,f96])).
% 0.20/0.29 thf(f98,plain,(
% 0.20/0.29 ($true = ((sK8 @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK3 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK5 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f97])).
% 0.20/0.29 thf(f100,plain,(
% 0.20/0.29 ( ! [X0 : a] : (($true != $true) | ($true != ((sK8 @ X0 @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | (sK9 != ((cP @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ X0)))) ) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f84,f98])).
% 0.20/0.29 thf(f103,plain,(
% 0.20/0.29 ( ! [X0 : a] : ((sK9 != ((cP @ (sK1 @ sK9 @ sK10 @ sK11 @ sK7) @ X0))) | ($true != ((sK8 @ X0 @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7))))) ) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f100])).
% 0.20/0.29 thf(f105,plain,(
% 0.20/0.29 (sK9 != sK9) | ($true != ((sK8 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f103,f68])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 ($true != ((sK8 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f105])).
% 0.20/0.29 thf(f107,plain,(
% 0.20/0.29 ($true != $true) | ($false = ((sK7 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f106,f60])).
% 0.20/0.29 thf(f110,plain,(
% 0.20/0.29 ($false = ((sK7 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f107])).
% 0.20/0.29 thf(f165,plain,(
% 0.20/0.29 ($true != $true) | ($true = ((sK7 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f19,f41])).
% 0.20/0.29 thf(f168,plain,(
% 0.20/0.29 ($true = ((sK7 @ (sK2 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK4 @ sK9 @ sK10 @ sK11 @ sK7) @ (sK6 @ sK9 @ sK10 @ sK11 @ sK7)))) | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f165])).
% 0.20/0.29 thf(f169,plain,(
% 0.20/0.29 ($true = $false) | ~spl12_3),
% 0.20/0.29 inference(constrained_superposition,[],[f168,f110])).
% 0.20/0.29 thf(f175,plain,(
% 0.20/0.29 $false | ~spl12_3),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f169])).
% 0.20/0.29 thf(f176,plain,(
% 0.20/0.29 ~spl12_3),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f175])).
% 0.20/0.29 cnf(s1, plain, spl12_1 | spl12_2 | spl12_3, inference(sat_conversion,[],[f42])).
% 0.20/0.29 cnf(s2, plain, spl12_2 | spl12_3 | spl12_4, inference(sat_conversion,[],[f47])).
% 0.20/0.29 cnf(s3, plain, spl12_1 | spl12_3 | spl12_5, inference(sat_conversion,[],[f52])).
% 0.20/0.29 cnf(s4, plain, spl12_3 | spl12_4 | spl12_5, inference(sat_conversion,[],[f53])).
% 0.20/0.29 cnf(s5, plain, ~spl12_1 | ~spl12_4, inference(sat_conversion,[],[f54])).
% 0.20/0.29 cnf(s6, plain, ~spl12_2 | ~spl12_5, inference(sat_conversion,[],[f55])).
% 0.20/0.29 cnf(s9, plain, ~spl12_3, inference(sat_conversion,[],[f176])).
% 0.20/0.29 cnf(s10, plain, spl12_4 | spl12_5, inference(rat,[],[s4,s9])).
% 0.20/0.29 cnf(s11, plain, spl12_1 | spl12_5, inference(rat,[],[s3,s9])).
% 0.20/0.29 cnf(s12, plain, spl12_2 | spl12_4, inference(rat,[],[s2,s9])).
% 0.20/0.29 cnf(s13, plain, spl12_1 | spl12_2, inference(rat,[],[s1,s9])).
% 0.20/0.29 cnf(s14, plain, spl12_1, inference(rat,[],[s6,s13,s11])).
% 0.20/0.29 cnf(s15, plain, ~spl12_4, inference(rat,[],[s5,s14])).
% 0.20/0.29 cnf(s16, plain, spl12_5, inference(rat,[],[s10,s15])).
% 0.20/0.29 cnf(s17, plain, spl12_2, inference(rat,[],[s12,s15])).
% 0.20/0.29 cnf(s18, plain, $false, inference(rat,[],[s6,s16,s17])).
% 0.20/0.29 thf(f177,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s18])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (453127)------------------------------
% 0.20/0.29 % (453127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (453127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (453127)CaDiCaL version: 2.1.3
% 0.20/0.29 % (453127)Termination reason: Refutation
% 0.20/0.29 % (453127)Time elapsed: 0.015 s
% 0.20/0.29 % (453127)Peak memory usage: 13 MB
% 0.20/0.29 % (453127)Instructions burned: 27 (million)
% 0.20/0.29 % (453102)Success in time 0.056 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------