%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV107^5 : 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 : n004.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 08:39:00 AM UTC 2026
% Result : Theorem 0.23s 0.38s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV107^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 % Computer : n004.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 15:10:37 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.23/0.30 Running first-order model finding
% 0.23/0.30 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
% 0.23/0.38 % (1410751)Will run a generic schedule for satisfiability detection.
% 0.23/0.38 % (1410756)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=568085658_2999 on theBenchmark for (2999ds/0Mi)
% 0.23/0.38 % Exception at run slice level
% 0.23/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.38 % (1410757)% WARNING: option uhcvi not known.
% 0.23/0.38 % (1410759)dis+10_1_sil=32000:sp=arity:random_seed=1120891754:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.23/0.38 % (1410758)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4042333773:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.23/0.38 % (1410760)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1112148894:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.23/0.38 % (1410761)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4014815529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.38 % (1410762)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=358526447:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.23/0.38 % (1410760)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.38 % (1410764)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4141527905:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.23/0.38 % Exception at run slice level
% 0.23/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.38 % (1410757)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=696354078:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.23/0.38 % (1410757)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.38 % (1410757)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.23/0.38 % (1410759) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1410751-1410759"...
% 0.23/0.38 % (1410761) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1410751-1410761"...
% 0.23/0.38 % (1410760) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1410751-1410760"...
% 0.23/0.38 % (1410759)...printing done.
% 0.23/0.38 % (1410771)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=265717371:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.23/0.38 % (1410761)...printing done.
% 0.23/0.38 % (1410760)...printing done.
% 0.23/0.38 % (1410759)Refutation found. Thanks to Tanya!
% 0.23/0.38 % SZS status Theorem for theBenchmark
% 0.23/0.38 % SZS output start Proof for theBenchmark
% 0.23/0.38 thf(type_def_5, type, a: $tType).
% 0.23/0.38 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.38 thf(func_def_0, type, z: a).
% 0.23/0.38 thf(func_def_1, type, cR: (a > a > $o)).
% 0.23/0.38 thf(func_def_2, type, f: (a > $i > $o)).
% 0.23/0.38 thf(func_def_3, type, cS: ($i > $i > $o)).
% 0.23/0.38 thf(func_def_7, type, sP0: $o).
% 0.23/0.38 thf(func_def_9, type, sK2: a).
% 0.23/0.38 thf(func_def_10, type, sK3: a).
% 0.23/0.38 thf(func_def_12, type, sK5: (a > a)).
% 0.23/0.38 thf(func_def_13, type, sK6: a).
% 0.23/0.38 thf(func_def_14, type, sK7: ($i > a)).
% 0.23/0.38 thf(func_def_15, type, sK8: (a > $i)).
% 0.23/0.38 thf(f1,conjecture,(
% 0.23/0.38 (! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X7 : a,X8 : a,X4 : $i] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : $i,X6 : $i] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4)) => (! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)) & ! [X4 : $i,X7 : a,X8 : a] : ((! [X2 : a] : (((cR @ X8 @ z) & ~(f @ X2 @ X4)) | (f @ X8 @ X4)) & ! [X2 : a] : (((cR @ X7 @ z) & ~(f @ X2 @ X4)) | (f @ X7 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4))))),
% 0.23/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM552B_pme)).
% 0.23/0.38 thf(f2,negated_conjecture,(
% 0.23/0.38 ~((! [X3 : a] : (cR @ X3 @ X3) & ! [X0 : a,X1 : a,X2 : a] : (((cR @ X2 @ X1) & (cR @ X0 @ X1)) => (cR @ X0 @ X2))) => ((! [X7 : a,X8 : a,X4 : $i] : (((f @ X8 @ X4) & (f @ X7 @ X4)) => (cR @ X7 @ X8)) & ! [X3 : a,X5 : $i,X6 : $i] : (((f @ X3 @ X6) & (f @ X3 @ X5)) => (cS @ X5 @ X6)) & ! [X3 : a] : ? [X4 : $i] : (f @ X3 @ X4)) => (! [X4 : $i] : ? [X3 : a] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)) & ! [X4 : $i,X7 : a,X8 : a] : ((! [X2 : a] : (((cR @ X8 @ z) & ~(f @ X2 @ X4)) | (f @ X8 @ X4)) & ! [X2 : a] : (((cR @ X7 @ z) & ~(f @ X2 @ X4)) | (f @ X7 @ X4))) => (cR @ X7 @ X8)) & ! [X3 : a] : ? [X4 : $i] : ! [X2 : a] : (((cR @ X3 @ z) & ~(f @ X2 @ X4)) | (f @ X3 @ X4)))))),
% 0.23/0.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.38 thf(f3,plain,(
% 0.23/0.38 ~((! [X0 : a] : (cR @ X0 @ X0) & ! [X1 : a,X2 : a,X3 : a] : (((cR @ X3 @ X2) & (cR @ X1 @ X2)) => (cR @ X1 @ X3))) => ((! [X4 : a,X5 : a,X6 : $i] : (((f @ X5 @ X6) & (f @ X4 @ X6)) => (cR @ X4 @ X5)) & ! [X7 : a,X8 : $i,X9 : $i] : (((f @ X7 @ X9) & (f @ X7 @ X8)) => (cS @ X8 @ X9)) & ! [X10 : a] : ? [X11 : $i] : (f @ X10 @ X11)) => (! [X12 : $i] : ? [X13 : a] : ! [X14 : a] : (((cR @ X13 @ z) & ~(f @ X14 @ X12)) | (f @ X13 @ X12)) & ! [X15 : $i,X16 : a,X17 : a] : ((! [X18 : a] : (((cR @ X17 @ z) & ~(f @ X18 @ X15)) | (f @ X17 @ X15)) & ! [X19 : a] : (((cR @ X16 @ z) & ~(f @ X19 @ X15)) | (f @ X16 @ X15))) => (cR @ X16 @ X17)) & ! [X20 : a] : ? [X21 : $i] : ! [X22 : a] : (((cR @ X20 @ z) & ~(f @ X22 @ X21)) | (f @ X20 @ X21)))))),
% 0.23/0.38 inference(rectify,[],[f2])).
% 0.23/0.38 thf(f4,plain,(
% 0.23/0.38 ~((! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : (((((cR @ X3 @ X2)) = $true) & (((cR @ X1 @ X2)) = $true)) => (((cR @ X1 @ X3)) = $true))) => ((! [X4 : a,X5 : a,X6 : $i] : (((((f @ X5 @ X6)) = $true) & (((f @ X4 @ X6)) = $true)) => (((cR @ X4 @ X5)) = $true)) & ! [X7 : a,X8 : $i,X9 : $i] : (((((f @ X7 @ X9)) = $true) & (((f @ X7 @ X8)) = $true)) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : $i] : (((f @ X10 @ X11)) = $true)) => (! [X12 : $i] : ? [X13 : a] : ! [X14 : a] : (((((cR @ X13 @ z)) = $true) & ~ (((f @ X14 @ X12)) = $true)) | (((f @ X13 @ X12)) = $true)) & ! [X15 : $i,X16 : a,X17 : a] : ((! [X18 : a] : (((((cR @ X17 @ z)) = $true) & ~ (((f @ X18 @ X15)) = $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & ~ (((f @ X19 @ X15)) = $true)) | (((f @ X16 @ X15)) = $true))) => (((cR @ X16 @ X17)) = $true)) & ! [X20 : a] : ? [X21 : $i] : ! [X22 : a] : (((((cR @ X20 @ z)) = $true) & ~ (((f @ X22 @ X21)) = $true)) | (((f @ X20 @ X21)) = $true)))))),
% 0.23/0.38 inference(fool_elimination,[],[f3])).
% 0.23/0.38 thf(f5,plain,(
% 0.23/0.38 ~((! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : (((((cR @ X3 @ X2)) = $true) & (((cR @ X1 @ X2)) = $true)) => (((cR @ X1 @ X3)) = $true))) => ((! [X4 : a,X5 : a,X6 : $i] : (((((f @ X5 @ X6)) = $true) & (((f @ X4 @ X6)) = $true)) => (((cR @ X4 @ X5)) = $true)) & ! [X7 : a,X8 : $i,X9 : $i] : (((((f @ X7 @ X9)) = $true) & (((f @ X7 @ X8)) = $true)) => (((cS @ X8 @ X9)) = $true)) & ! [X10 : a] : ? [X11 : $i] : (((f @ X10 @ X11)) = $true)) => (! [X12 : $i] : ? [X13 : a] : ! [X14 : a] : (((((cR @ X13 @ z)) = $true) & (((f @ X14 @ X12)) != $true)) | (((f @ X13 @ X12)) = $true)) & ! [X15 : $i,X16 : a,X17 : a] : ((! [X18 : a] : (((((cR @ X17 @ z)) = $true) & (((f @ X18 @ X15)) != $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & (((f @ X19 @ X15)) != $true)) | (((f @ X16 @ X15)) = $true))) => (((cR @ X16 @ X17)) = $true)) & ! [X20 : a] : ? [X21 : $i] : ! [X22 : a] : (((((cR @ X20 @ z)) = $true) & (((f @ X22 @ X21)) != $true)) | (((f @ X20 @ X21)) = $true)))))),
% 0.23/0.38 inference(flattening,[],[f4])).
% 0.23/0.38 thf(f6,plain,(
% 0.23/0.38 ((? [X12 : $i] : ! [X13 : a] : ? [X14 : a] : (((((cR @ X13 @ z)) != $true) | (((f @ X14 @ X12)) = $true)) & (((f @ X13 @ X12)) != $true)) | ? [X15 : $i,X16 : a,X17 : a] : ((((cR @ X16 @ X17)) != $true) & (! [X18 : a] : (((((cR @ X17 @ z)) = $true) & (((f @ X18 @ X15)) != $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & (((f @ X19 @ X15)) != $true)) | (((f @ X16 @ X15)) = $true)))) | ? [X20 : a] : ! [X21 : $i] : ? [X22 : a] : (((((cR @ X20 @ z)) != $true) | (((f @ X22 @ X21)) = $true)) & (((f @ X20 @ X21)) != $true))) & (! [X4 : a,X5 : a,X6 : $i] : ((((cR @ X4 @ X5)) = $true) | ((((f @ X5 @ X6)) != $true) | (((f @ X4 @ X6)) != $true))) & ! [X7 : a,X8 : $i,X9 : $i] : ((((cS @ X8 @ X9)) = $true) | ((((f @ X7 @ X9)) != $true) | (((f @ X7 @ X8)) != $true))) & ! [X10 : a] : ? [X11 : $i] : (((f @ X10 @ X11)) = $true))) & (! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((cR @ X1 @ X3)) = $true) | ((((cR @ X3 @ X2)) != $true) | (((cR @ X1 @ X2)) != $true))))),
% 0.23/0.38 inference(ennf_transformation,[],[f5])).
% 0.23/0.38 thf(f7,plain,(
% 0.23/0.38 (? [X12 : $i] : ! [X13 : a] : ? [X14 : a] : (((((cR @ X13 @ z)) != $true) | (((f @ X14 @ X12)) = $true)) & (((f @ X13 @ X12)) != $true)) | ? [X15 : $i,X16 : a,X17 : a] : ((((cR @ X16 @ X17)) != $true) & ! [X18 : a] : (((((cR @ X17 @ z)) = $true) & (((f @ X18 @ X15)) != $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & (((f @ X19 @ X15)) != $true)) | (((f @ X16 @ X15)) = $true))) | ? [X20 : a] : ! [X21 : $i] : ? [X22 : a] : (((((cR @ X20 @ z)) != $true) | (((f @ X22 @ X21)) = $true)) & (((f @ X20 @ X21)) != $true))) & ! [X4 : a,X5 : a,X6 : $i] : ((((cR @ X4 @ X5)) = $true) | (((f @ X5 @ X6)) != $true) | (((f @ X4 @ X6)) != $true)) & ! [X7 : a,X8 : $i,X9 : $i] : ((((cS @ X8 @ X9)) = $true) | (((f @ X7 @ X9)) != $true) | (((f @ X7 @ X8)) != $true)) & ! [X10 : a] : ? [X11 : $i] : (((f @ X10 @ X11)) = $true) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((cR @ X1 @ X3)) = $true) | (((cR @ X3 @ X2)) != $true) | (((cR @ X1 @ X2)) != $true))),
% 0.23/0.38 inference(flattening,[],[f6])).
% 0.23/0.38 thf(f8,definition,(
% 0.23/0.38 ? [X15 : $i,X16 : a,X17 : a] : ((((cR @ X16 @ X17)) != $true) & ! [X18 : a] : (((((cR @ X17 @ z)) = $true) & (((f @ X18 @ X15)) != $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & (((f @ X19 @ X15)) != $true)) | (((f @ X16 @ X15)) = $true))) | ~ ($true = sP0)),
% 0.23/0.38 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.23/0.38 thf(f9,plain,(
% 0.23/0.38 (? [X12 : $i] : ! [X13 : a] : ? [X14 : a] : (((((cR @ X13 @ z)) != $true) | (((f @ X14 @ X12)) = $true)) & (((f @ X13 @ X12)) != $true)) | ($true = sP0) | ? [X20 : a] : ! [X21 : $i] : ? [X22 : a] : (((((cR @ X20 @ z)) != $true) | (((f @ X22 @ X21)) = $true)) & (((f @ X20 @ X21)) != $true))) & ! [X4 : a,X5 : a,X6 : $i] : ((((cR @ X4 @ X5)) = $true) | (((f @ X5 @ X6)) != $true) | (((f @ X4 @ X6)) != $true)) & ! [X7 : a,X8 : $i,X9 : $i] : ((((cS @ X8 @ X9)) = $true) | (((f @ X7 @ X9)) != $true) | (((f @ X7 @ X8)) != $true)) & ! [X10 : a] : ? [X11 : $i] : (((f @ X10 @ X11)) = $true) & ! [X0 : a] : (((cR @ X0 @ X0)) = $true) & ! [X1 : a,X2 : a,X3 : a] : ((((cR @ X1 @ X3)) = $true) | (((cR @ X3 @ X2)) != $true) | (((cR @ X1 @ X2)) != $true))),
% 0.23/0.38 inference(definition_folding,[],[f7,f8])).
% 0.23/0.38 thf(f10,plain,(
% 0.23/0.38 ? [X15 : $i,X16 : a,X17 : a] : ((((cR @ X16 @ X17)) != $true) & ! [X18 : a] : (((((cR @ X17 @ z)) = $true) & (((f @ X18 @ X15)) != $true)) | (((f @ X17 @ X15)) = $true)) & ! [X19 : a] : (((((cR @ X16 @ z)) = $true) & (((f @ X19 @ X15)) != $true)) | (((f @ X16 @ X15)) = $true))) | ($true != sP0)),
% 0.23/0.38 inference(nnf_transformation,[],[f8])).
% 0.23/0.38 thf(f11,plain,(
% 0.23/0.38 ? [X0 : $i,X1 : a,X2 : a] : ((((cR @ X1 @ X2)) != $true) & ! [X3 : a] : ((($true = ((cR @ X2 @ z))) & ($true != ((f @ X3 @ X0)))) | ($true = ((f @ X2 @ X0)))) & ! [X4 : a] : ((($true = ((cR @ X1 @ z))) & ($true != ((f @ X4 @ X0)))) | ($true = ((f @ X1 @ X0))))) | ($true != sP0)),
% 0.23/0.38 inference(rectify,[],[f10])).
% 0.23/0.38 thf(f12,plain,(
% 0.23/0.38 (($true != ((cR @ sK2 @ sK3))) & ! [X3 : a] : ((($true = ((cR @ sK3 @ z))) & ($true != ((f @ X3 @ sK1)))) | ($true = ((f @ sK3 @ sK1)))) & ! [X4 : a] : ((($true = ((cR @ sK2 @ z))) & ($true != ((f @ X4 @ sK1)))) | ($true = ((f @ sK2 @ sK1))))) | ($true != sP0)),
% 0.23/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f11])).
% 0.23/0.38 thf(f13,plain,(
% 0.23/0.38 (? [X0 : $i] : ! [X1 : a] : ? [X2 : a] : ((($true != ((cR @ X1 @ z))) | ($true = ((f @ X2 @ X0)))) & ($true != ((f @ X1 @ X0)))) | ($true = sP0) | ? [X3 : a] : ! [X4 : $i] : ? [X5 : a] : (((((cR @ X3 @ z)) != $true) | ($true = ((f @ X5 @ X4)))) & (((f @ X3 @ X4)) != $true))) & ! [X6 : a,X7 : a,X8 : $i] : (($true = ((cR @ X6 @ X7))) | (((f @ X7 @ X8)) != $true) | ($true != ((f @ X6 @ X8)))) & ! [X9 : a,X10 : $i,X11 : $i] : (($true = ((cS @ X10 @ X11))) | ($true != ((f @ X9 @ X11))) | ($true != ((f @ X9 @ X10)))) & ! [X12 : a] : ? [X13 : $i] : ($true = ((f @ X12 @ X13))) & ! [X14 : a] : ($true = ((cR @ X14 @ X14))) & ! [X15 : a,X16 : a,X17 : a] : (($true = ((cR @ X15 @ X17))) | ($true != ((cR @ X17 @ X16))) | ($true != ((cR @ X15 @ X16))))),
% 0.23/0.39 inference(rectify,[],[f9])).
% 0.23/0.39 thf(f14,plain,(
% 0.23/0.39 (! [X1 : a] : ((($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK5 @ X1) @ sK4)))) & ($true != ((f @ X1 @ sK4)))) | ($true = sP0) | ! [X4 : $i] : ((($true != ((cR @ sK6 @ z))) | ($true = ((f @ (sK7 @ X4) @ X4)))) & ($true != ((f @ sK6 @ X4))))) & ! [X6 : a,X7 : a,X8 : $i] : (($true = ((cR @ X6 @ X7))) | (((f @ X7 @ X8)) != $true) | ($true != ((f @ X6 @ X8)))) & ! [X9 : a,X10 : $i,X11 : $i] : (($true = ((cS @ X10 @ X11))) | ($true != ((f @ X9 @ X11))) | ($true != ((f @ X9 @ X10)))) & ! [X12 : a] : ($true = ((f @ X12 @ (sK8 @ X12)))) & ! [X14 : a] : ($true = ((cR @ X14 @ X14))) & ! [X15 : a,X16 : a,X17 : a] : (($true = ((cR @ X15 @ X17))) | ($true != ((cR @ X17 @ X16))) | ($true != ((cR @ X15 @ X16))))),
% 0.23/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,vAPP,sK6,vAPP,vAPP]),skolemize(X0,sK4),skolemize(X13,sK8 @ X12),skolemize(X3,sK6),skolemize(X13,sK8 @ X12),skolemize(X13,sK8 @ X12)],[f13])).
% 0.23/0.39 thf(f15,plain,(
% 0.23/0.39 ( ! [X4 : a] : (($true != ((f @ X4 @ sK1))) | ($true = ((f @ sK2 @ sK1))) | ($true != sP0)) )),
% 0.23/0.39 inference(cnf_transformation,[],[f12])).
% 0.23/0.39 thf(f16,plain,(
% 0.23/0.39 ($true = ((cR @ sK2 @ z))) | ($true = ((f @ sK2 @ sK1))) | ($true != sP0)),
% 0.23/0.39 inference(cnf_transformation,[],[f12])).
% 0.23/0.39 thf(f17,plain,(
% 0.23/0.39 ( ! [X3 : a] : (($true != ((f @ X3 @ sK1))) | ($true = ((f @ sK3 @ sK1))) | ($true != sP0)) )),
% 0.23/0.39 inference(cnf_transformation,[],[f12])).
% 0.23/0.39 thf(f18,plain,(
% 0.23/0.39 ($true = ((cR @ sK3 @ z))) | ($true = ((f @ sK3 @ sK1))) | ($true != sP0)),
% 0.23/0.39 inference(cnf_transformation,[],[f12])).
% 0.23/0.39 thf(f19,plain,(
% 0.23/0.39 ($true != ((cR @ sK2 @ sK3))) | ($true != sP0)),
% 0.23/0.39 inference(cnf_transformation,[],[f12])).
% 0.23/0.39 thf(f20,plain,(
% 0.23/0.39 ( ! [X16 : a,X17 : a,X15 : a] : (($true != ((cR @ X17 @ X16))) | ($true = ((cR @ X15 @ X17))) | ($true != ((cR @ X15 @ X16)))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f21,plain,(
% 0.23/0.39 ( ! [X14 : a] : (($true = ((cR @ X14 @ X14)))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f22,plain,(
% 0.23/0.39 ( ! [X12 : a] : (($true = ((f @ X12 @ (sK8 @ X12))))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f24,plain,(
% 0.23/0.39 ( ! [X8 : $i,X6 : a,X7 : a] : (($true != ((f @ X6 @ X8))) | (((f @ X7 @ X8)) != $true) | ($true = ((cR @ X6 @ X7)))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f25,plain,(
% 0.23/0.39 ( ! [X1 : a,X4 : $i] : (($true != ((f @ X1 @ sK4))) | ($true = sP0) | ($true != ((f @ sK6 @ X4)))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f27,plain,(
% 0.23/0.39 ( ! [X1 : a,X4 : $i] : (($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK5 @ X1) @ sK4))) | ($true = sP0) | ($true != ((f @ sK6 @ X4)))) )),
% 0.23/0.39 inference(cnf_transformation,[],[f14])).
% 0.23/0.39 thf(f32,definition,(
% 0.23/0.39 spl9_1 <=> ! [X4 : $i] : ($true != ((f @ sK6 @ X4)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.23/0.39 thf(f33,plain,(
% 0.23/0.39 ( ! [X4 : $i] : (($true != ((f @ sK6 @ X4)))) ) | ~spl9_1),
% 0.23/0.39 inference(avatar_component_clause,[],[f32])).
% 0.23/0.39 thf(f35,definition,(
% 0.23/0.39 spl9_2 <=> ($true = sP0)),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.23/0.39 thf(f39,definition,(
% 0.23/0.39 spl9_3 <=> ! [X1 : a] : ($true != ((f @ X1 @ sK4)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
% 0.23/0.39 thf(f40,plain,(
% 0.23/0.39 ( ! [X1 : a] : (($true != ((f @ X1 @ sK4)))) ) | ~spl9_3),
% 0.23/0.39 inference(avatar_component_clause,[],[f39])).
% 0.23/0.39 thf(f41,plain,(
% 0.23/0.39 spl9_1 | spl9_2 | spl9_3),
% 0.23/0.39 inference(avatar_split_clause,[],[f25,f39,f35,f32])).
% 0.23/0.39 thf(f51,definition,(
% 0.23/0.39 spl9_6 <=> ! [X1 : a] : (($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK5 @ X1) @ sK4))))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition])).
% 0.23/0.39 thf(f52,plain,(
% 0.23/0.39 ( ! [X1 : a] : (($true != ((cR @ X1 @ z))) | ($true = ((f @ (sK5 @ X1) @ sK4)))) ) | ~spl9_6),
% 0.23/0.39 inference(avatar_component_clause,[],[f51])).
% 0.23/0.39 thf(f53,plain,(
% 0.23/0.39 spl9_1 | spl9_2 | spl9_6),
% 0.23/0.39 inference(avatar_split_clause,[],[f27,f51,f35,f32])).
% 0.23/0.39 thf(f56,definition,(
% 0.23/0.39 spl9_7 <=> ($true = ((f @ sK2 @ sK1)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition])).
% 0.23/0.39 thf(f58,plain,(
% 0.23/0.39 ($true = ((f @ sK2 @ sK1))) | ~spl9_7),
% 0.23/0.39 inference(avatar_component_clause,[],[f56])).
% 0.23/0.39 thf(f60,definition,(
% 0.23/0.39 spl9_8 <=> ! [X4 : a] : ($true != ((f @ X4 @ sK1)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
% 0.23/0.39 thf(f61,plain,(
% 0.23/0.39 ( ! [X4 : a] : (($true != ((f @ X4 @ sK1)))) ) | ~spl9_8),
% 0.23/0.39 inference(avatar_component_clause,[],[f60])).
% 0.23/0.39 thf(f62,plain,(
% 0.23/0.39 ~spl9_2 | spl9_7 | spl9_8),
% 0.23/0.39 inference(avatar_split_clause,[],[f15,f60,f56,f35])).
% 0.23/0.39 thf(f64,definition,(
% 0.23/0.39 spl9_9 <=> ($true = ((cR @ sK2 @ z)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
% 0.23/0.39 thf(f66,plain,(
% 0.23/0.39 ($true = ((cR @ sK2 @ z))) | ~spl9_9),
% 0.23/0.39 inference(avatar_component_clause,[],[f64])).
% 0.23/0.39 thf(f67,plain,(
% 0.23/0.39 ~spl9_2 | spl9_7 | spl9_9),
% 0.23/0.39 inference(avatar_split_clause,[],[f16,f64,f56,f35])).
% 0.23/0.39 thf(f69,definition,(
% 0.23/0.39 spl9_10 <=> ($true = ((f @ sK3 @ sK1)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition])).
% 0.23/0.39 thf(f71,plain,(
% 0.23/0.39 ($true = ((f @ sK3 @ sK1))) | ~spl9_10),
% 0.23/0.39 inference(avatar_component_clause,[],[f69])).
% 0.23/0.39 thf(f72,plain,(
% 0.23/0.39 ~spl9_2 | spl9_10 | spl9_8),
% 0.23/0.39 inference(avatar_split_clause,[],[f17,f60,f69,f35])).
% 0.23/0.39 thf(f74,definition,(
% 0.23/0.39 spl9_11 <=> ($true = ((cR @ sK3 @ z)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition])).
% 0.23/0.39 thf(f76,plain,(
% 0.23/0.39 ($true = ((cR @ sK3 @ z))) | ~spl9_11),
% 0.23/0.39 inference(avatar_component_clause,[],[f74])).
% 0.23/0.39 thf(f77,plain,(
% 0.23/0.39 ~spl9_2 | spl9_10 | spl9_11),
% 0.23/0.39 inference(avatar_split_clause,[],[f18,f74,f69,f35])).
% 0.23/0.39 thf(f79,definition,(
% 0.23/0.39 spl9_12 <=> ($true = ((cR @ sK2 @ sK3)))),
% 0.23/0.39 introduced(definition,[new_symbols(definition,[spl9_12])],[avatar_definition])).
% 0.23/0.39 thf(f81,plain,(
% 0.23/0.39 ($true != ((cR @ sK2 @ sK3))) | spl9_12),
% 0.23/0.39 inference(avatar_component_clause,[],[f79])).
% 0.23/0.39 thf(f82,plain,(
% 0.23/0.39 ~spl9_2 | ~spl9_12),
% 0.23/0.39 inference(avatar_split_clause,[],[f19,f79,f35])).
% 0.23/0.39 thf(f83,plain,(
% 0.23/0.39 ( ! [X1 : a] : (($true != ((cR @ X1 @ z)))) ) | (~spl9_3 | ~spl9_6)),
% 0.23/0.39 inference(forward_subsumption_resolution,[],[f52,f40])).
% 0.23/0.39 thf(f84,plain,(
% 0.23/0.39 ($true != $true) | (~spl9_3 | ~spl9_6)),
% 0.23/0.39 inference(constrained_superposition,[],[f83,f21])).
% 0.23/0.39 thf(f85,plain,(
% 0.23/0.39 $false | (~spl9_3 | ~spl9_6)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f84])).
% 0.23/0.39 thf(f86,plain,(
% 0.23/0.39 ~spl9_3 | ~spl9_6),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f85])).
% 0.23/0.39 thf(f136,plain,(
% 0.23/0.39 ( ! [X0 : a] : (($true != $true) | ($true = ((cR @ X0 @ sK3))) | ($true != ((cR @ X0 @ z)))) ) | ~spl9_11),
% 0.23/0.39 inference(constrained_superposition,[],[f20,f76])).
% 0.23/0.39 thf(f137,plain,(
% 0.23/0.39 ( ! [X0 : a] : (($true != ((cR @ X0 @ z))) | ($true = ((cR @ X0 @ sK3)))) ) | ~spl9_11),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f136])).
% 0.23/0.39 thf(f159,plain,(
% 0.23/0.39 ($true != $true) | ($true = ((cR @ sK2 @ sK3))) | (~spl9_9 | ~spl9_11)),
% 0.23/0.39 inference(constrained_superposition,[],[f137,f66])).
% 0.23/0.39 thf(f162,plain,(
% 0.23/0.39 ($true = ((cR @ sK2 @ sK3))) | (~spl9_9 | ~spl9_11)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f159])).
% 0.23/0.39 thf(f165,plain,(
% 0.23/0.39 $false | (~spl9_9 | ~spl9_11 | spl9_12)),
% 0.23/0.39 inference(forward_subsumption_resolution,[],[f162,f81])).
% 0.23/0.39 thf(f166,plain,(
% 0.23/0.39 ~spl9_9 | ~spl9_11 | spl9_12),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f165])).
% 0.23/0.39 thf(f167,plain,(
% 0.23/0.39 $false | (~spl9_8 | ~spl9_10)),
% 0.23/0.39 inference(forward_subsumption_resolution,[],[f71,f61])).
% 0.23/0.39 thf(f168,plain,(
% 0.23/0.39 ~spl9_8 | ~spl9_10),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f167])).
% 0.23/0.39 thf(f171,plain,(
% 0.23/0.39 ( ! [X0 : a] : (($true != $true) | ($true != ((f @ X0 @ sK1))) | ($true = ((cR @ sK2 @ X0)))) ) | ~spl9_7),
% 0.23/0.39 inference(constrained_superposition,[],[f24,f58])).
% 0.23/0.39 thf(f176,plain,(
% 0.23/0.39 ( ! [X0 : a] : (($true != ((f @ X0 @ sK1))) | ($true = ((cR @ sK2 @ X0)))) ) | ~spl9_7),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f171])).
% 0.23/0.39 thf(f193,plain,(
% 0.23/0.39 ($true != $true) | ($true = ((cR @ sK2 @ sK3))) | (~spl9_7 | ~spl9_10)),
% 0.23/0.39 inference(constrained_superposition,[],[f176,f71])).
% 0.23/0.39 thf(f194,plain,(
% 0.23/0.39 ($true = ((cR @ sK2 @ sK3))) | (~spl9_7 | ~spl9_10)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f193])).
% 0.23/0.39 thf(f197,plain,(
% 0.23/0.39 $false | (~spl9_7 | ~spl9_10 | spl9_12)),
% 0.23/0.39 inference(forward_subsumption_resolution,[],[f194,f81])).
% 0.23/0.39 thf(f198,plain,(
% 0.23/0.39 ~spl9_7 | ~spl9_10 | spl9_12),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f197])).
% 0.23/0.39 thf(f204,plain,(
% 0.23/0.39 ($true != $true) | (~spl9_7 | ~spl9_8)),
% 0.23/0.39 inference(constrained_superposition,[],[f61,f58])).
% 0.23/0.39 thf(f205,plain,(
% 0.23/0.39 $false | (~spl9_7 | ~spl9_8)),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f204])).
% 0.23/0.39 thf(f206,plain,(
% 0.23/0.39 ~spl9_7 | ~spl9_8),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f205])).
% 0.23/0.39 thf(f211,plain,(
% 0.23/0.39 ($true != $true) | ~spl9_1),
% 0.23/0.39 inference(constrained_superposition,[],[f33,f22])).
% 0.23/0.39 thf(f212,plain,(
% 0.23/0.39 $false | ~spl9_1),
% 0.23/0.39 inference(trivial_inequality_removal,[],[f211])).
% 0.23/0.39 thf(f213,plain,(
% 0.23/0.39 ~spl9_1),
% 0.23/0.39 inference(avatar_contradiction_clause,[],[f212])).
% 0.23/0.39 cnf(s1, plain, spl9_1 | spl9_2 | spl9_3, inference(sat_conversion,[],[f41])).
% 0.23/0.39 cnf(s3, plain, spl9_1 | spl9_2 | spl9_6, inference(sat_conversion,[],[f53])).
% 0.23/0.39 cnf(s5, plain, ~spl9_2 | spl9_7 | spl9_8, inference(sat_conversion,[],[f62])).
% 0.23/0.39 cnf(s6, plain, ~spl9_2 | spl9_7 | spl9_9, inference(sat_conversion,[],[f67])).
% 0.23/0.39 cnf(s7, plain, ~spl9_2 | spl9_8 | spl9_10, inference(sat_conversion,[],[f72])).
% 0.23/0.39 cnf(s8, plain, ~spl9_2 | spl9_10 | spl9_11, inference(sat_conversion,[],[f77])).
% 0.23/0.39 cnf(s9, plain, ~spl9_2 | ~spl9_12, inference(sat_conversion,[],[f82])).
% 0.23/0.39 cnf(s10, plain, ~spl9_3 | ~spl9_6, inference(sat_conversion,[],[f86])).
% 0.23/0.39 cnf(s11, plain, ~spl9_9 | ~spl9_11 | spl9_12, inference(sat_conversion,[],[f166])).
% 0.23/0.39 cnf(s12, plain, ~spl9_8 | ~spl9_10, inference(sat_conversion,[],[f168])).
% 0.23/0.39 cnf(s13, plain, ~spl9_7 | ~spl9_10 | spl9_12, inference(sat_conversion,[],[f198])).
% 0.23/0.39 cnf(s14, plain, ~spl9_7 | ~spl9_8, inference(sat_conversion,[],[f206])).
% 0.23/0.39 cnf(s15, plain, ~spl9_1, inference(sat_conversion,[],[f213])).
% 0.23/0.39 cnf(s16, plain, spl9_2 | spl9_6, inference(rat,[],[s3,s15])).
% 0.23/0.39 cnf(s17, plain, spl9_2 | spl9_3, inference(rat,[],[s1,s15])).
% 0.23/0.39 cnf(s18, plain, spl9_2, inference(rat,[],[s10,s17,s16])).
% 0.23/0.39 cnf(s19, plain, ~spl9_12, inference(rat,[],[s9,s18])).
% 0.23/0.39 cnf(s20, plain, spl9_7, inference(rat,[],[s8,s12,s11,s5,s6,s18,s19])).
% 0.23/0.39 cnf(s21, plain, ~spl9_8, inference(rat,[],[s14,s20])).
% 0.23/0.39 cnf(s22, plain, ~spl9_10, inference(rat,[],[s13,s19,s20])).
% 0.23/0.39 cnf(s23, plain, $false, inference(rat,[],[s7,s18,s21,s22])).
% 0.23/0.39 thf(f215,plain,(
% 0.23/0.39 $false),
% 0.23/0.39 inference(avatar_sat_refutation,[],[s23])).
% 0.23/0.39 % SZS output end Proof for theBenchmark
% 0.23/0.39 % (1410759)------------------------------
% 0.23/0.39 % (1410759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.39 % (1410759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.39 % (1410759)CaDiCaL version: 2.1.3
% 0.23/0.39 % (1410759)Termination reason: Refutation
% 0.23/0.39 % (1410759)Time elapsed: 0.021 s
% 0.23/0.39 % (1410759)Peak memory usage: 12 MB
% 0.23/0.39 % (1410759)Instructions burned: 20 (million)
% 0.23/0.39 % (1410751)Success in time 0.075 s
% 0.23/0.39 % Vampire exiting
%------------------------------------------------------------------------------