%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV137^5 : 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 : n005.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 08:39:03 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV137^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n005.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:16:01 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.21/0.30 % (1784918)Will run a generic schedule for satisfiability detection.
% 0.21/0.30 % (1784923)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3826492117_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.30 % (1784926)dis+10_1_sil=32000:sp=arity:random_seed=1600942747:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (1784924)% WARNING: option uhcvi not known.
% 0.21/0.30 % (1784924)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2318413575:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.30 % (1784929)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1143317310:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.30 % (1784925)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3318052231:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.30 % (1784924)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % (1784924)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.30 % (1784932)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3729683041:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.30 % (1784927)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4042204224:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.30 % (1784927)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.30 % Exception at run slice level
% 0.21/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.30 % (1784928)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1728984111:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.30 % (1784926) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1784918-1784926"...
% 0.21/0.30 % (1784926)...printing done.
% 0.21/0.30 % (1784926)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, a: $tType).
% 0.21/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_3, type, sK0: (a > a > $o)).
% 0.21/0.30 thf(func_def_4, type, sK1: a).
% 0.21/0.30 thf(func_def_5, type, sK2: a).
% 0.21/0.30 thf(func_def_6, type, sK3: a).
% 0.21/0.30 thf(func_def_7, type, sK4: (a > $o)).
% 0.21/0.30 thf(func_def_8, type, sK5: ((a > $o) > a)).
% 0.21/0.30 thf(func_def_9, type, sK6: ((a > $o) > a)).
% 0.21/0.30 thf(func_def_10, type, sK7: ((a > $o) > a)).
% 0.21/0.30 thf(func_def_11, type, sK8: ((a > $o) > a)).
% 0.21/0.30 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.30 thf(func_def_14, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_15, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(f1,conjecture,(
% 0.21/0.30 ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X2) => (X4 @ X3))) & ! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X2)))) => ! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X3))))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM204_pme)).
% 0.21/0.30 thf(f2,negated_conjecture,(
% 0.21/0.30 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X2) => (X4 @ X3))) & ! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X2)))) => ! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X1) => (X4 @ X3))))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.30 thf(f3,plain,(
% 0.21/0.30 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((X4 @ X5) & (X0 @ X5 @ X6)) => (X4 @ X6)) => ((X4 @ X2) => (X4 @ X3))) & ! [X7 : (a > $o)] : (! [X8 : a,X9 : a] : (((X7 @ X8) & (X0 @ X8 @ X9)) => (X7 @ X9)) => ((X7 @ X1) => (X7 @ X2)))) => ! [X10 : (a > $o)] : (! [X11 : a,X12 : a] : (((X10 @ X11) & (X0 @ X11 @ X12)) => (X10 @ X12)) => ((X10 @ X1) => (X10 @ X3))))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f4,plain,(
% 0.21/0.30 ~ ! [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : ((! [X4 : (a > $o)] : (! [X5 : a,X6 : a] : (((((X4 @ X5)) = $true) & (((X0 @ X5 @ X6)) = $true)) => (((X4 @ X6)) = $true)) => ((((X4 @ X2)) = $true) => (((X4 @ X3)) = $true))) & ! [X7 : (a > $o)] : (! [X8 : a,X9 : a] : (((((X7 @ X8)) = $true) & (((X0 @ X8 @ X9)) = $true)) => (((X7 @ X9)) = $true)) => ((((X7 @ X1)) = $true) => (((X7 @ X2)) = $true)))) => ! [X10 : (a > $o)] : (! [X11 : a,X12 : a] : (((((X10 @ X11)) = $true) & (((X0 @ X11 @ X12)) = $true)) => (((X10 @ X12)) = $true)) => ((((X10 @ X1)) = $true) => (((X10 @ X3)) = $true))))),
% 0.21/0.30 inference(fool_elimination,[],[f3])).
% 0.21/0.30 thf(f5,plain,(
% 0.21/0.30 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X10 : (a > $o)] : (((((X10 @ X3)) != $true) & (((X10 @ X1)) = $true)) & ! [X11 : a,X12 : a] : ((((X10 @ X12)) = $true) | ((((X10 @ X11)) != $true) | (((X0 @ X11 @ X12)) != $true)))) & (! [X4 : (a > $o)] : (((((X4 @ X3)) = $true) | (((X4 @ X2)) != $true)) | ? [X5 : a,X6 : a] : ((((X4 @ X6)) != $true) & ((((X4 @ X5)) = $true) & (((X0 @ X5 @ X6)) = $true)))) & ! [X7 : (a > $o)] : (((((X7 @ X2)) = $true) | (((X7 @ X1)) != $true)) | ? [X8 : a,X9 : a] : ((((X7 @ X9)) != $true) & ((((X7 @ X8)) = $true) & (((X0 @ X8 @ X9)) = $true))))))),
% 0.21/0.30 inference(ennf_transformation,[],[f4])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X10 : (a > $o)] : ((((X10 @ X3)) != $true) & (((X10 @ X1)) = $true) & ! [X11 : a,X12 : a] : ((((X10 @ X12)) = $true) | (((X10 @ X11)) != $true) | (((X0 @ X11 @ X12)) != $true))) & ! [X4 : (a > $o)] : ((((X4 @ X3)) = $true) | (((X4 @ X2)) != $true) | ? [X5 : a,X6 : a] : ((((X4 @ X6)) != $true) & (((X4 @ X5)) = $true) & (((X0 @ X5 @ X6)) = $true))) & ! [X7 : (a > $o)] : ((((X7 @ X2)) = $true) | (((X7 @ X1)) != $true) | ? [X8 : a,X9 : a] : ((((X7 @ X9)) != $true) & (((X7 @ X8)) = $true) & (((X0 @ X8 @ X9)) = $true))))),
% 0.21/0.30 inference(flattening,[],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ? [X0 : (a > a > $o),X1 : a,X2 : a,X3 : a] : (? [X4 : (a > $o)] : ((((X4 @ X3)) != $true) & (((X4 @ X1)) = $true) & ! [X5 : a,X6 : a] : ((((X4 @ X6)) = $true) | (((X4 @ X5)) != $true) | (((X0 @ X5 @ X6)) != $true))) & ! [X7 : (a > $o)] : (($true = ((X7 @ X3))) | (((X7 @ X2)) != $true) | ? [X8 : a,X9 : a] : ((((X7 @ X9)) != $true) & (((X7 @ X8)) = $true) & (((X0 @ X8 @ X9)) = $true))) & ! [X10 : (a > $o)] : (($true = ((X10 @ X2))) | (((X10 @ X1)) != $true) | ? [X11 : a,X12 : a] : ((((X10 @ X12)) != $true) & (((X10 @ X11)) = $true) & (((X0 @ X11 @ X12)) = $true))))),
% 0.21/0.30 inference(rectify,[],[f6])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 (($true != ((sK4 @ sK3))) & ($true = ((sK4 @ sK1))) & ! [X5 : a,X6 : a] : (($true = ((sK4 @ X6))) | ($true != ((sK4 @ X5))) | ($true != ((sK0 @ X5 @ X6))))) & ! [X7 : (a > $o)] : (($true = ((X7 @ sK3))) | ($true != ((X7 @ sK2))) | (($true != ((X7 @ (sK6 @ X7)))) & ($true = ((X7 @ (sK5 @ X7)))) & ($true = ((sK0 @ (sK5 @ X7) @ (sK6 @ X7)))))) & ! [X10 : (a > $o)] : (($true = ((X10 @ sK2))) | ($true != ((X10 @ sK1))) | (($true != ((X10 @ (sK8 @ X10)))) & ($true = ((X10 @ (sK7 @ X10)))) & ($true = ((sK0 @ (sK7 @ X10) @ (sK8 @ X10))))))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP,vAPP,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X12,sK8 @ X10),skolemize(X12,sK8 @ X10),skolemize(X12,sK8 @ X10),skolemize(X12,sK8 @ X10)],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ( ! [X10 : (a > $o)] : (($true != ((X10 @ sK1))) | ($true = ((X10 @ sK2))) | ($true = ((sK0 @ (sK7 @ X10) @ (sK8 @ X10))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 ( ! [X10 : (a > $o)] : (($true != ((X10 @ sK1))) | ($true = ((X10 @ sK2))) | ($true = ((X10 @ (sK7 @ X10))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ( ! [X10 : (a > $o)] : (($true != ((X10 @ (sK8 @ X10)))) | ($true != ((X10 @ sK1))) | ($true = ((X10 @ sK2)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ( ! [X7 : (a > $o)] : (($true != ((X7 @ sK2))) | ($true = ((X7 @ sK3))) | ($true = ((sK0 @ (sK5 @ X7) @ (sK6 @ X7))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 ( ! [X7 : (a > $o)] : (($true != ((X7 @ sK2))) | ($true = ((X7 @ sK3))) | ($true = ((X7 @ (sK5 @ X7))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f14,plain,(
% 0.21/0.30 ( ! [X7 : (a > $o)] : (($true != ((X7 @ (sK6 @ X7)))) | ($true != ((X7 @ sK2))) | ($true = ((X7 @ sK3)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ( ! [X6 : a,X5 : a] : (($true != ((sK0 @ X5 @ X6))) | ($true != ((sK4 @ X5))) | ($true = ((sK4 @ X6)))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f16,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK1)))),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ($true != ((sK4 @ sK3)))),
% 0.21/0.30 inference(cnf_transformation,[],[f8])).
% 0.21/0.30 thf(f25,plain,(
% 0.21/0.30 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))))),
% 0.21/0.30 inference(constrained_superposition,[],[f10,f16])).
% 0.21/0.30 thf(f33,plain,(
% 0.21/0.30 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))))),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f25])).
% 0.21/0.30 thf(f34,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK2))) | ($true = ((sK4 @ (sK7 @ sK4))))),
% 0.21/0.30 inference(beta-eta_normalization,[],[f33])).
% 0.21/0.30 thf(f48,definition,(
% 0.21/0.30 spl9_1 <=> ($true = ((sK4 @ (sK7 @ sK4))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition])).
% 0.21/0.30 thf(f50,plain,(
% 0.21/0.30 ($true = ((sK4 @ (sK7 @ sK4)))) | ~spl9_1),
% 0.21/0.30 inference(avatar_component_clause,[],[f48])).
% 0.21/0.30 thf(f52,definition,(
% 0.21/0.30 spl9_2 <=> ($true = ((sK4 @ sK2)))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition])).
% 0.21/0.30 thf(f53,plain,(
% 0.21/0.30 ($true != ((sK4 @ sK2))) | spl9_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f52])).
% 0.21/0.30 thf(f54,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK2))) | ~spl9_2),
% 0.21/0.30 inference(avatar_component_clause,[],[f52])).
% 0.21/0.30 thf(f55,plain,(
% 0.21/0.30 spl9_1 | spl9_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f34,f52,f48])).
% 0.21/0.30 thf(f210,plain,(
% 0.21/0.30 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))))),
% 0.21/0.30 inference(constrained_superposition,[],[f9,f16])).
% 0.21/0.30 thf(f216,plain,(
% 0.21/0.30 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = ((sK0 @ (sK7 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK8 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))))))),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f210])).
% 0.21/0.30 thf(f217,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK2))) | ($true = ((sK0 @ (sK7 @ sK4) @ (sK8 @ sK4))))),
% 0.21/0.30 inference(beta-eta_normalization,[],[f216])).
% 0.21/0.30 thf(f224,definition,(
% 0.21/0.30 spl9_13 <=> ($true = ((sK0 @ (sK7 @ sK4) @ (sK8 @ sK4))))),
% 0.21/0.30 introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition])).
% 0.21/0.30 thf(f226,plain,(
% 0.21/0.30 ($true = ((sK0 @ (sK7 @ sK4) @ (sK8 @ sK4)))) | ~spl9_13),
% 0.21/0.30 inference(avatar_component_clause,[],[f224])).
% 0.21/0.30 thf(f227,plain,(
% 0.21/0.30 spl9_13 | spl9_2),
% 0.21/0.30 inference(avatar_split_clause,[],[f217,f52,f224])).
% 0.21/0.30 thf(f251,plain,(
% 0.21/0.30 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f12,f54])).
% 0.21/0.30 thf(f253,plain,(
% 0.21/0.30 ($true != $true) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f13,f54])).
% 0.21/0.30 thf(f258,plain,(
% 0.21/0.30 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f253])).
% 0.21/0.30 thf(f259,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK3))) | ($true = ((sK4 @ (sK5 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(beta-eta_normalization,[],[f258])).
% 0.21/0.30 thf(f262,plain,(
% 0.21/0.30 ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ($true = ((sK0 @ (sK5 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0)))) @ (sK6 @ (^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))))))) | ~spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f251])).
% 0.21/0.30 thf(f263,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK3))) | ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(beta-eta_normalization,[],[f262])).
% 0.21/0.30 thf(f273,plain,(
% 0.21/0.30 ($true = ((sK4 @ (sK5 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f259,f17])).
% 0.21/0.30 thf(f274,plain,(
% 0.21/0.30 ($true = ((sK0 @ (sK5 @ sK4) @ (sK6 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f263,f17])).
% 0.21/0.30 thf(f540,plain,(
% 0.21/0.30 ($true != $true) | ($true != ((sK4 @ (sK5 @ sK4)))) | ($true = ((sK4 @ (sK6 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f15,f274])).
% 0.21/0.30 thf(f541,plain,(
% 0.21/0.30 ($true != ((sK4 @ (sK5 @ sK4)))) | ($true = ((sK4 @ (sK6 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f540])).
% 0.21/0.30 thf(f554,plain,(
% 0.21/0.30 ($true = ((sK4 @ (sK6 @ sK4)))) | ~spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f541,f273])).
% 0.21/0.30 thf(f560,plain,(
% 0.21/0.30 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ~spl9_2),
% 0.21/0.30 inference(constrained_superposition,[],[f14,f554])).
% 0.21/0.30 thf(f570,plain,(
% 0.21/0.30 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK3))) | ~spl9_2),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f560])).
% 0.21/0.30 thf(f571,plain,(
% 0.21/0.30 ($true != ((sK4 @ sK2))) | ($true = ((sK4 @ sK3))) | ~spl9_2),
% 0.21/0.30 inference(beta-eta_normalization,[],[f570])).
% 0.21/0.30 thf(f579,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK3))) | ~spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f571,f54])).
% 0.21/0.30 thf(f580,plain,(
% 0.21/0.30 $false | ~spl9_2),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f579,f17])).
% 0.21/0.30 thf(f581,plain,(
% 0.21/0.30 ~spl9_2),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f580])).
% 0.21/0.30 thf(f621,plain,(
% 0.21/0.30 ($true != $true) | ($true != ((sK4 @ (sK7 @ sK4)))) | ($true = ((sK4 @ (sK8 @ sK4)))) | ~spl9_13),
% 0.21/0.30 inference(constrained_superposition,[],[f15,f226])).
% 0.21/0.30 thf(f622,plain,(
% 0.21/0.30 ($true != ((sK4 @ (sK7 @ sK4)))) | ($true = ((sK4 @ (sK8 @ sK4)))) | ~spl9_13),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f621])).
% 0.21/0.30 thf(f635,plain,(
% 0.21/0.30 ($true = ((sK4 @ (sK8 @ sK4)))) | (~spl9_1 | ~spl9_13)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f622,f50])).
% 0.21/0.30 thf(f639,plain,(
% 0.21/0.30 ($true != $true) | ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | (~spl9_1 | ~spl9_13)),
% 0.21/0.30 inference(constrained_superposition,[],[f11,f635])).
% 0.21/0.30 thf(f652,plain,(
% 0.21/0.30 ($true != (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK1))) | ($true = (((^[Y0 : a]: (sK4 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ sK2))) | (~spl9_1 | ~spl9_13)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f639])).
% 0.21/0.30 thf(f653,plain,(
% 0.21/0.30 ($true != ((sK4 @ sK1))) | ($true = ((sK4 @ sK2))) | (~spl9_1 | ~spl9_13)),
% 0.21/0.30 inference(beta-eta_normalization,[],[f652])).
% 0.21/0.30 thf(f659,plain,(
% 0.21/0.30 ($true = ((sK4 @ sK2))) | (~spl9_1 | ~spl9_13)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f653,f16])).
% 0.21/0.30 thf(f660,plain,(
% 0.21/0.30 $false | (~spl9_1 | spl9_2 | ~spl9_13)),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f659,f53])).
% 0.21/0.30 thf(f661,plain,(
% 0.21/0.30 ~spl9_1 | spl9_2 | ~spl9_13),
% 0.21/0.30 inference(avatar_contradiction_clause,[],[f660])).
% 0.21/0.30 cnf(s1, plain, spl9_1 | spl9_2, inference(sat_conversion,[],[f55])).
% 0.21/0.30 cnf(s12, plain, spl9_2 | spl9_13, inference(sat_conversion,[],[f227])).
% 0.21/0.30 cnf(s20, plain, ~spl9_2, inference(sat_conversion,[],[f581])).
% 0.21/0.30 cnf(s21, plain, ~spl9_1 | spl9_2 | ~spl9_13, inference(sat_conversion,[],[f661])).
% 0.21/0.30 cnf(s22, plain, spl9_13, inference(rat,[],[s12,s20])).
% 0.21/0.30 cnf(s23, plain, ~spl9_1, inference(rat,[],[s21,s20,s22])).
% 0.21/0.30 cnf(s26, plain, $false, inference(rat,[],[s1,s20,s23])).
% 0.21/0.30 thf(f662,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(avatar_sat_refutation,[],[s26])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (1784926)------------------------------
% 0.21/0.30 % (1784926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1784926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1784926)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1784926)Termination reason: Refutation
% 0.21/0.30 % (1784926)Time elapsed: 0.025 s
% 0.21/0.30 % (1784926)Peak memory usage: 13 MB
% 0.21/0.30 % (1784926)Instructions burned: 45 (million)
% 0.21/0.30 % (1784918)Success in time 0.057 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------