%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU708^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:33:03 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU708^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:15:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.25 % (139881)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (139892)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=204660677:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.25 % (139887)% WARNING: option uhcvi not known.
% 0.07/0.25 % (139890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2719166810:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (139889)dis+10_1_sil=32000:sp=arity:random_seed=1150676403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (139888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4119010953:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (139887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3799048486:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.25 % (139891)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1077698901:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (139892) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-139881-139892"...
% 0.07/0.25 % (139890)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (139887)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (139887)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.07/0.25 % (139892)...printing done.
% 0.07/0.25 % (139892)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% 0.07/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.25 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.07/0.25 thf(func_def_1, type, setunion: ($i > $i)).
% 0.07/0.25 thf(func_def_2, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.07/0.25 thf(func_def_3, type, singleton: ($i > $o)).
% 0.07/0.25 thf(func_def_4, type, iffalseProp1: $o).
% 0.07/0.25 thf(func_def_6, type, ifSingleton: $o).
% 0.07/0.25 thf(func_def_7, type, if: ($i > $o > $i > $i > $i)).
% 0.07/0.25 thf(func_def_8, type, theeq: $o).
% 0.07/0.25 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.07/0.25 thf(func_def_10, type, vIMP: ($o > $o > $o)).
% 0.07/0.25 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.07/0.25 thf(func_def_15, type, vOR: ($o > $o > $o)).
% 0.07/0.25 thf(func_def_16, type, vAND: ($o > $o > $o)).
% 0.07/0.25 thf(func_def_17, type, db3: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_18, type, db4: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_19, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.07/0.25 thf(func_def_20, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.25 thf(func_def_24, type, sK1: $o).
% 0.07/0.25 thf(func_def_28, type, sK5: ($o > $i)).
% 0.07/0.25 thf(func_def_29, type, sK6: ($i > $i)).
% 0.07/0.25 thf(func_def_30, type, sK7: ($i > $i)).
% 0.07/0.25 thf(func_def_31, type, sK8: ($i > $i)).
% 0.07/0.25 thf(f1,axiom,(
% 0.07/0.25 (iffalseProp1 = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1)))))))))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1)).
% 0.07/0.25 thf(f2,axiom,(
% 0.07/0.25 (ifSingleton = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton)).
% 0.07/0.25 thf(f3,axiom,(
% 0.07/0.25 (if = (^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : ((setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',if)).
% 0.07/0.25 thf(f4,axiom,(
% 0.07/0.25 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq)).
% 0.07/0.25 thf(f5,conjecture,(
% 0.07/0.25 iffalseProp1 => (ifSingleton => (theeq => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X3))))))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse)).
% 0.07/0.25 thf(f6,negated_conjecture,(
% 0.07/0.25 ~(iffalseProp1 => (ifSingleton => (theeq => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X3)))))))),
% 0.07/0.25 inference(negated_conjecture,[status(cth)],[f5])).
% 0.07/0.25 thf(f7,plain,(
% 0.07/0.25 (iffalseProp1 = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (in @ X3 @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1)))))))))),
% 0.07/0.25 inference(rectify,[],[f1])).
% 0.07/0.25 thf(f8,plain,(
% 0.07/0.25 (iffalseProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4)))))))))))))))))))),
% 0.07/0.25 inference(fool_elimination,[],[f7])).
% 0.07/0.25 thf(f9,plain,(
% 0.07/0.25 (ifSingleton = ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))))),
% 0.07/0.25 inference(rectify,[],[f2])).
% 0.07/0.25 thf(f10,plain,(
% 0.07/0.25 (ifSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))))))),
% 0.07/0.25 inference(fool_elimination,[],[f9])).
% 0.07/0.25 thf(f11,plain,(
% 0.07/0.25 (if = (^[X0 : $i, X1 : $o, X2 : $i, X3 : $i] : ((setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (((X4 = X3) & ~X1) | ((X4 = X2) & X1))))))))),
% 0.07/0.25 inference(rectify,[],[f3])).
% 0.07/0.25 thf(f12,plain,(
% 0.07/0.25 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 0.07/0.25 inference(fool_elimination,[],[f11])).
% 0.07/0.25 thf(f13,plain,(
% 0.07/0.25 (theeq = ! [X0 : $i] : ((singleton @ X0) => ! [X1 : $i] : ((in @ X1 @ X0) => (((setunion @ X0)) = X1))))),
% 0.07/0.25 inference(rectify,[],[f4])).
% 0.07/0.25 thf(f14,plain,(
% 0.07/0.25 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 0.07/0.25 inference(fool_elimination,[],[f13])).
% 0.07/0.25 thf(f15,plain,(
% 0.07/0.25 ~(iffalseProp1 => (ifSingleton => (theeq => ! [X0 : $i,X1 : $o,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => (~X1 => (((if @ X0 @ X1 @ X2 @ X3)) = X3)))))))),
% 0.07/0.25 inference(rectify,[],[f6])).
% 0.07/0.25 thf(f16,plain,(
% 0.07/0.25 ~((iffalseProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0 : $i,X1 : $o,X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (~ ($true = X1) => (((if @ X0 @ X1 @ X2 @ X3)) = X3)))))))),
% 0.07/0.25 inference(fool_elimination,[],[f15])).
% 0.07/0.25 thf(f17,plain,(
% 0.07/0.25 ~((iffalseProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0 : $i,X1 : $o,X2 : $i] : ((((in @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (($true != X1) => (((if @ X0 @ X1 @ X2 @ X3)) = X3)))))))),
% 0.07/0.25 inference(flattening,[],[f16])).
% 0.07/0.25 thf(f18,plain,(
% 0.07/0.25 ((? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : (((((if @ X0 @ X1 @ X2 @ X3)) != X3) & ($true != X1)) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)) & (theeq = $true)) & (ifSingleton = $true)) & (iffalseProp1 = $true)),
% 0.07/0.25 inference(ennf_transformation,[],[f17])).
% 0.07/0.25 thf(f19,plain,(
% 0.07/0.25 ? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : ((((if @ X0 @ X1 @ X2 @ X3)) != X3) & ($true != X1) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ X0)) = $true)) & (theeq = $true) & (ifSingleton = $true) & (iffalseProp1 = $true)),
% 0.07/0.25 inference(flattening,[],[f18])).
% 0.07/0.25 thf(f20,plain,(
% 0.07/0.25 (((sK3 != ((if @ sK0 @ sK1 @ sK2 @ sK3))) & ($true != sK1) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((in @ sK2 @ sK0)))) & (theeq = $true) & (ifSingleton = $true) & (iffalseProp1 = $true)),
% 0.07/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19])).
% 0.07/0.25 thf(f21,plain,(
% 0.07/0.25 (iffalseProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4)))))))))))))))))))),
% 0.07/0.25 inference(cnf_transformation,[],[f8])).
% 0.07/0.25 thf(f22,plain,(
% 0.07/0.25 (ifSingleton = ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))))))),
% 0.07/0.25 inference(cnf_transformation,[],[f10])).
% 0.07/0.25 thf(f23,plain,(
% 0.07/0.25 (if = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))),
% 0.07/0.25 inference(cnf_transformation,[],[f12])).
% 0.07/0.25 thf(f24,plain,(
% 0.07/0.25 (theeq = ((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))))),
% 0.07/0.25 inference(cnf_transformation,[],[f14])).
% 0.07/0.25 thf(f25,plain,(
% 0.07/0.25 (iffalseProp1 = $true)),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f26,plain,(
% 0.07/0.25 (ifSingleton = $true)),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f27,plain,(
% 0.07/0.25 (theeq = $true)),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f28,plain,(
% 0.07/0.25 ($true = ((in @ sK2 @ sK0)))),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f29,plain,(
% 0.07/0.25 ($true = ((in @ sK3 @ sK0)))),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f30,plain,(
% 0.07/0.25 ($true != sK1)),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f31,plain,(
% 0.07/0.25 (sK3 != ((if @ sK0 @ sK1 @ sK2 @ sK3)))),
% 0.07/0.25 inference(cnf_transformation,[],[f20])).
% 0.07/0.25 thf(f33,definition,(
% 0.07/0.25 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.07/0.25 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.07/0.25 thf(f34,plain,(
% 0.07/0.25 (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4)))))))))))))))))) = $true)),
% 0.07/0.25 inference(definition_unfolding,[],[f21,f25])).
% 0.07/0.25 thf(f35,plain,(
% 0.07/0.25 (((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))))) = $true)),
% 0.07/0.25 inference(definition_unfolding,[],[f22,f26])).
% 0.07/0.25 thf(f36,plain,(
% 0.07/0.25 (((!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))))) = $true)),
% 0.07/0.25 inference(definition_unfolding,[],[f24,f27])).
% 0.07/0.25 thf(f37,plain,(
% 0.07/0.25 (sK3 != (((^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: ((Y1 & (Y2 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))) @ sK0 @ sK1 @ sK2 @ sK3)))),
% 0.07/0.25 inference(definition_unfolding,[],[f31,f23])).
% 0.07/0.25 thf(f38,plain,(
% 0.07/0.25 (sK3 != ((setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: ((sK1 & (sK2 = Y0)) | ((~ sK1) & (sK3 = Y0))))))))),
% 0.07/0.25 inference(beta-eta_normalization,[],[f37])).
% 0.07/0.25 thf(f39,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((singleton @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((setunion @ Y0) = Y1)))))) @ X1)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f36])).
% 0.07/0.25 thf(f40,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = (((singleton @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((setunion @ X1) = Y0)))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f39])).
% 0.07/0.25 thf(f41,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($false = ((singleton @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((setunion @ X1) = Y0))))))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f40])).
% 0.07/0.25 thf(f42,plain,(
% 0.07/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((singleton @ X1))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X1) => ((setunion @ X1) = Y0))) @ X2)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f41])).
% 0.07/0.25 thf(f43,plain,(
% 0.07/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((singleton @ X1))) | ($true = (((in @ X2 @ X1) => ((setunion @ X1) = X2))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f42])).
% 0.07/0.25 thf(f44,plain,(
% 0.07/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((singleton @ X1))) | ($false = ((in @ X2 @ X1))) | ($true = (((setunion @ X1) = X2)))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f43])).
% 0.07/0.25 thf(f45,plain,(
% 0.07/0.25 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X2 @ X1))) | ($false = ((singleton @ X1))) | (((setunion @ X1)) = X2)) )),
% 0.07/0.25 inference(equality_proxy_clausification,[],[f44])).
% 0.07/0.25 thf(f46,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4))))))))))))))) @ X1)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f35])).
% 0.07/0.25 thf(f47,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (singleton @ (dsetconstr @ Y1 @ (^[Y3 : $i]: ((Y0 & (X1 = Y3)) | ((~ Y0) & (Y2 = Y3))))))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f46])).
% 0.07/0.25 thf(f48,plain,(
% 0.07/0.25 ( ! [X2 : $o,X1 : $i] : (($true = (((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (singleton @ (dsetconstr @ Y1 @ (^[Y3 : $i]: ((Y0 & (X1 = Y3)) | ((~ Y0) & (Y2 = Y3))))))))))))) @ X2)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f47])).
% 0.07/0.25 thf(f49,plain,(
% 0.07/0.25 ( ! [X2 : $o,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: ((X2 & (X1 = Y2)) | ((~ X2) & (Y1 = Y2))))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f48])).
% 0.07/0.25 thf(f50,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: ((X2 & (X1 = Y2)) | ((~ X2) & (Y1 = Y2))))))))))) @ X3)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f49])).
% 0.07/0.25 thf(f51,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f50])).
% 0.07/0.25 thf(f52,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1)))))))))))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f51])).
% 0.07/0.25 thf(f53,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1)))))))) @ X4)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f52])).
% 0.07/0.25 thf(f54,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X4 @ X3) => (singleton @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0)))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f53])).
% 0.07/0.25 thf(f55,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($true = ((singleton @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0)))))))) | ($false = ((in @ X4 @ X3))) | ($false = ((in @ X1 @ X3)))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f54])).
% 0.07/0.25 thf(f56,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((~ Y1) => (in @ Y3 @ (dsetconstr @ Y2 @ (^[Y4 : $i]: ((Y1 & (Y0 = Y4)) | ((~ Y1) & (Y3 = Y4)))))))))))))))) @ X1)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f34])).
% 0.07/0.25 thf(f57,plain,(
% 0.07/0.25 ( ! [X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ Y0) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: ((Y0 & (X1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f56])).
% 0.07/0.25 thf(f58,plain,(
% 0.07/0.25 ( ! [X2 : $o,X1 : $i] : (($true = (((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ Y0) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: ((Y0 & (X1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))))) @ X2)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f57])).
% 0.07/0.25 thf(f59,plain,(
% 0.07/0.25 ( ! [X2 : $o,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ X2) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y2 : $i]: ((X2 & (X1 = Y2)) | ((~ X2) & (Y1 = Y2)))))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f58])).
% 0.07/0.25 thf(f60,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ X2) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y2 : $i]: ((X2 & (X1 = Y2)) | ((~ X2) & (Y1 = Y2)))))))))))) @ X3)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f59])).
% 0.07/0.25 thf(f61,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((~ X2) => (in @ Y0 @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1)))))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f60])).
% 0.07/0.25 thf(f62,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((~ X2) => (in @ Y0 @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1))))))))))))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f61])).
% 0.07/0.25 thf(f63,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => ((~ X2) => (in @ Y0 @ (dsetconstr @ X3 @ (^[Y1 : $i]: ((X2 & (X1 = Y1)) | ((~ X2) & (Y0 = Y1))))))))) @ X4)))) )),
% 0.07/0.25 inference(pi_proxy_clausification,[],[f62])).
% 0.07/0.25 thf(f64,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X4 @ X3) => ((~ X2) => (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0))))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f63])).
% 0.07/0.25 thf(f65,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($false = ((in @ X4 @ X3))) | ($true = (((~ X2) => (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0)))))))))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f64])).
% 0.07/0.25 thf(f66,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ X3))) | ($false = ((in @ X4 @ X3))) | ($false = ((~ X2))) | ($true = ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0))))))))) )),
% 0.07/0.25 inference(imp_proxy_clausification,[],[f65])).
% 0.07/0.25 thf(f67,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: ((X2 & (X1 = Y0)) | ((~ X2) & (X4 = Y0)))))))) | ($false = ((in @ X4 @ X3))) | ($true = X2) | ($false = ((in @ X1 @ X3)))) )),
% 0.07/0.25 inference(not_proxy_clausification,[],[f66])).
% 0.07/0.25 thf(f96,plain,(
% 0.07/0.25 ($true != $true) | (sK1 = $false)),
% 0.07/0.25 inference(constrained_superposition,[],[f30,f33])).
% 0.07/0.25 thf(f98,plain,(
% 0.07/0.25 (sK1 = $false)),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f96])).
% 0.07/0.25 thf(f109,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X3 = Y0)) | ((~ X2) & (X0 = Y0)))))))) | (((setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X3 = Y0)) | ((~ X2) & (X0 = Y0))))))) = X0) | ($false = ((in @ X0 @ X1))) | ($true = X2) | ($false = ((in @ X3 @ X1)))) )),
% 0.07/0.25 inference(constrained_superposition,[],[f45,f67])).
% 0.07/0.25 thf(f110,plain,(
% 0.07/0.25 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($false = ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X3 = Y0)) | ((~ X2) & (X0 = Y0)))))))) | (((setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: ((X2 & (X3 = Y0)) | ((~ X2) & (X0 = Y0))))))) = X0) | ($false = ((in @ X0 @ X1))) | ($true = X2) | ($false = ((in @ X3 @ X1)))) )),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f109])).
% 0.07/0.25 thf(f114,plain,(
% 0.07/0.25 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o,X6 : $i,X4 : $o,X5 : $i] : (($true = $false) | (((in @ X3 @ X0)) = $false) | (((in @ X2 @ X0)) = $false) | (((setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X6 = Y0))))))) = X6) | ($false = ((in @ X6 @ X0))) | ($true = X4) | ($false = ((in @ X5 @ X0))) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (X5))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X6))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4)))) )),
% 0.07/0.25 inference(constrained_superposition,[],[f55,f110])).
% 0.07/0.25 thf(f115,plain,(
% 0.07/0.25 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o,X6 : $i,X4 : $o,X5 : $i] : (($true = $false) | (((in @ X3 @ X0)) = $false) | (((in @ X2 @ X0)) = $false) | (((setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X6 = Y0))))))) = X6) | ($false = ((in @ X6 @ X0))) | ($true = X4) | ($false = ((in @ X5 @ X0))) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (X5))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X6))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4)))) )),
% 0.07/0.25 inference(duplicate_literal_removal,[],[f114])).
% 0.07/0.25 thf(f116,plain,(
% 0.07/0.25 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o,X6 : $i,X4 : $o,X5 : $i] : ((((in @ X3 @ X0)) = $false) | (((in @ X2 @ X0)) = $false) | (((setunion @ (dsetconstr @ X0 @ (^[Y0 : $i]: ((X4 & (X5 = Y0)) | ((~ X4) & (X6 = Y0))))))) = X6) | ($false = ((in @ X6 @ X0))) | ($true = X4) | ($false = ((in @ X5 @ X0))) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (X5))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X6))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4)))) )),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f115])).
% 0.07/0.25 thf(f123,plain,(
% 0.07/0.25 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : ((sK3 != X0) | ($false = ((in @ X1 @ sK0))) | ($false = ((in @ X2 @ sK0))) | ($false = ((in @ X0 @ sK0))) | ($true = sK1) | (((in @ sK2 @ sK0)) = $false) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (sK2))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK1))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3)))) )),
% 0.07/0.25 inference(constrained_superposition,[],[f38,f116])).
% 0.07/0.25 thf(f132,definition,(
% 0.07/0.25 spl4_4 <=> ! [X3 : $o] : ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK1)))),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.07/0.25 thf(f133,plain,(
% 0.07/0.25 ( ! [X3 : $o] : (((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK1)))) ) | ~spl4_4),
% 0.07/0.25 inference(avatar_component_clause,[],[f132])).
% 0.07/0.25 thf(f135,definition,(
% 0.07/0.25 spl4_5 <=> (((in @ sK2 @ sK0)) = $false)),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.07/0.25 thf(f137,plain,(
% 0.07/0.25 (((in @ sK2 @ sK0)) = $false) | ~spl4_5),
% 0.07/0.25 inference(avatar_component_clause,[],[f135])).
% 0.07/0.25 thf(f139,definition,(
% 0.07/0.25 spl4_6 <=> ($true = sK1)),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
% 0.07/0.25 thf(f141,plain,(
% 0.07/0.25 ($true = sK1) | ~spl4_6),
% 0.07/0.25 inference(avatar_component_clause,[],[f139])).
% 0.07/0.25 thf(f143,definition,(
% 0.07/0.25 spl4_7 <=> ! [X2 : $i] : (($false = ((in @ X2 @ sK0))) | ((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (sK2))))),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition])).
% 0.07/0.25 thf(f144,plain,(
% 0.07/0.25 ( ! [X2 : $i] : (((^[Y0 : $i]: (X2)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ X2 @ sK0)))) ) | ~spl4_7),
% 0.07/0.25 inference(avatar_component_clause,[],[f143])).
% 0.07/0.25 thf(f146,definition,(
% 0.07/0.25 spl4_8 <=> ! [X0 : $i,X1 : $i] : ((sK3 != X0) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3))) | ($false = ((in @ X0 @ sK0))) | ($false = ((in @ X1 @ sK0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0))))),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition])).
% 0.07/0.25 thf(f147,plain,(
% 0.07/0.25 ( ! [X0 : $i,X1 : $i] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3))) | (sK3 != X0) | ($false = ((in @ X0 @ sK0))) | ($false = ((in @ X1 @ sK0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0)))) ) | ~spl4_8),
% 0.07/0.25 inference(avatar_component_clause,[],[f146])).
% 0.07/0.25 thf(f148,plain,(
% 0.07/0.25 spl4_4 | spl4_5 | spl4_6 | spl4_7 | spl4_8),
% 0.07/0.25 inference(avatar_split_clause,[],[f123,f146,f143,f139,f135,f132])).
% 0.07/0.25 thf(f157,plain,(
% 0.07/0.25 $false | ~spl4_4),
% 0.07/0.25 inference(equality_resolution,[],[f133])).
% 0.07/0.25 thf(f158,plain,(
% 0.07/0.25 ~spl4_4),
% 0.07/0.25 inference(avatar_contradiction_clause,[],[f157])).
% 0.07/0.25 thf(f168,plain,(
% 0.07/0.25 ($true = $false) | ~spl4_5),
% 0.07/0.25 inference(constrained_superposition,[],[f137,f28])).
% 0.07/0.25 thf(f172,plain,(
% 0.07/0.25 $false | ~spl4_5),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f168])).
% 0.07/0.25 thf(f173,plain,(
% 0.07/0.25 ~spl4_5),
% 0.07/0.25 inference(avatar_contradiction_clause,[],[f172])).
% 0.07/0.25 thf(f175,plain,(
% 0.07/0.25 ($true = $false) | ~spl4_6),
% 0.07/0.25 inference(constrained_superposition,[],[f141,f98])).
% 0.07/0.25 thf(f182,plain,(
% 0.07/0.25 $false | ~spl4_6),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f175])).
% 0.07/0.25 thf(f183,plain,(
% 0.07/0.25 ~spl4_6),
% 0.07/0.25 inference(avatar_contradiction_clause,[],[f182])).
% 0.07/0.25 thf(f189,plain,(
% 0.07/0.25 (((in @ sK2 @ sK0)) = $false) | ~spl4_7),
% 0.07/0.25 inference(equality_resolution,[],[f144])).
% 0.07/0.25 thf(f191,plain,(
% 0.07/0.25 spl4_5 | ~spl4_7),
% 0.07/0.25 inference(avatar_split_clause,[],[f189,f143,f135])).
% 0.07/0.25 thf(f314,plain,(
% 0.07/0.25 ( ! [X0 : $i] : ((sK3 != sK3) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3)))) ) | ~spl4_8),
% 0.07/0.25 inference(equality_resolution,[],[f147])).
% 0.07/0.25 thf(f315,plain,(
% 0.07/0.25 ( ! [X0 : $i] : ((((in @ sK3 @ sK0)) = $false) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3)))) ) | ~spl4_8),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f314])).
% 0.07/0.25 thf(f319,definition,(
% 0.07/0.25 spl4_13 <=> ! [X0 : $i] : (($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3))))),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition])).
% 0.07/0.25 thf(f320,plain,(
% 0.07/0.25 ( ! [X0 : $i] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK3))) | ($false = ((in @ X0 @ sK0)))) ) | ~spl4_13),
% 0.07/0.25 inference(avatar_component_clause,[],[f319])).
% 0.07/0.25 thf(f322,definition,(
% 0.07/0.25 spl4_14 <=> (((in @ sK3 @ sK0)) = $false)),
% 0.07/0.25 introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition])).
% 0.07/0.25 thf(f324,plain,(
% 0.07/0.25 (((in @ sK3 @ sK0)) = $false) | ~spl4_14),
% 0.07/0.25 inference(avatar_component_clause,[],[f322])).
% 0.07/0.25 thf(f325,plain,(
% 0.07/0.25 spl4_13 | spl4_14 | ~spl4_8),
% 0.07/0.25 inference(avatar_split_clause,[],[f315,f146,f322,f319])).
% 0.07/0.25 thf(f331,plain,(
% 0.07/0.25 (((in @ sK3 @ sK0)) = $false) | ~spl4_13),
% 0.07/0.25 inference(equality_resolution,[],[f320])).
% 0.07/0.25 thf(f333,plain,(
% 0.07/0.25 spl4_14 | ~spl4_13),
% 0.07/0.25 inference(avatar_split_clause,[],[f331,f319,f322])).
% 0.07/0.25 thf(f335,plain,(
% 0.07/0.25 ($true = $false) | ~spl4_14),
% 0.07/0.25 inference(constrained_superposition,[],[f324,f29])).
% 0.07/0.25 thf(f339,plain,(
% 0.07/0.25 $false | ~spl4_14),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f335])).
% 0.07/0.25 thf(f340,plain,(
% 0.07/0.25 ~spl4_14),
% 0.07/0.25 inference(avatar_contradiction_clause,[],[f339])).
% 0.07/0.25 cnf(s5, plain, spl4_4 | spl4_5 | spl4_6 | spl4_7 | spl4_8, inference(sat_conversion,[],[f148])).
% 0.07/0.25 cnf(s7, plain, ~spl4_4, inference(sat_conversion,[],[f158])).
% 0.07/0.25 cnf(s10, plain, ~spl4_5, inference(sat_conversion,[],[f173])).
% 0.07/0.25 cnf(s13, plain, ~spl4_6, inference(sat_conversion,[],[f183])).
% 0.07/0.25 cnf(s14, plain, spl4_5 | ~spl4_7, inference(sat_conversion,[],[f191])).
% 0.07/0.25 cnf(s17, plain, ~spl4_8 | spl4_13 | spl4_14, inference(sat_conversion,[],[f325])).
% 0.07/0.25 cnf(s18, plain, ~spl4_13 | spl4_14, inference(sat_conversion,[],[f333])).
% 0.07/0.25 cnf(s20, plain, ~spl4_14, inference(sat_conversion,[],[f340])).
% 0.07/0.25 cnf(s21, plain, ~spl4_13, inference(rat,[],[s18,s20])).
% 0.07/0.25 cnf(s22, plain, ~spl4_8, inference(rat,[],[s17,s20,s21])).
% 0.07/0.25 cnf(s23, plain, ~spl4_7, inference(rat,[],[s14,s10])).
% 0.07/0.25 cnf(s25, plain, $false, inference(rat,[],[s5,s22,s23,s13,s10,s7])).
% 0.07/0.25 thf(f342,plain,(
% 0.07/0.25 $false),
% 0.07/0.25 inference(avatar_sat_refutation,[],[s25])).
% 0.07/0.25 % SZS output end Proof for theBenchmark
% 0.07/0.25 % (139892)------------------------------
% 0.07/0.25 % (139892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (139892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (139892)CaDiCaL version: 2.1.3
% 0.07/0.25 % (139892)Termination reason: Refutation
% 0.07/0.25 % (139892)Time elapsed: 0.010 s
% 0.07/0.25 % (139892)Peak memory usage: 13 MB
% 0.07/0.25 % (139892)Instructions burned: 33 (million)
% 0.07/0.25 % (139881)Success in time 0.035 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------