%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN978^4 : 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 : 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 08:42:04 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN978^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:14:53 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.26 % (527130)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (527138)dis+10_1_sil=32000:sp=arity:random_seed=2918511815:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.26 % (527136)% WARNING: option uhcvi not known.
% 0.20/0.26 % (527135)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2547988353_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.26 % (527136)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1775511265:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.26 % (527137)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3237873320:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.26 % (527140)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3695439326:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.26 % (527138) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-527130-527138"...
% 0.20/0.26 % (527139)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2764804205:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.26 % (527141)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=269249282:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.26 % (527136)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % (527139)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.26 % Exception at run slice level
% 0.20/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.26 % (527136)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.26 % (527138)...printing done.
% 0.20/0.26 % (527138)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_2, type, mnot: (($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_3, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_4, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_5, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_6, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_7, type, iatom: (($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_8, type, inot: (($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_9, type, itrue: ($i > $o)).
% 0.20/0.26 thf(func_def_10, type, ifalse: ($i > $o)).
% 0.20/0.26 thf(func_def_11, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_12, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_13, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_14, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_15, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_16, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.26 thf(func_def_17, type, ivalid: (($i > $o) > $o)).
% 0.20/0.26 thf(func_def_18, type, isatisfiable: (($i > $o) > $o)).
% 0.20/0.26 thf(func_def_19, type, icountersatisfiable: (($i > $o) > $o)).
% 0.20/0.26 thf(func_def_20, type, iinvalid: (($i > $o) > $o)).
% 0.20/0.26 thf(func_def_21, type, a: ($i > $o)).
% 0.20/0.26 thf(func_def_22, type, b: ($i > $o)).
% 0.20/0.26 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.26 thf(func_def_29, type, vOR: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.26 thf(func_def_31, type, vAND: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.26 thf(func_def_33, type, vIMP: ($o > $o > $o)).
% 0.20/0.26 thf(func_def_34, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.26 thf(f2,axiom,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : (((irel @ X1 @ X2) & (irel @ X0 @ X1)) => (irel @ X0 @ X2))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom)).
% 0.20/0.26 thf(f3,axiom,(
% 0.20/0.26 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot)).
% 0.20/0.26 thf(f4,axiom,(
% 0.20/0.26 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor)).
% 0.20/0.26 thf(f5,axiom,(
% 0.20/0.26 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand)).
% 0.20/0.26 thf(f6,axiom,(
% 0.20/0.26 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mnot @ X0) @ X1))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies)).
% 0.20/0.26 thf(f7,axiom,(
% 0.20/0.26 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4)).
% 0.20/0.26 thf(f8,axiom,(
% 0.20/0.26 (iatom = (^[X0 : ($i > $o)] : (X0)))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom)).
% 0.20/0.26 thf(f12,axiom,(
% 0.20/0.26 (iand = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mand @ X0 @ X1))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand)).
% 0.20/0.26 thf(f14,axiom,(
% 0.20/0.26 (iimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies)).
% 0.20/0.26 thf(f16,axiom,(
% 0.20/0.26 (iequiv = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0)))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iequiv)).
% 0.20/0.26 thf(f18,axiom,(
% 0.20/0.26 (ivalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid)).
% 0.20/0.26 thf(f22,conjecture,(
% 0.20/0.26 (ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this)).
% 0.20/0.26 thf(f23,negated_conjecture,(
% 0.20/0.26 ~(ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f22])).
% 0.20/0.26 thf(f26,plain,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : (((irel @ X1 @ X2) & (irel @ X0 @ X1)) => (irel @ X0 @ X2))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f27,plain,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : (((((irel @ X1 @ X2)) = $true) & (((irel @ X0 @ X1)) = $true)) => (((irel @ X0 @ X2)) = $true))),
% 0.20/0.26 inference(fool_elimination,[],[f26])).
% 0.20/0.26 thf(f28,plain,(
% 0.20/0.26 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.26 inference(rectify,[],[f3])).
% 0.20/0.26 thf(f29,plain,(
% 0.20/0.26 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.26 inference(fool_elimination,[],[f28])).
% 0.20/0.26 thf(f30,plain,(
% 0.20/0.26 (mor = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.26 inference(rectify,[],[f4])).
% 0.20/0.26 thf(f31,plain,(
% 0.20/0.26 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.26 inference(fool_elimination,[],[f30])).
% 0.20/0.26 thf(f32,plain,(
% 0.20/0.26 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 0.20/0.26 inference(rectify,[],[f5])).
% 0.20/0.26 thf(f33,plain,(
% 0.20/0.26 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.20/0.26 inference(fool_elimination,[],[f32])).
% 0.20/0.26 thf(f34,plain,(
% 0.20/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.26 inference(fool_elimination,[],[f6])).
% 0.20/0.26 thf(f35,plain,(
% 0.20/0.26 (mbox_s4 = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.20/0.26 inference(rectify,[],[f7])).
% 0.20/0.26 thf(f36,plain,(
% 0.20/0.26 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.26 inference(fool_elimination,[],[f35])).
% 0.20/0.26 thf(f37,plain,(
% 0.20/0.26 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.26 inference(fool_elimination,[],[f8])).
% 0.20/0.26 thf(f40,plain,(
% 0.20/0.26 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.20/0.26 inference(fool_elimination,[],[f12])).
% 0.20/0.26 thf(f42,plain,(
% 0.20/0.26 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.26 inference(fool_elimination,[],[f14])).
% 0.20/0.26 thf(f44,plain,(
% 0.20/0.26 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.20/0.26 inference(fool_elimination,[],[f16])).
% 0.20/0.26 thf(f46,plain,(
% 0.20/0.26 (ivalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.20/0.26 inference(rectify,[],[f18])).
% 0.20/0.26 thf(f47,plain,(
% 0.20/0.26 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.26 inference(fool_elimination,[],[f46])).
% 0.20/0.26 thf(f54,plain,(
% 0.20/0.26 ~(ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))),
% 0.20/0.26 inference(rectify,[],[f23])).
% 0.20/0.26 thf(f55,plain,(
% 0.20/0.26 ~ (((ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))) = $true)),
% 0.20/0.26 inference(fool_elimination,[],[f54])).
% 0.20/0.26 thf(f56,plain,(
% 0.20/0.26 (((ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))) != $true)),
% 0.20/0.26 inference(flattening,[],[f55])).
% 0.20/0.26 thf(f57,plain,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : ((((irel @ X0 @ X2)) = $true) | ((((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X1)) != $true)))),
% 0.20/0.26 inference(ennf_transformation,[],[f27])).
% 0.20/0.26 thf(f58,plain,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : ((((irel @ X0 @ X2)) = $true) | (((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X1)) != $true))),
% 0.20/0.26 inference(flattening,[],[f57])).
% 0.20/0.26 thf(f60,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((irel @ X1 @ X2)) != $true) | (((irel @ X0 @ X2)) = $true) | (((irel @ X0 @ X1)) != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f58])).
% 0.20/0.26 thf(f61,plain,(
% 0.20/0.26 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f29])).
% 0.20/0.26 thf(f62,plain,(
% 0.20/0.26 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f31])).
% 0.20/0.26 thf(f63,plain,(
% 0.20/0.26 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f33])).
% 0.20/0.26 thf(f64,plain,(
% 0.20/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.26 inference(cnf_transformation,[],[f34])).
% 0.20/0.26 thf(f65,plain,(
% 0.20/0.26 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f36])).
% 0.20/0.26 thf(f66,plain,(
% 0.20/0.26 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.20/0.26 inference(cnf_transformation,[],[f37])).
% 0.20/0.26 thf(f70,plain,(
% 0.20/0.26 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.20/0.26 inference(cnf_transformation,[],[f40])).
% 0.20/0.26 thf(f72,plain,(
% 0.20/0.26 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f42])).
% 0.20/0.26 thf(f74,plain,(
% 0.20/0.26 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.20/0.26 inference(cnf_transformation,[],[f44])).
% 0.20/0.26 thf(f76,plain,(
% 0.20/0.26 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.26 inference(cnf_transformation,[],[f47])).
% 0.20/0.26 thf(f80,plain,(
% 0.20/0.26 (((ivalid @ (iimplies @ (iand @ (iatom @ a) @ (iatom @ b)) @ (iequiv @ (iatom @ a) @ (iatom @ b))))) != $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f56])).
% 0.20/0.26 thf(f82,definition,(
% 0.20/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.26 thf(f83,plain,(
% 0.20/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.26 inference(definition_unfolding,[],[f64,f62,f61])).
% 0.20/0.26 thf(f86,plain,(
% 0.20/0.26 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ Y0 @ Y1)))))),
% 0.20/0.26 inference(definition_unfolding,[],[f70,f63])).
% 0.20/0.26 thf(f88,plain,(
% 0.20/0.26 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.20/0.26 inference(definition_unfolding,[],[f72,f83,f65,f65])).
% 0.20/0.26 thf(f90,plain,(
% 0.20/0.26 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 0.20/0.26 inference(definition_unfolding,[],[f74,f86,f88,f88])).
% 0.20/0.26 thf(f92,plain,(
% 0.20/0.26 ($true != (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ a) @ ((^[Y0 : $i > $o]: (Y0)) @ b)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a) @ ((^[Y0 : $i > $o]: (Y0)) @ b))))))),
% 0.20/0.26 inference(definition_unfolding,[],[f80,f76,f88,f86,f66,f66,f90,f66,f66])).
% 0.20/0.26 thf(f93,plain,(
% 0.20/0.26 ($true != ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((a @ Y1) & (b @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (b @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (b @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a @ Y2))))))))))))))),
% 0.20/0.26 inference(beta-eta_normalization,[],[f92])).
% 0.20/0.26 thf(f94,plain,(
% 0.20/0.26 ($false = (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((a @ Y1) & (b @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (b @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (b @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a @ Y2))))))))))) @ sK0)))),
% 0.20/0.26 inference(sigma_proxy_clausification,[],[f93])).
% 0.20/0.26 thf(f95,plain,(
% 0.20/0.26 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((a @ Y0) & (b @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))))))))))),
% 0.20/0.26 inference(beta-eta_normalization,[],[f94])).
% 0.20/0.26 thf(f96,plain,(
% 0.20/0.26 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1)))))))))))),
% 0.20/0.26 inference(or_proxy_clausification,[],[f95])).
% 0.20/0.26 thf(f97,plain,(
% 0.20/0.26 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((a @ Y0) & (b @ Y0))))))))),
% 0.20/0.26 inference(or_proxy_clausification,[],[f95])).
% 0.20/0.26 thf(f98,plain,(
% 0.20/0.26 ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((a @ Y0) & (b @ Y0)))))))),
% 0.20/0.26 inference(not_proxy_clausification,[],[f97])).
% 0.20/0.26 thf(f99,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => ((a @ Y0) & (b @ Y0)))) @ X1)))) )),
% 0.20/0.26 inference(pi_proxy_clausification,[],[f98])).
% 0.20/0.26 thf(f100,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($true = (((irel @ sK0 @ X1) => ((a @ X1) & (b @ X1)))))) )),
% 0.20/0.26 inference(beta-eta_normalization,[],[f99])).
% 0.20/0.26 thf(f101,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($true = (((a @ X1) & (b @ X1))))) )),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f100])).
% 0.20/0.26 thf(f102,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($true = ((b @ X1)))) )),
% 0.20/0.26 inference(and_proxy_clausification,[],[f101])).
% 0.20/0.26 thf(f103,plain,(
% 0.20/0.26 ( ! [X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($true = ((a @ X1)))) )),
% 0.20/0.26 inference(and_proxy_clausification,[],[f101])).
% 0.20/0.26 thf(f104,plain,(
% 0.20/0.26 ($false = (((^[Y0 : $i]: ((irel @ sK0 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1)))))))) @ sK1)))),
% 0.20/0.26 inference(sigma_proxy_clausification,[],[f96])).
% 0.20/0.26 thf(f105,plain,(
% 0.20/0.26 ($false = (((irel @ sK0 @ sK1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0)))))))))),
% 0.20/0.26 inference(beta-eta_normalization,[],[f104])).
% 0.20/0.26 thf(f106,plain,(
% 0.20/0.26 ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))))))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f105])).
% 0.20/0.26 thf(f107,plain,(
% 0.20/0.26 ($true = ((irel @ sK0 @ sK1)))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f105])).
% 0.20/0.26 thf(f108,plain,(
% 0.20/0.26 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0)))))))),
% 0.20/0.26 inference(and_proxy_clausification,[],[f106])).
% 0.20/0.26 thf(f109,plain,(
% 0.20/0.26 ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0)))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0)))))))),
% 0.20/0.26 inference(or_proxy_clausification,[],[f108])).
% 0.20/0.26 thf(f125,plain,(
% 0.20/0.26 ($false = (((^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))) @ sK3))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0)))))))),
% 0.20/0.26 inference(sigma_proxy_clausification,[],[f109])).
% 0.20/0.26 thf(f126,plain,(
% 0.20/0.26 ($false = (((^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))) @ sK3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))))))),
% 0.20/0.26 inference(or_proxy_clausification,[],[f125])).
% 0.20/0.26 thf(f135,plain,(
% 0.20/0.26 ($false = (((^[Y0 : $i]: ((irel @ sK1 @ Y0) => (a @ Y0))) @ sK3))) | ($false = (((^[Y0 : $i]: ((irel @ sK1 @ Y0) => (b @ Y0))) @ sK4)))),
% 0.20/0.26 inference(sigma_proxy_clausification,[],[f126])).
% 0.20/0.26 thf(f136,plain,(
% 0.20/0.26 ($false = (((irel @ sK1 @ sK3) => (a @ sK3)))) | ($false = (((irel @ sK1 @ sK4) => (b @ sK4))))),
% 0.20/0.26 inference(beta-eta_normalization,[],[f135])).
% 0.20/0.26 thf(f137,plain,(
% 0.20/0.26 ($false = ((a @ sK3))) | ($false = (((irel @ sK1 @ sK4) => (b @ sK4))))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f136])).
% 0.20/0.26 thf(f138,plain,(
% 0.20/0.26 ($true = ((irel @ sK1 @ sK3))) | ($false = (((irel @ sK1 @ sK4) => (b @ sK4))))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f136])).
% 0.20/0.26 thf(f139,plain,(
% 0.20/0.26 ($true = ((irel @ sK1 @ sK3))) | ($false = ((b @ sK4)))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f138])).
% 0.20/0.26 thf(f140,plain,(
% 0.20/0.26 ($true = ((irel @ sK1 @ sK3))) | ($true = ((irel @ sK1 @ sK4)))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f138])).
% 0.20/0.26 thf(f141,plain,(
% 0.20/0.26 ($false = ((a @ sK3))) | ($false = ((b @ sK4)))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f137])).
% 0.20/0.26 thf(f142,plain,(
% 0.20/0.26 ($false = ((a @ sK3))) | ($true = ((irel @ sK1 @ sK4)))),
% 0.20/0.26 inference(imp_proxy_clausification,[],[f137])).
% 0.20/0.26 thf(f161,definition,(
% 0.20/0.26 spl5_5 <=> ($true = ((irel @ sK1 @ sK3)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 0.20/0.26 thf(f163,plain,(
% 0.20/0.26 ($true = ((irel @ sK1 @ sK3))) | ~spl5_5),
% 0.20/0.26 inference(avatar_component_clause,[],[f161])).
% 0.20/0.26 thf(f166,definition,(
% 0.20/0.26 spl5_6 <=> ($false = ((a @ sK3)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.20/0.26 thf(f168,plain,(
% 0.20/0.26 ($false = ((a @ sK3))) | ~spl5_6),
% 0.20/0.26 inference(avatar_component_clause,[],[f166])).
% 0.20/0.26 thf(f171,definition,(
% 0.20/0.26 spl5_7 <=> ($true = ((irel @ sK1 @ sK4)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.20/0.26 thf(f173,plain,(
% 0.20/0.26 ($true = ((irel @ sK1 @ sK4))) | ~spl5_7),
% 0.20/0.26 inference(avatar_component_clause,[],[f171])).
% 0.20/0.26 thf(f174,plain,(
% 0.20/0.26 spl5_7 | spl5_5),
% 0.20/0.26 inference(avatar_split_clause,[],[f140,f161,f171])).
% 0.20/0.26 thf(f176,definition,(
% 0.20/0.26 spl5_8 <=> ($false = ((b @ sK4)))),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 0.20/0.26 thf(f178,plain,(
% 0.20/0.26 ($false = ((b @ sK4))) | ~spl5_8),
% 0.20/0.26 inference(avatar_component_clause,[],[f176])).
% 0.20/0.26 thf(f179,plain,(
% 0.20/0.26 spl5_8 | spl5_5),
% 0.20/0.26 inference(avatar_split_clause,[],[f139,f161,f176])).
% 0.20/0.26 thf(f180,plain,(
% 0.20/0.26 spl5_7 | spl5_6),
% 0.20/0.26 inference(avatar_split_clause,[],[f142,f166,f171])).
% 0.20/0.26 thf(f181,plain,(
% 0.20/0.26 spl5_8 | spl5_6),
% 0.20/0.26 inference(avatar_split_clause,[],[f141,f166,f176])).
% 0.20/0.26 thf(f205,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((irel @ X2 @ X1))) | ($true != ((irel @ X2 @ X0))) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.26 inference(constrained_superposition,[],[f60,f82])).
% 0.20/0.26 thf(f206,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((irel @ X2 @ X0))) | ($true = ((irel @ X2 @ X1))) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f205])).
% 0.20/0.26 thf(f209,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((irel @ sK0 @ X0))) | ($false = ((irel @ sK1 @ X0)))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f206,f107])).
% 0.20/0.26 thf(f213,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((irel @ X0 @ X2)) = $true) | (((irel @ X1 @ X2)) = $false) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.26 inference(constrained_superposition,[],[f206,f82])).
% 0.20/0.27 thf(f214,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((irel @ X0 @ X2)) = $true) | (((irel @ X1 @ X2)) = $false) | (((irel @ X0 @ X1)) = $false)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f213])).
% 0.20/0.27 thf(f217,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($false = ((irel @ sK1 @ X0))) | ($true = ((irel @ sK0 @ X0)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f209])).
% 0.20/0.27 thf(f243,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = ((b @ X0))) | ($false = ((irel @ X1 @ X0))) | ($false = ((irel @ sK0 @ X1)))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f102,f214])).
% 0.20/0.27 thf(f262,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : $i] : (($false = ((irel @ sK0 @ X1))) | ($false = ((irel @ X1 @ X0))) | ($true = ((b @ X0)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f243])).
% 0.20/0.27 thf(f312,plain,(
% 0.20/0.27 ($true = $false) | ($true = ((irel @ sK0 @ sK3))) | ~spl5_5),
% 0.20/0.27 inference(constrained_superposition,[],[f163,f217])).
% 0.20/0.27 thf(f313,plain,(
% 0.20/0.27 ($true = ((irel @ sK0 @ sK3))) | ~spl5_5),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f312])).
% 0.20/0.27 thf(f348,plain,(
% 0.20/0.27 ($true = $false) | ($true = ((a @ sK3))) | ~spl5_5),
% 0.20/0.27 inference(constrained_superposition,[],[f313,f103])).
% 0.20/0.27 thf(f363,plain,(
% 0.20/0.27 ($true = ((a @ sK3))) | ~spl5_5),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f348])).
% 0.20/0.27 thf(f367,plain,(
% 0.20/0.27 ($true = $false) | (~spl5_5 | ~spl5_6)),
% 0.20/0.27 inference(forward_demodulation,[],[f363,f168])).
% 0.20/0.27 thf(f368,plain,(
% 0.20/0.27 $false | (~spl5_5 | ~spl5_6)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f367])).
% 0.20/0.27 thf(f369,plain,(
% 0.20/0.27 ~spl5_5 | ~spl5_6),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f368])).
% 0.20/0.27 thf(f467,plain,(
% 0.20/0.27 ($true = $false) | ($false = ((irel @ sK0 @ sK1))) | ($true = ((b @ sK4))) | ~spl5_7),
% 0.20/0.27 inference(constrained_superposition,[],[f262,f173])).
% 0.20/0.27 thf(f470,plain,(
% 0.20/0.27 ($false = ((irel @ sK0 @ sK1))) | ($true = ((b @ sK4))) | ~spl5_7),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f467])).
% 0.20/0.27 thf(f483,plain,(
% 0.20/0.27 ($true = $false) | ($true = ((b @ sK4))) | ~spl5_7),
% 0.20/0.27 inference(forward_demodulation,[],[f470,f107])).
% 0.20/0.27 thf(f484,plain,(
% 0.20/0.27 ($true = ((b @ sK4))) | ~spl5_7),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f483])).
% 0.20/0.27 thf(f495,plain,(
% 0.20/0.27 ($true = $false) | (~spl5_7 | ~spl5_8)),
% 0.20/0.27 inference(forward_demodulation,[],[f484,f178])).
% 0.20/0.27 thf(f496,plain,(
% 0.20/0.27 $false | (~spl5_7 | ~spl5_8)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f495])).
% 0.20/0.27 thf(f497,plain,(
% 0.20/0.27 ~spl5_7 | ~spl5_8),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f496])).
% 0.20/0.27 cnf(s6, plain, spl5_5 | spl5_7, inference(sat_conversion,[],[f174])).
% 0.20/0.27 cnf(s7, plain, spl5_5 | spl5_8, inference(sat_conversion,[],[f179])).
% 0.20/0.27 cnf(s8, plain, spl5_6 | spl5_7, inference(sat_conversion,[],[f180])).
% 0.20/0.27 cnf(s9, plain, spl5_6 | spl5_8, inference(sat_conversion,[],[f181])).
% 0.20/0.27 cnf(s11, plain, ~spl5_5 | ~spl5_6, inference(sat_conversion,[],[f369])).
% 0.20/0.27 cnf(s14, plain, ~spl5_7 | ~spl5_8, inference(sat_conversion,[],[f497])).
% 0.20/0.27 cnf(s17, plain, spl5_6, inference(rat,[],[s14,s8,s9])).
% 0.20/0.27 cnf(s18, plain, ~spl5_5, inference(rat,[],[s11,s17])).
% 0.20/0.27 cnf(s19, plain, spl5_8, inference(rat,[],[s7,s18])).
% 0.20/0.27 cnf(s20, plain, spl5_7, inference(rat,[],[s6,s18])).
% 0.20/0.27 cnf(s21, plain, $false, inference(rat,[],[s14,s19,s20])).
% 0.20/0.27 thf(f501,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s21])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (527138)------------------------------
% 0.20/0.27 % (527138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (527138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (527138)CaDiCaL version: 2.1.3
% 0.20/0.27 % (527138)Termination reason: Refutation
% 0.20/0.27 % (527138)Time elapsed: 0.009 s
% 0.20/0.27 % (527138)Peak memory usage: 13 MB
% 0.20/0.27 % (527138)Instructions burned: 33 (million)
% 0.20/0.27 % (527130)Success in time 0.033 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------