TSTP Solution File: SYO266^5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO266^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:10:47 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO266^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:33:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (22450)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (22457)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36 % Exception at run slice level% (22453)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.36 % (22454)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.36
% 0.13/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36 % (22453)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.36 % (22454)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.36 % Exception at run slice level
% 0.13/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36 % (22451)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.36 % Exception at run slice level
% 0.13/0.36 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (22452)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (22453)First to succeed.
% 0.13/0.37 % (22456)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37 % (22455)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37 % (22453)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22450"
% 0.13/0.37 % (22453)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% 0.13/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.13/0.37 thf(func_def_0, type, cQ: $i > $o).
% 0.13/0.37 thf(func_def_1, type, cP: $i > $o).
% 0.13/0.37 thf(func_def_6, type, sK1: ($i > $o) > $i).
% 0.13/0.37 thf(func_def_7, type, sK2: $i > $o).
% 0.13/0.37 thf(func_def_9, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.13/0.37 thf(func_def_10, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.13/0.37 thf(func_def_11, type, vAND: $o > $o > $o).
% 0.13/0.37 thf(func_def_12, type, vOR: $o > $o > $o).
% 0.13/0.37 thf(func_def_13, type, vIMP: $o > $o > $o).
% 0.13/0.37 thf(func_def_14, type, vNOT: $o > $o).
% 0.13/0.37 thf(func_def_15, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.13/0.37 thf(f361,plain,(
% 0.13/0.37 $false),
% 0.13/0.37 inference(avatar_sat_refutation,[],[f59,f67,f123,f148,f157,f229,f243,f275,f283,f360])).
% 0.13/0.37 thf(f360,plain,(
% 0.13/0.37 ~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8),
% 0.13/0.37 inference(avatar_contradiction_clause,[],[f359])).
% 0.13/0.37 thf(f359,plain,(
% 0.13/0.37 $false | (~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8)),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f358])).
% 0.13/0.37 thf(f358,plain,(
% 0.13/0.37 ($true != $true) | (~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8)),
% 0.13/0.37 inference(duplicate_literal_removal,[],[f354])).
% 0.13/0.37 thf(f354,plain,(
% 0.13/0.37 ($true != $true) | ($true != $true) | (~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8)),
% 0.13/0.37 inference(superposition,[],[f147,f351])).
% 0.13/0.37 thf(f351,plain,(
% 0.13/0.37 ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8)),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f350])).
% 0.13/0.37 thf(f350,plain,(
% 0.13/0.37 ($true = $false) | ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_1 | ~spl3_5 | ~spl3_6 | ~spl3_8)),
% 0.13/0.37 inference(superposition,[],[f252,f339])).
% 0.13/0.37 thf(f339,plain,(
% 0.13/0.37 ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_5 | ~spl3_8)),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f338])).
% 0.13/0.37 thf(f338,plain,(
% 0.13/0.37 ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_5 | ~spl3_8)),
% 0.13/0.37 inference(duplicate_literal_removal,[],[f323])).
% 0.13/0.37 thf(f323,plain,(
% 0.13/0.37 ($true != $true) | ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_5 | ~spl3_8)),
% 0.13/0.37 inference(superposition,[],[f147,f290])).
% 0.13/0.37 thf(f290,plain,(
% 0.13/0.37 ( ! [X0 : $i > $o] : (($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | ~spl3_8),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f289])).
% 0.13/0.37 thf(f289,plain,(
% 0.13/0.37 ( ! [X0 : $i > $o] : (($true != $true) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | ~spl3_8),
% 0.13/0.37 inference(superposition,[],[f287,f4])).
% 0.13/0.37 thf(f4,plain,(
% 0.13/0.37 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.13/0.37 introduced(fool_axiom,[])).
% 0.13/0.37 thf(f287,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | ~spl3_8),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f286])).
% 0.13/0.37 thf(f286,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : (($true != $true) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | ~spl3_8),
% 0.13/0.37 inference(forward_demodulation,[],[f22,f273])).
% 0.13/0.37 thf(f273,plain,(
% 0.13/0.37 ($true = vAPP($i,$o,cQ,sK0)) | ~spl3_8),
% 0.13/0.37 inference(avatar_component_clause,[],[f272])).
% 0.13/0.37 thf(f272,plain,(
% 0.13/0.37 spl3_8 <=> ($true = vAPP($i,$o,cQ,sK0))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl3_8])])).
% 0.13/0.37 thf(f22,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cQ,sK0)) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1)))) )),
% 0.13/0.37 inference(cnf_transformation,[],[f14])).
% 0.13/0.37 thf(f14,plain,(
% 0.13/0.37 ((($true != vAPP($i,$o,cQ,sK0)) & ($true != vAPP($i,$o,cP,sK0))) | ! [X1 : $i > $o] : ((($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) & ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) | (($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))) & ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))))) & (! [X3] : (($true = vAPP($i,$o,cQ,X3)) | ($true = vAPP($i,$o,cP,X3))) | ! [X5] : ((($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,sK2,X5))) & (($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,sK2,X5)))))),
% 0.13/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f13,f12,f11])).
% 0.13/0.37 thf(f11,plain,(
% 0.13/0.37 ? [X0] : (($true != vAPP($i,$o,cQ,X0)) & ($true != vAPP($i,$o,cP,X0))) => (($true != vAPP($i,$o,cQ,sK0)) & ($true != vAPP($i,$o,cP,sK0)))),
% 0.13/0.37 introduced(choice_axiom,[])).
% 0.13/0.37 thf(f12,plain,(
% 0.13/0.37 ! [X1 : $i > $o] : (? [X2] : (((vAPP($i,$o,cQ,X2) != $true) & ($true = vAPP($i,$o,X1,X2))) | ((vAPP($i,$o,cP,X2) != $true) & ($true != vAPP($i,$o,X1,X2)))) => ((($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) & ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) | (($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))) & ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))))))),
% 0.13/0.37 introduced(choice_axiom,[])).
% 0.13/0.37 thf(f13,plain,(
% 0.13/0.37 ? [X4 : $i > $o] : ! [X5] : ((($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,X4,X5))) & (($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,X4,X5)))) => ! [X5] : ((($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,sK2,X5))) & (($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,sK2,X5))))),
% 0.13/0.37 introduced(choice_axiom,[])).
% 0.13/0.37 thf(f10,plain,(
% 0.13/0.37 (? [X0] : (($true != vAPP($i,$o,cQ,X0)) & ($true != vAPP($i,$o,cP,X0))) | ! [X1 : $i > $o] : ? [X2] : (((vAPP($i,$o,cQ,X2) != $true) & ($true = vAPP($i,$o,X1,X2))) | ((vAPP($i,$o,cP,X2) != $true) & ($true != vAPP($i,$o,X1,X2))))) & (! [X3] : (($true = vAPP($i,$o,cQ,X3)) | ($true = vAPP($i,$o,cP,X3))) | ? [X4 : $i > $o] : ! [X5] : ((($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,X4,X5))) & (($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,X4,X5)))))),
% 0.13/0.37 inference(rectify,[],[f9])).
% 0.13/0.37 thf(f9,plain,(
% 0.13/0.37 (? [X2] : ((vAPP($i,$o,cQ,X2) != $true) & (vAPP($i,$o,cP,X2) != $true)) | ! [X0 : $i > $o] : ? [X1] : (((vAPP($i,$o,cQ,X1) != $true) & (vAPP($i,$o,X0,X1) = $true)) | ((vAPP($i,$o,cP,X1) != $true) & (vAPP($i,$o,X0,X1) != $true)))) & (! [X2] : ((vAPP($i,$o,cQ,X2) = $true) | (vAPP($i,$o,cP,X2) = $true)) | ? [X0 : $i > $o] : ! [X1] : (((vAPP($i,$o,cQ,X1) = $true) | (vAPP($i,$o,X0,X1) != $true)) & ((vAPP($i,$o,cP,X1) = $true) | (vAPP($i,$o,X0,X1) = $true))))),
% 0.13/0.37 inference(nnf_transformation,[],[f8])).
% 0.13/0.37 thf(f8,plain,(
% 0.13/0.37 ? [X0 : $i > $o] : ! [X1] : (((vAPP($i,$o,cQ,X1) = $true) | (vAPP($i,$o,X0,X1) != $true)) & ((vAPP($i,$o,cP,X1) = $true) | (vAPP($i,$o,X0,X1) = $true))) <~> ! [X2] : ((vAPP($i,$o,cQ,X2) = $true) | (vAPP($i,$o,cP,X2) = $true))),
% 0.13/0.37 inference(ennf_transformation,[],[f7])).
% 0.13/0.37 thf(f7,plain,(
% 0.13/0.37 ~(? [X0 : $i > $o] : ! [X1] : (((vAPP($i,$o,cQ,X1) = $true) | (vAPP($i,$o,X0,X1) != $true)) & ((vAPP($i,$o,cP,X1) = $true) | (vAPP($i,$o,X0,X1) = $true))) <=> ! [X2] : ((vAPP($i,$o,cQ,X2) = $true) | (vAPP($i,$o,cP,X2) = $true)))),
% 0.13/0.37 inference(flattening,[],[f6])).
% 0.13/0.37 thf(f6,plain,(
% 0.13/0.37 ~(? [X0 : $i > $o] : ! [X1] : (((vAPP($i,$o,cQ,X1) = $true) | ~(vAPP($i,$o,X0,X1) = $true)) & ((vAPP($i,$o,cP,X1) = $true) | (vAPP($i,$o,X0,X1) = $true))) <=> ! [X2] : ((vAPP($i,$o,cQ,X2) = $true) | (vAPP($i,$o,cP,X2) = $true)))),
% 0.13/0.37 inference(fool_elimination,[],[f5])).
% 0.13/0.37 thf(f5,plain,(
% 0.13/0.37 ~(? [X0 : $i > $o] : ! [X1] : ((vAPP($i,$o,cQ,X1) | ~vAPP($i,$o,X0,X1)) & (vAPP($i,$o,cP,X1) | vAPP($i,$o,X0,X1))) <=> ! [X2] : (vAPP($i,$o,cQ,X2) | vAPP($i,$o,cP,X2)))),
% 0.13/0.37 inference(rectify,[],[f2])).
% 0.13/0.37 thf(f2,negated_conjecture,(
% 0.13/0.37 ~(? [X0 : $i > $o] : ! [X1] : ((vAPP($i,$o,cQ,X1) | ~vAPP($i,$o,X0,X1)) & (vAPP($i,$o,cP,X1) | vAPP($i,$o,X0,X1))) <=> ! [X2] : (vAPP($i,$o,cQ,X2) | vAPP($i,$o,cP,X2)))),
% 0.13/0.37 inference(negated_conjecture,[],[f1])).
% 0.13/0.37 thf(f1,conjecture,(
% 0.13/0.37 ? [X0 : $i > $o] : ! [X1] : ((vAPP($i,$o,cQ,X1) | ~vAPP($i,$o,X0,X1)) & (vAPP($i,$o,cP,X1) | vAPP($i,$o,X0,X1))) <=> ! [X2] : (vAPP($i,$o,cQ,X2) | vAPP($i,$o,cP,X2))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM44)).
% 0.13/0.37 thf(f252,plain,(
% 0.13/0.37 ( ! [X0 : $i] : (($true = vAPP($i,$o,cP,X0)) | ($true = vAPP($i,$o,cQ,X0))) ) | (~spl3_1 | ~spl3_6)),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f251])).
% 0.13/0.37 thf(f251,plain,(
% 0.13/0.37 ( ! [X0 : $i] : (($true != $true) | ($true = vAPP($i,$o,cQ,X0)) | ($true = vAPP($i,$o,cP,X0))) ) | (~spl3_1 | ~spl3_6)),
% 0.13/0.37 inference(superposition,[],[f156,f55])).
% 0.13/0.37 thf(f55,plain,(
% 0.13/0.37 ( ! [X5 : $i] : (($true = vAPP($i,$o,sK2,X5)) | ($true = vAPP($i,$o,cP,X5))) ) | ~spl3_1),
% 0.13/0.37 inference(avatar_component_clause,[],[f54])).
% 0.13/0.37 thf(f54,plain,(
% 0.13/0.37 spl3_1 <=> ! [X5] : (($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,sK2,X5)))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.13/0.37 thf(f156,plain,(
% 0.13/0.37 ( ! [X5 : $i] : (($true != vAPP($i,$o,sK2,X5)) | ($true = vAPP($i,$o,cQ,X5))) ) | ~spl3_6),
% 0.13/0.37 inference(avatar_component_clause,[],[f155])).
% 0.13/0.37 thf(f155,plain,(
% 0.13/0.37 spl3_6 <=> ! [X5] : (($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,sK2,X5)))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl3_6])])).
% 0.13/0.37 thf(f147,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | ~spl3_5),
% 0.13/0.37 inference(avatar_component_clause,[],[f146])).
% 0.13/0.37 thf(f146,plain,(
% 0.13/0.37 spl3_5 <=> ! [X1 : $i > $o] : (($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))))),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_5])])).
% 0.13/0.38 thf(f283,plain,(
% 0.13/0.38 ~spl3_1 | spl3_4 | ~spl3_6 | spl3_8),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f282])).
% 0.13/0.38 thf(f282,plain,(
% 0.13/0.38 $false | (~spl3_1 | spl3_4 | ~spl3_6 | spl3_8)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f281])).
% 0.13/0.38 thf(f281,plain,(
% 0.13/0.38 ($true = $false) | (~spl3_1 | spl3_4 | ~spl3_6 | spl3_8)),
% 0.13/0.38 inference(forward_demodulation,[],[f266,f277])).
% 0.13/0.38 thf(f277,plain,(
% 0.13/0.38 ($false = vAPP($i,$o,cQ,sK0)) | spl3_8),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f276])).
% 0.13/0.38 thf(f276,plain,(
% 0.13/0.38 ($true != $true) | ($false = vAPP($i,$o,cQ,sK0)) | spl3_8),
% 0.13/0.38 inference(superposition,[],[f274,f4])).
% 0.13/0.38 thf(f274,plain,(
% 0.13/0.38 ($true != vAPP($i,$o,cQ,sK0)) | spl3_8),
% 0.13/0.38 inference(avatar_component_clause,[],[f272])).
% 0.13/0.38 thf(f266,plain,(
% 0.13/0.38 ($true = vAPP($i,$o,cQ,sK0)) | (~spl3_1 | spl3_4 | ~spl3_6)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f265])).
% 0.13/0.38 thf(f265,plain,(
% 0.13/0.38 ($true = $false) | ($true = vAPP($i,$o,cQ,sK0)) | (~spl3_1 | spl3_4 | ~spl3_6)),
% 0.13/0.38 inference(superposition,[],[f245,f252])).
% 0.13/0.38 thf(f245,plain,(
% 0.13/0.38 ($false = vAPP($i,$o,cP,sK0)) | spl3_4),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f244])).
% 0.13/0.38 thf(f244,plain,(
% 0.13/0.38 ($true != $true) | ($false = vAPP($i,$o,cP,sK0)) | spl3_4),
% 0.13/0.38 inference(superposition,[],[f66,f4])).
% 0.13/0.38 thf(f66,plain,(
% 0.13/0.38 ($true != vAPP($i,$o,cP,sK0)) | spl3_4),
% 0.13/0.38 inference(avatar_component_clause,[],[f64])).
% 0.13/0.38 thf(f64,plain,(
% 0.13/0.38 spl3_4 <=> ($true = vAPP($i,$o,cP,sK0))),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_4])])).
% 0.13/0.38 thf(f275,plain,(
% 0.13/0.38 spl3_5 | ~spl3_8),
% 0.13/0.38 inference(avatar_split_clause,[],[f23,f272,f146])).
% 0.13/0.38 thf(f23,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cQ,sK0)) | ($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) )),
% 0.13/0.38 inference(cnf_transformation,[],[f14])).
% 0.13/0.38 thf(f243,plain,(
% 0.13/0.38 ~spl3_2 | ~spl3_3 | ~spl3_5),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f242])).
% 0.13/0.38 thf(f242,plain,(
% 0.13/0.38 $false | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f241])).
% 0.13/0.38 thf(f241,plain,(
% 0.13/0.38 ($true != $true) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(duplicate_literal_removal,[],[f240])).
% 0.13/0.38 thf(f240,plain,(
% 0.13/0.38 ($true != $true) | ($true != $true) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(superposition,[],[f147,f235])).
% 0.13/0.38 thf(f235,plain,(
% 0.13/0.38 ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f234])).
% 0.13/0.38 thf(f234,plain,(
% 0.13/0.38 ($true = $false) | ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | ~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(superposition,[],[f168,f58])).
% 0.13/0.38 thf(f58,plain,(
% 0.13/0.38 ( ! [X3 : $i] : (($true = vAPP($i,$o,cP,X3)) | ($true = vAPP($i,$o,cQ,X3))) ) | ~spl3_2),
% 0.13/0.38 inference(avatar_component_clause,[],[f57])).
% 0.13/0.38 thf(f57,plain,(
% 0.13/0.38 spl3_2 <=> ! [X3] : (($true = vAPP($i,$o,cQ,X3)) | ($true = vAPP($i,$o,cP,X3)))),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.13/0.38 thf(f168,plain,(
% 0.13/0.38 ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f167])).
% 0.13/0.38 thf(f167,plain,(
% 0.13/0.38 ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(duplicate_literal_removal,[],[f164])).
% 0.13/0.38 thf(f164,plain,(
% 0.13/0.38 ($true != $true) | ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_3 | ~spl3_5)),
% 0.13/0.38 inference(superposition,[],[f147,f126])).
% 0.13/0.38 thf(f126,plain,(
% 0.13/0.38 ( ! [X0 : $i > $o] : (($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | ~spl3_3),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f125])).
% 0.13/0.38 thf(f125,plain,(
% 0.13/0.38 ( ! [X0 : $i > $o] : (($true != $true) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | ~spl3_3),
% 0.13/0.38 inference(superposition,[],[f62,f4])).
% 0.13/0.38 thf(f62,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | ~spl3_3),
% 0.13/0.38 inference(avatar_component_clause,[],[f61])).
% 0.13/0.38 thf(f61,plain,(
% 0.13/0.38 spl3_3 <=> ! [X1 : $i > $o] : (($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))))),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl3_3])])).
% 0.13/0.38 thf(f229,plain,(
% 0.13/0.38 ~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f228])).
% 0.13/0.38 thf(f228,plain,(
% 0.13/0.38 $false | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f227])).
% 0.13/0.38 thf(f227,plain,(
% 0.13/0.38 ($true != $true) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6)),
% 0.13/0.38 inference(duplicate_literal_removal,[],[f226])).
% 0.13/0.38 thf(f226,plain,(
% 0.13/0.38 ($true != $true) | ($true != $true) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6)),
% 0.13/0.38 inference(superposition,[],[f147,f211])).
% 0.13/0.38 thf(f211,plain,(
% 0.13/0.38 ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f208])).
% 0.13/0.38 thf(f208,plain,(
% 0.13/0.38 ($true = $false) | ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_1 | ~spl3_3 | ~spl3_5 | ~spl3_6)),
% 0.13/0.38 inference(superposition,[],[f168,f186])).
% 0.13/0.38 thf(f186,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (($true = vAPP($i,$o,cP,X0)) | ($true = vAPP($i,$o,cQ,X0))) ) | (~spl3_1 | ~spl3_6)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f183])).
% 0.13/0.38 thf(f183,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (($true != $true) | ($true = vAPP($i,$o,cQ,X0)) | ($true = vAPP($i,$o,cP,X0))) ) | (~spl3_1 | ~spl3_6)),
% 0.13/0.38 inference(superposition,[],[f156,f55])).
% 0.13/0.38 thf(f157,plain,(
% 0.13/0.38 spl3_6 | spl3_2),
% 0.13/0.38 inference(avatar_split_clause,[],[f16,f57,f155])).
% 0.13/0.38 thf(f16,plain,(
% 0.13/0.38 ( ! [X3 : $i,X5 : $i] : (($true = vAPP($i,$o,cQ,X3)) | ($true = vAPP($i,$o,cP,X3)) | ($true = vAPP($i,$o,cQ,X5)) | ($true != vAPP($i,$o,sK2,X5))) )),
% 0.13/0.38 inference(cnf_transformation,[],[f14])).
% 0.13/0.38 thf(f148,plain,(
% 0.13/0.38 spl3_5 | ~spl3_4),
% 0.13/0.38 inference(avatar_split_clause,[],[f19,f64,f146])).
% 0.13/0.38 thf(f19,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cP,sK0)) | ($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) )),
% 0.13/0.38 inference(cnf_transformation,[],[f14])).
% 0.13/0.38 thf(f123,plain,(
% 0.13/0.38 ~spl3_2 | spl3_4),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f122])).
% 0.13/0.38 thf(f122,plain,(
% 0.13/0.38 $false | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f121])).
% 0.13/0.38 thf(f121,plain,(
% 0.13/0.38 ($true != $true) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(duplicate_literal_removal,[],[f120])).
% 0.13/0.38 thf(f120,plain,(
% 0.13/0.38 ($true != $true) | ($true != $true) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(superposition,[],[f105,f117])).
% 0.13/0.38 thf(f117,plain,(
% 0.13/0.38 ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f116])).
% 0.13/0.38 thf(f116,plain,(
% 0.13/0.38 ($true = $false) | ($true = vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(superposition,[],[f58,f110])).
% 0.13/0.38 thf(f110,plain,(
% 0.13/0.38 ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f109])).
% 0.13/0.38 thf(f109,plain,(
% 0.13/0.38 ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(duplicate_literal_removal,[],[f106])).
% 0.13/0.38 thf(f106,plain,(
% 0.13/0.38 ($true != $true) | ($true != $true) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,cQ))) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(superposition,[],[f105,f85])).
% 0.13/0.38 thf(f85,plain,(
% 0.13/0.38 ( ! [X0 : $i > $o] : (($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f84])).
% 0.13/0.38 thf(f84,plain,(
% 0.13/0.38 ( ! [X0 : $i > $o] : (($true != $true) | ($true = vAPP($i,$o,X0,vAPP(sTfun($i,$o),$i,sK1,X0))) | ($false = vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X0)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(superposition,[],[f82,f4])).
% 0.13/0.38 thf(f82,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f81])).
% 0.13/0.38 thf(f81,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != $true) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(forward_demodulation,[],[f22,f71])).
% 0.13/0.38 thf(f71,plain,(
% 0.13/0.38 ($true = vAPP($i,$o,cQ,sK0)) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f68])).
% 0.13/0.38 thf(f68,plain,(
% 0.13/0.38 ($true != $true) | ($true = vAPP($i,$o,cQ,sK0)) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(superposition,[],[f66,f58])).
% 0.13/0.38 thf(f105,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f104])).
% 0.13/0.38 thf(f104,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != $true) | ($true != vAPP($i,$o,cQ,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1)))) ) | (~spl3_2 | spl3_4)),
% 0.13/0.38 inference(forward_demodulation,[],[f23,f71])).
% 0.13/0.38 thf(f67,plain,(
% 0.13/0.38 spl3_3 | ~spl3_4),
% 0.13/0.38 inference(avatar_split_clause,[],[f18,f64,f61])).
% 0.13/0.38 thf(f18,plain,(
% 0.13/0.38 ( ! [X1 : $i > $o] : (($true != vAPP($i,$o,cP,sK0)) | ($true = vAPP($i,$o,X1,vAPP(sTfun($i,$o),$i,sK1,X1))) | ($true != vAPP($i,$o,cP,vAPP(sTfun($i,$o),$i,sK1,X1)))) )),
% 0.13/0.38 inference(cnf_transformation,[],[f14])).
% 0.13/0.38 thf(f59,plain,(
% 0.13/0.38 spl3_1 | spl3_2),
% 0.13/0.38 inference(avatar_split_clause,[],[f15,f57,f54])).
% 0.13/0.38 thf(f15,plain,(
% 0.13/0.38 ( ! [X3 : $i,X5 : $i] : (($true = vAPP($i,$o,cQ,X3)) | ($true = vAPP($i,$o,cP,X3)) | ($true = vAPP($i,$o,cP,X5)) | ($true = vAPP($i,$o,sK2,X5))) )),
% 0.13/0.38 inference(cnf_transformation,[],[f14])).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (22453)------------------------------
% 0.13/0.38 % (22453)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.38 % (22453)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (22453)Memory used [KB]: 892
% 0.13/0.38 % (22453)Time elapsed: 0.015 s
% 0.13/0.38 % (22453)Instructions burned: 24 (million)
% 0.13/0.38 % (22450)Success in time 0.039 s
%------------------------------------------------------------------------------