TSTP Solution File: SYO113^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO113^5 : 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 : n032.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 09:10:21 EDT 2024
% Result : Theorem 0.13s 0.31s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SYO113^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon May 20 10:22:08 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.08/0.29 % (31313)Running in auto input_syntax mode. Trying TPTP
% 0.08/0.30 % (31319)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.08/0.30 % (31314)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.08/0.30 % (31317)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.08/0.30 % (31318)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.08/0.30 % (31315)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.08/0.30 % (31320)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)
% 0.08/0.30 % (31316)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)
% 0.08/0.30 % (31317)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.08/0.30 % (31316)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.08/0.31 % Exception at run slice level% Exception at run slice level
% 0.08/0.31 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.31 % Exception at run slice level
% 0.08/0.31 % Exception at run slice levelUser error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.31
% 0.08/0.31 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.31
% 0.08/0.31 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.31 % (31316)First to succeed.
% 0.13/0.31 % (31319)Also succeeded, but the first one will report.
% 0.13/0.31 % (31316)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31313"
% 0.13/0.31 % (31316)Refutation found. Thanks to Tanya!
% 0.13/0.31 % SZS status Theorem for theBenchmark
% 0.13/0.31 % SZS output start Proof for theBenchmark
% 0.13/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.13/0.31 thf(func_def_0, type, cNUMBER: $i > $o).
% 0.13/0.31 thf(func_def_1, type, cODD: $i > $o).
% 0.13/0.31 thf(func_def_2, type, cEVEN: $i > $o).
% 0.13/0.31 thf(func_def_3, type, cS: $i > $i).
% 0.13/0.31 thf(func_def_11, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 0.13/0.31 thf(func_def_12, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 0.13/0.31 thf(func_def_13, type, vAND: $o > $o > $o).
% 0.13/0.31 thf(func_def_14, type, vOR: $o > $o > $o).
% 0.13/0.31 thf(func_def_15, type, vIMP: $o > $o > $o).
% 0.13/0.31 thf(func_def_16, type, vNOT: $o > $o).
% 0.13/0.31 thf(func_def_17, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 0.13/0.31 thf(f233,plain,(
% 0.13/0.31 $false),
% 0.13/0.31 inference(avatar_sat_refutation,[],[f114,f119,f126,f175,f186,f232])).
% 0.13/0.31 thf(f232,plain,(
% 0.13/0.31 ~spl2_2 | spl2_5),
% 0.13/0.31 inference(avatar_contradiction_clause,[],[f231])).
% 0.13/0.31 thf(f231,plain,(
% 0.13/0.31 $false | (~spl2_2 | spl2_5)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f230])).
% 0.13/0.31 thf(f230,plain,(
% 0.13/0.31 ($true = $false) | (~spl2_2 | spl2_5)),
% 0.13/0.31 inference(forward_demodulation,[],[f199,f213])).
% 0.13/0.31 thf(f213,plain,(
% 0.13/0.31 ($false = vAPP($i,$o,cODD,sK1)) | spl2_5),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f212])).
% 0.13/0.31 thf(f212,plain,(
% 0.13/0.31 ($true != $true) | ($false = vAPP($i,$o,cODD,sK1)) | spl2_5),
% 0.13/0.31 inference(superposition,[],[f192,f4])).
% 0.13/0.31 thf(f4,plain,(
% 0.13/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.13/0.31 introduced(fool_axiom,[])).
% 0.13/0.31 thf(f192,plain,(
% 0.13/0.31 ($true != vAPP($i,$o,cODD,sK1)) | spl2_5),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f187])).
% 0.13/0.31 thf(f187,plain,(
% 0.13/0.31 ($true != $true) | ($true != vAPP($i,$o,cODD,sK1)) | spl2_5),
% 0.13/0.31 inference(superposition,[],[f185,f98])).
% 0.13/0.31 thf(f98,plain,(
% 0.13/0.31 ( ! [X0 : $i] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) | (vAPP($i,$o,cODD,X0) != $true)) )),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f97])).
% 0.13/0.31 thf(f97,plain,(
% 0.13/0.31 ( ! [X0 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) | (vAPP($i,$o,cODD,X0) != $true)) )),
% 0.13/0.31 inference(superposition,[],[f27,f18])).
% 0.13/0.31 thf(f18,plain,(
% 0.13/0.31 ( ! [X4 : $i] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cODD,X4))) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f14,plain,(
% 0.13/0.31 ($true != vAPP($i,$o,cNUMBER,sK0)) & ! [X1] : (((vAPP($i,$o,cNUMBER,X1) = $true) | (($true != vAPP($i,$o,cODD,X1)) & ($true != vAPP($i,$o,cEVEN,X1)))) & (($true = vAPP($i,$o,cODD,X1)) | ($true = vAPP($i,$o,cEVEN,X1)) | (vAPP($i,$o,cNUMBER,X1) != $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | ((($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1)))) & ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) & ($true = vAPP($i,$o,cNUMBER,sK1))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) & ! [X4] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cODD,X4))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X5] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X5)))) | ($true != vAPP($i,$o,cEVEN,X5))) & (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f13,f12])).
% 0.13/0.31 thf(f12,plain,(
% 0.13/0.31 ? [X0] : (vAPP($i,$o,cNUMBER,X0) != $true) => ($true != vAPP($i,$o,cNUMBER,sK0))),
% 0.13/0.31 introduced(choice_axiom,[])).
% 0.13/0.31 thf(f13,plain,(
% 0.13/0.31 ? [X3] : ((($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X3)))) & ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X3))) & ($true = vAPP($i,$o,cNUMBER,X3))) => ((($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1)))) & ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) & ($true = vAPP($i,$o,cNUMBER,sK1)))),
% 0.13/0.31 introduced(choice_axiom,[])).
% 0.13/0.31 thf(f11,plain,(
% 0.13/0.31 ? [X0] : (vAPP($i,$o,cNUMBER,X0) != $true) & ! [X1] : (((vAPP($i,$o,cNUMBER,X1) = $true) | (($true != vAPP($i,$o,cODD,X1)) & ($true != vAPP($i,$o,cEVEN,X1)))) & (($true = vAPP($i,$o,cODD,X1)) | ($true = vAPP($i,$o,cEVEN,X1)) | (vAPP($i,$o,cNUMBER,X1) != $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | ? [X3] : ((($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X3)))) & ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X3))) & ($true = vAPP($i,$o,cNUMBER,X3))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) & ! [X4] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cODD,X4))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X5] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X5)))) | ($true != vAPP($i,$o,cEVEN,X5))) & (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(rectify,[],[f10])).
% 0.13/0.31 thf(f10,plain,(
% 0.13/0.31 ? [X5] : ($true != vAPP($i,$o,cNUMBER,X5)) & ! [X0] : (((vAPP($i,$o,cNUMBER,X0) = $true) | ((vAPP($i,$o,cODD,X0) != $true) & (vAPP($i,$o,cEVEN,X0) != $true))) & ((vAPP($i,$o,cODD,X0) = $true) | (vAPP($i,$o,cEVEN,X0) = $true) | (vAPP($i,$o,cNUMBER,X0) != $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | ? [X1] : (((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) != $true) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) != $true)) & (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true) & (vAPP($i,$o,cNUMBER,X1) = $true)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) & ! [X3] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cODD,X3))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X4] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cEVEN,X4))) & (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(flattening,[],[f9])).
% 0.13/0.31 thf(f9,plain,(
% 0.13/0.31 ? [X5] : ($true != vAPP($i,$o,cNUMBER,X5)) & ! [X0] : (((vAPP($i,$o,cNUMBER,X0) = $true) | ((vAPP($i,$o,cODD,X0) != $true) & (vAPP($i,$o,cEVEN,X0) != $true))) & (((vAPP($i,$o,cODD,X0) = $true) | (vAPP($i,$o,cEVEN,X0) = $true)) | (vAPP($i,$o,cNUMBER,X0) != $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | ? [X1] : (((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) != $true) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) != $true)) & (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true) & (vAPP($i,$o,cNUMBER,X1) = $true)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) & ! [X3] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cODD,X3))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X4] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cEVEN,X4))) & (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(nnf_transformation,[],[f8])).
% 0.13/0.31 thf(f8,plain,(
% 0.13/0.31 ? [X5] : ($true != vAPP($i,$o,cNUMBER,X5)) & ! [X0] : ((vAPP($i,$o,cNUMBER,X0) = $true) <=> ((vAPP($i,$o,cODD,X0) = $true) | (vAPP($i,$o,cEVEN,X0) = $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | ? [X1] : (((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) != $true) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) != $true)) & (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true) & (vAPP($i,$o,cNUMBER,X1) = $true)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) & ! [X3] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cODD,X3))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X4] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cEVEN,X4))) & (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(flattening,[],[f7])).
% 0.13/0.31 thf(f7,plain,(
% 0.13/0.31 ? [X5] : ($true != vAPP($i,$o,cNUMBER,X5)) & (! [X0] : ((vAPP($i,$o,cNUMBER,X0) = $true) <=> ((vAPP($i,$o,cODD,X0) = $true) | (vAPP($i,$o,cEVEN,X0) = $true))) & (! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2))) | (? [X1] : (((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) != $true) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) != $true)) & ((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true) & (vAPP($i,$o,cNUMBER,X1) = $true))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true))) & ! [X3] : (($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) | ($true != vAPP($i,$o,cODD,X3))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X4] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) | ($true != vAPP($i,$o,cEVEN,X4))) & (vAPP($i,$o,cEVEN,c0) = $true))),
% 0.13/0.31 inference(ennf_transformation,[],[f6])).
% 0.13/0.31 thf(f6,plain,(
% 0.13/0.31 ~((! [X0] : ((vAPP($i,$o,cNUMBER,X0) = $true) <=> ((vAPP($i,$o,cODD,X0) = $true) | (vAPP($i,$o,cEVEN,X0) = $true))) & ((! [X1] : (((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true) & (vAPP($i,$o,cNUMBER,X1) = $true)) => ((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) = $true) & (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) = $true))) & (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) = $true) & (vAPP($i,$o,cNUMBER,c0) = $true)) => ! [X2] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2))) & ($true = vAPP($i,$o,cNUMBER,X2)))) & ! [X3] : (($true = vAPP($i,$o,cODD,X3)) => ($true = vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3))))) & (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true) & ! [X4] : (($true = vAPP($i,$o,cEVEN,X4)) => ($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4))))) & (vAPP($i,$o,cEVEN,c0) = $true)) => ! [X5] : ($true = vAPP($i,$o,cNUMBER,X5)))),
% 0.13/0.31 inference(fool_elimination,[],[f5])).
% 0.13/0.31 thf(f5,plain,(
% 0.13/0.31 ~((! [X0] : (vAPP($i,$o,cNUMBER,X0) <=> (vAPP($i,$o,cODD,X0) | vAPP($i,$o,cEVEN,X0))) & ((! [X1] : ((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) & vAPP($i,$o,cNUMBER,X1)) => (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) & vAPP($i,$o,cNUMBER,c0)) => ! [X2] : (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X2)) & vAPP($i,$o,cNUMBER,X2))) & ! [X3] : (vAPP($i,$o,cODD,X3) => vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X3)))) & vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) & ! [X4] : (vAPP($i,$o,cEVEN,X4) => vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X4)))) & vAPP($i,$o,cEVEN,c0)) => ! [X5] : vAPP($i,$o,cNUMBER,X5))),
% 0.13/0.31 inference(rectify,[],[f2])).
% 0.13/0.31 thf(f2,negated_conjecture,(
% 0.13/0.31 ~((! [X0] : (vAPP($i,$o,cNUMBER,X0) <=> (vAPP($i,$o,cODD,X0) | vAPP($i,$o,cEVEN,X0))) & ((! [X1] : ((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) & vAPP($i,$o,cNUMBER,X1)) => (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) & vAPP($i,$o,cNUMBER,c0)) => ! [X1] : (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) & vAPP($i,$o,cNUMBER,X1))) & ! [X0] : (vAPP($i,$o,cODD,X0) => vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) & vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) & ! [X0] : (vAPP($i,$o,cEVEN,X0) => vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) & vAPP($i,$o,cEVEN,c0)) => ! [X0] : vAPP($i,$o,cNUMBER,X0))),
% 0.13/0.31 inference(negated_conjecture,[],[f1])).
% 0.13/0.31 thf(f1,conjecture,(
% 0.13/0.31 (! [X0] : (vAPP($i,$o,cNUMBER,X0) <=> (vAPP($i,$o,cODD,X0) | vAPP($i,$o,cEVEN,X0))) & ((! [X1] : ((vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) & vAPP($i,$o,cNUMBER,X1)) => (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X1))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)))) & vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) & vAPP($i,$o,cNUMBER,c0)) => ! [X1] : (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,X1)) & vAPP($i,$o,cNUMBER,X1))) & ! [X0] : (vAPP($i,$o,cODD,X0) => vAPP($i,$o,cODD,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) & vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) & ! [X0] : (vAPP($i,$o,cEVEN,X0) => vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) & vAPP($i,$o,cEVEN,c0)) => ! [X0] : vAPP($i,$o,cNUMBER,X0)),
% 0.13/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM350)).
% 0.13/0.31 thf(f27,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true != vAPP($i,$o,cODD,X1)) | (vAPP($i,$o,cNUMBER,X1) = $true)) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f185,plain,(
% 0.13/0.31 ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | spl2_5),
% 0.13/0.31 inference(avatar_component_clause,[],[f183])).
% 0.13/0.31 thf(f183,plain,(
% 0.13/0.31 spl2_5 <=> ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1))))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
% 0.13/0.31 thf(f199,plain,(
% 0.13/0.31 ($true = vAPP($i,$o,cODD,sK1)) | (~spl2_2 | spl2_5)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f198])).
% 0.13/0.31 thf(f198,plain,(
% 0.13/0.31 ($true != $true) | ($true = vAPP($i,$o,cODD,sK1)) | (~spl2_2 | spl2_5)),
% 0.13/0.31 inference(forward_demodulation,[],[f197,f110])).
% 0.13/0.31 thf(f110,plain,(
% 0.13/0.31 ($true = vAPP($i,$o,cNUMBER,sK1)) | ~spl2_2),
% 0.13/0.31 inference(avatar_component_clause,[],[f108])).
% 0.13/0.31 thf(f108,plain,(
% 0.13/0.31 spl2_2 <=> ($true = vAPP($i,$o,cNUMBER,sK1))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.13/0.31 thf(f197,plain,(
% 0.13/0.31 ($true = vAPP($i,$o,cODD,sK1)) | ($true != vAPP($i,$o,cNUMBER,sK1)) | spl2_5),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f193])).
% 0.13/0.31 thf(f193,plain,(
% 0.13/0.31 ($true != $true) | ($true = vAPP($i,$o,cODD,sK1)) | ($true != vAPP($i,$o,cNUMBER,sK1)) | spl2_5),
% 0.13/0.31 inference(superposition,[],[f191,f25])).
% 0.13/0.31 thf(f25,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true = vAPP($i,$o,cEVEN,X1)) | ($true = vAPP($i,$o,cODD,X1)) | (vAPP($i,$o,cNUMBER,X1) != $true)) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f191,plain,(
% 0.13/0.31 ($true != vAPP($i,$o,cEVEN,sK1)) | spl2_5),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f188])).
% 0.13/0.31 thf(f188,plain,(
% 0.13/0.31 ($true != $true) | ($true != vAPP($i,$o,cEVEN,sK1)) | spl2_5),
% 0.13/0.31 inference(superposition,[],[f185,f92])).
% 0.13/0.31 thf(f92,plain,(
% 0.13/0.31 ( ! [X0 : $i] : (($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) | (vAPP($i,$o,cEVEN,X0) != $true)) )),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f91])).
% 0.13/0.31 thf(f91,plain,(
% 0.13/0.31 ( ! [X0 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,X0)))) | (vAPP($i,$o,cEVEN,X0) != $true)) )),
% 0.13/0.31 inference(superposition,[],[f26,f16])).
% 0.13/0.31 thf(f16,plain,(
% 0.13/0.31 ( ! [X5 : $i] : (($true = vAPP($i,$o,cEVEN,vAPP($i,$i,cS,vAPP($i,$i,cS,X5)))) | ($true != vAPP($i,$o,cEVEN,X5))) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f26,plain,(
% 0.13/0.31 ( ! [X1 : $i] : (($true != vAPP($i,$o,cEVEN,X1)) | (vAPP($i,$o,cNUMBER,X1) = $true)) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f186,plain,(
% 0.13/0.31 ~spl2_5 | spl2_3 | ~spl2_4),
% 0.13/0.31 inference(avatar_split_clause,[],[f181,f172,f112,f183])).
% 0.13/0.31 thf(f112,plain,(
% 0.13/0.31 spl2_3 <=> ! [X2] : ($true = vAPP($i,$o,cNUMBER,X2))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.13/0.31 thf(f172,plain,(
% 0.13/0.31 spl2_4 <=> ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1)))),
% 0.13/0.31 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
% 0.13/0.31 thf(f181,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1))))) ) | ~spl2_4),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f180])).
% 0.13/0.31 thf(f180,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1))))) ) | ~spl2_4),
% 0.13/0.31 inference(forward_demodulation,[],[f179,f65])).
% 0.13/0.31 thf(f65,plain,(
% 0.13/0.31 (vAPP($i,$o,cNUMBER,c0) = $true)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f62])).
% 0.13/0.31 thf(f62,plain,(
% 0.13/0.31 ($true != $true) | (vAPP($i,$o,cNUMBER,c0) = $true)),
% 0.13/0.31 inference(superposition,[],[f26,f15])).
% 0.13/0.31 thf(f15,plain,(
% 0.13/0.31 (vAPP($i,$o,cEVEN,c0) = $true)),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f179,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | (vAPP($i,$o,cNUMBER,c0) != $true)) ) | ~spl2_4),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f178])).
% 0.13/0.31 thf(f178,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | (vAPP($i,$o,cNUMBER,c0) != $true)) ) | ~spl2_4),
% 0.13/0.31 inference(forward_demodulation,[],[f177,f69])).
% 0.13/0.31 thf(f69,plain,(
% 0.13/0.31 (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) = $true)),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f66])).
% 0.13/0.31 thf(f66,plain,(
% 0.13/0.31 ($true != $true) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) = $true)),
% 0.13/0.31 inference(superposition,[],[f27,f17])).
% 0.13/0.31 thf(f17,plain,(
% 0.13/0.31 (vAPP($i,$o,cODD,vAPP($i,$i,cS,c0)) = $true)),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f177,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) ) | ~spl2_4),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f176])).
% 0.13/0.31 thf(f176,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) ) | ~spl2_4),
% 0.13/0.31 inference(forward_demodulation,[],[f21,f174])).
% 0.13/0.31 thf(f174,plain,(
% 0.13/0.31 ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) | ~spl2_4),
% 0.13/0.31 inference(avatar_component_clause,[],[f172])).
% 0.13/0.31 thf(f21,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,vAPP($i,$i,cS,sK1)))) | ($true != vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) )),
% 0.13/0.31 inference(cnf_transformation,[],[f14])).
% 0.13/0.31 thf(f175,plain,(
% 0.13/0.31 spl2_4 | spl2_3),
% 0.13/0.31 inference(avatar_split_clause,[],[f170,f112,f172])).
% 0.13/0.31 thf(f170,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1)))) )),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f169])).
% 0.13/0.31 thf(f169,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1)))) )),
% 0.13/0.31 inference(forward_demodulation,[],[f168,f65])).
% 0.13/0.31 thf(f168,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) | (vAPP($i,$o,cNUMBER,c0) != $true)) )),
% 0.13/0.31 inference(trivial_inequality_removal,[],[f167])).
% 0.13/0.31 thf(f167,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) | (vAPP($i,$o,cNUMBER,c0) != $true)) )),
% 0.13/0.31 inference(forward_demodulation,[],[f20,f69])).
% 0.13/0.31 thf(f20,plain,(
% 0.13/0.31 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,sK1))) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) )),
% 0.13/0.32 inference(cnf_transformation,[],[f14])).
% 0.13/0.32 thf(f126,plain,(
% 0.13/0.32 ~spl2_3),
% 0.13/0.32 inference(avatar_contradiction_clause,[],[f125])).
% 0.13/0.32 thf(f125,plain,(
% 0.13/0.32 $false | ~spl2_3),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f121])).
% 0.13/0.32 thf(f121,plain,(
% 0.13/0.32 ($true = $false) | ~spl2_3),
% 0.13/0.32 inference(superposition,[],[f113,f40])).
% 0.13/0.32 thf(f40,plain,(
% 0.13/0.32 ($false = vAPP($i,$o,cNUMBER,sK0))),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f38])).
% 0.13/0.32 thf(f38,plain,(
% 0.13/0.32 ($true != $true) | ($false = vAPP($i,$o,cNUMBER,sK0))),
% 0.13/0.32 inference(superposition,[],[f28,f4])).
% 0.13/0.32 thf(f28,plain,(
% 0.13/0.32 ($true != vAPP($i,$o,cNUMBER,sK0))),
% 0.13/0.32 inference(cnf_transformation,[],[f14])).
% 0.13/0.32 thf(f113,plain,(
% 0.13/0.32 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2))) ) | ~spl2_3),
% 0.13/0.32 inference(avatar_component_clause,[],[f112])).
% 0.13/0.32 thf(f119,plain,(
% 0.13/0.32 spl2_1),
% 0.13/0.32 inference(avatar_contradiction_clause,[],[f118])).
% 0.13/0.32 thf(f118,plain,(
% 0.13/0.32 $false | spl2_1),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f115])).
% 0.13/0.32 thf(f115,plain,(
% 0.13/0.32 ($true != $true) | spl2_1),
% 0.13/0.32 inference(superposition,[],[f106,f69])).
% 0.13/0.32 thf(f106,plain,(
% 0.13/0.32 (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | spl2_1),
% 0.13/0.32 inference(avatar_component_clause,[],[f104])).
% 0.13/0.32 thf(f104,plain,(
% 0.13/0.32 spl2_1 <=> (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) = $true)),
% 0.13/0.32 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.13/0.32 thf(f114,plain,(
% 0.13/0.32 ~spl2_1 | spl2_2 | spl2_3),
% 0.13/0.32 inference(avatar_split_clause,[],[f102,f112,f108,f104])).
% 0.13/0.32 thf(f102,plain,(
% 0.13/0.32 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,sK1)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true)) )),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f101])).
% 0.13/0.32 thf(f101,plain,(
% 0.13/0.32 ( ! [X2 : $i] : (($true != $true) | ($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,sK1)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true)) )),
% 0.13/0.32 inference(forward_demodulation,[],[f19,f65])).
% 0.13/0.32 thf(f19,plain,(
% 0.13/0.32 ( ! [X2 : $i] : (($true = vAPP($i,$o,cNUMBER,X2)) | ($true = vAPP($i,$o,cNUMBER,sK1)) | (vAPP($i,$o,cNUMBER,vAPP($i,$i,cS,c0)) != $true) | (vAPP($i,$o,cNUMBER,c0) != $true)) )),
% 0.13/0.32 inference(cnf_transformation,[],[f14])).
% 0.13/0.32 % SZS output end Proof for theBenchmark
% 0.13/0.32 % (31316)------------------------------
% 0.13/0.32 % (31316)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.32 % (31316)Termination reason: Refutation
% 0.13/0.32
% 0.13/0.32 % (31316)Memory used [KB]: 861
% 0.13/0.32 % (31316)Time elapsed: 0.011 s
% 0.13/0.32 % (31316)Instructions burned: 18 (million)
% 0.13/0.32 % (31313)Success in time 0.022 s
%------------------------------------------------------------------------------