TSTP Solution File: ALG020+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG020+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 : Wed Aug 30 16:35:38 EDT 2023
% Result : Theorem 10.34s 2.06s
% Output : Proof 14.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG020+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 04:42:52 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.55 ________ _____
% 0.18/0.56 ___ __ \_________(_)________________________________
% 0.18/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.56
% 0.18/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.56 (2023-06-19)
% 0.18/0.56
% 0.18/0.56 (c) Philipp Rümmer, 2009-2023
% 0.18/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.56 Amanda Stjerna.
% 0.18/0.56 Free software under BSD-3-Clause.
% 0.18/0.56
% 0.18/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.56
% 0.18/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.57 Running up to 7 provers in parallel.
% 0.18/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.10/1.12 Prover 4: Preprocessing ...
% 3.74/1.16 Prover 1: Preprocessing ...
% 3.74/1.18 Prover 2: Preprocessing ...
% 3.74/1.18 Prover 5: Preprocessing ...
% 3.74/1.18 Prover 0: Preprocessing ...
% 3.74/1.18 Prover 6: Preprocessing ...
% 3.74/1.18 Prover 3: Preprocessing ...
% 6.67/1.58 Prover 2: Constructing countermodel ...
% 6.67/1.58 Prover 4: Constructing countermodel ...
% 6.67/1.59 Prover 0: Constructing countermodel ...
% 6.67/1.59 Prover 1: Constructing countermodel ...
% 7.05/1.60 Prover 3: Constructing countermodel ...
% 7.05/1.61 Prover 6: Constructing countermodel ...
% 8.12/1.83 Prover 5: Constructing countermodel ...
% 10.34/2.06 Prover 0: proved (1479ms)
% 10.34/2.06
% 10.34/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.34/2.06
% 10.34/2.06 Prover 6: stopped
% 10.34/2.06 Prover 3: stopped
% 10.34/2.06 Prover 2: stopped
% 10.34/2.08 Prover 5: stopped
% 10.34/2.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.34/2.08 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.34/2.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.34/2.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.67/2.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.67/2.13 Prover 7: Preprocessing ...
% 11.05/2.14 Prover 10: Preprocessing ...
% 11.05/2.15 Prover 8: Preprocessing ...
% 11.15/2.17 Prover 11: Preprocessing ...
% 11.15/2.18 Prover 13: Preprocessing ...
% 11.15/2.19 Prover 7: Constructing countermodel ...
% 11.15/2.20 Prover 10: Constructing countermodel ...
% 11.60/2.22 Prover 8: Constructing countermodel ...
% 11.92/2.29 Prover 11: Constructing countermodel ...
% 11.92/2.32 Prover 13: Constructing countermodel ...
% 13.48/2.51 Prover 1: Found proof (size 96)
% 13.48/2.51 Prover 1: proved (1935ms)
% 13.48/2.51 Prover 13: stopped
% 13.48/2.51 Prover 8: stopped
% 13.48/2.51 Prover 11: stopped
% 13.48/2.51 Prover 7: stopped
% 13.48/2.52 Prover 10: stopped
% 13.48/2.52 Prover 4: Found proof (size 96)
% 13.48/2.52 Prover 4: proved (1946ms)
% 13.48/2.52
% 13.48/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.48/2.52
% 13.48/2.54 % SZS output start Proof for theBenchmark
% 13.48/2.55 Assumptions after simplification:
% 13.48/2.55 ---------------------------------
% 13.48/2.55
% 13.48/2.55 (ax2)
% 13.48/2.55 ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e22 = e20) & ~ (e22 =
% 13.48/2.55 e21) & ~ (e20 = e21) & $i(e23) & $i(e22) & $i(e20) & $i(e21)
% 13.48/2.55
% 13.48/2.55 (ax4)
% 13.48/2.58 op1(e13, e13) = e10 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13,
% 13.48/2.58 e11) = e12 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12
% 13.48/2.58 & op1(e12, e11) = e13 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10,
% 13.48/2.58 e10) = e10 & op1(e10, e11) = e11 & op1(e11, e13) = e12 & op1(e11, e12) = e13
% 13.48/2.58 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & $i(e13) & $i(e12) & $i(e10) &
% 13.48/2.58 $i(e11)
% 13.48/2.58
% 13.48/2.58 (ax5)
% 13.48/2.59 op2(e23, e23) = e20 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23,
% 13.48/2.59 e21) = e22 & op2(e22, e23) = e21 & op2(e22, e22) = e23 & op2(e22, e20) = e22
% 13.48/2.59 & op2(e22, e21) = e20 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20,
% 13.48/2.59 e20) = e20 & op2(e20, e21) = e21 & op2(e21, e23) = e22 & op2(e21, e22) = e20
% 13.48/2.59 & op2(e21, e20) = e21 & op2(e21, e21) = e23 & $i(e23) & $i(e22) & $i(e20) &
% 13.48/2.59 $i(e21)
% 13.48/2.59
% 13.48/2.59 (co1)
% 14.10/2.60 $i(e23) & $i(e22) & $i(e20) & $i(e21) & $i(e13) & $i(e12) & $i(e10) & $i(e11)
% 14.10/2.60 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 14.10/2.60 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 14.10/2.60 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15:
% 14.10/2.60 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20:
% 14.10/2.60 $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25:
% 14.10/2.60 $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30:
% 14.10/2.60 $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ? [v35:
% 14.10/2.60 $i] : ? [v36: $i] : ? [v37: $i] : ? [v38: $i] : ? [v39: $i] : ? [v40:
% 14.10/2.60 $i] : ? [v41: $i] : ? [v42: $i] : ? [v43: $i] : ? [v44: $i] : ? [v45:
% 14.10/2.60 $i] : ? [v46: $i] : ? [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50:
% 14.10/2.60 $i] : ? [v51: $i] : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55:
% 14.10/2.60 $i] : ? [v56: $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60:
% 14.10/2.60 $i] : ? [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65:
% 14.10/2.60 $i] : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70:
% 14.10/2.60 $i] : ? [v71: $i] : (h(v38) = v39 & h(v36) = v37 & h(v34) = v35 & h(v32) =
% 14.10/2.60 v33 & h(v30) = v31 & h(v28) = v29 & h(v26) = v27 & h(v24) = v25 & h(v22) =
% 14.10/2.60 v23 & h(v20) = v21 & h(v18) = v19 & h(v16) = v17 & h(v14) = v15 & h(v12) =
% 14.10/2.60 v13 & h(v10) = v11 & h(v8) = v9 & h(v7) = e23 & h(v6) = e22 & h(v5) = e21 &
% 14.10/2.60 h(v4) = e20 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v70)
% 14.10/2.60 = v71 & j(v68) = v69 & j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & j(v60) =
% 14.10/2.60 v61 & j(v58) = v59 & j(v56) = v57 & j(v54) = v55 & j(v52) = v53 & j(v50) =
% 14.10/2.60 v51 & j(v48) = v49 & j(v46) = v47 & j(v44) = v45 & j(v42) = v43 & j(v40) =
% 14.10/2.60 v41 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e23) = v7 &
% 14.10/2.60 j(e22) = v6 & j(e20) = v4 & j(e21) = v5 & op2(v3, v3) = v39 & op2(v3, v2) =
% 14.10/2.60 v37 & op2(v3, v1) = v35 & op2(v3, v0) = v33 & op2(v2, v3) = v31 & op2(v2,
% 14.10/2.60 v2) = v29 & op2(v2, v1) = v27 & op2(v2, v0) = v25 & op2(v1, v3) = v23 &
% 14.10/2.60 op2(v1, v2) = v21 & op2(v1, v1) = v19 & op2(v1, v0) = v17 & op2(v0, v3) =
% 14.10/2.60 v15 & op2(v0, v2) = v13 & op2(v0, v1) = v11 & op2(v0, v0) = v9 & op2(e23,
% 14.10/2.60 e23) = v70 & op2(e23, e22) = v68 & op2(e23, e20) = v64 & op2(e23, e21) =
% 14.10/2.60 v66 & op2(e22, e23) = v62 & op2(e22, e22) = v60 & op2(e22, e20) = v56 &
% 14.10/2.60 op2(e22, e21) = v58 & op2(e20, e23) = v46 & op2(e20, e22) = v44 & op2(e20,
% 14.10/2.60 e20) = v40 & op2(e20, e21) = v42 & op2(e21, e23) = v54 & op2(e21, e22) =
% 14.10/2.60 v52 & op2(e21, e20) = v48 & op2(e21, e21) = v50 & op1(v7, v7) = v71 &
% 14.10/2.60 op1(v7, v6) = v69 & op1(v7, v5) = v67 & op1(v7, v4) = v65 & op1(v6, v7) =
% 14.10/2.60 v63 & op1(v6, v6) = v61 & op1(v6, v5) = v59 & op1(v6, v4) = v57 & op1(v5,
% 14.10/2.60 v7) = v55 & op1(v5, v6) = v53 & op1(v5, v5) = v51 & op1(v5, v4) = v49 &
% 14.10/2.60 op1(v4, v7) = v47 & op1(v4, v6) = v45 & op1(v4, v5) = v43 & op1(v4, v4) =
% 14.10/2.60 v41 & op1(e13, e13) = v38 & op1(e13, e12) = v36 & op1(e13, e10) = v32 &
% 14.10/2.60 op1(e13, e11) = v34 & op1(e12, e13) = v30 & op1(e12, e12) = v28 & op1(e12,
% 14.10/2.60 e10) = v24 & op1(e12, e11) = v26 & op1(e10, e13) = v14 & op1(e10, e12) =
% 14.10/2.60 v12 & op1(e10, e10) = v8 & op1(e10, e11) = v10 & op1(e11, e13) = v22 &
% 14.10/2.60 op1(e11, e12) = v20 & op1(e11, e10) = v16 & op1(e11, e11) = v18 & $i(v71) &
% 14.10/2.60 $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) & $i(v64) &
% 14.10/2.60 $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & $i(v58) & $i(v57) &
% 14.10/2.60 $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) & $i(v51) & $i(v50) &
% 14.10/2.60 $i(v49) & $i(v48) & $i(v47) & $i(v46) & $i(v45) & $i(v44) & $i(v43) &
% 14.10/2.60 $i(v42) & $i(v41) & $i(v40) & $i(v39) & $i(v38) & $i(v37) & $i(v36) &
% 14.10/2.60 $i(v35) & $i(v34) & $i(v33) & $i(v32) & $i(v31) & $i(v30) & $i(v29) &
% 14.10/2.60 $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) &
% 14.10/2.60 $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) &
% 14.10/2.60 $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 14.10/2.60 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v7 = e13 |
% 14.10/2.60 v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e13 | v6 = e12 | v6 = e10 | v6 =
% 14.10/2.60 e11) & (v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e13 | v4 = e12
% 14.10/2.60 | v4 = e10 | v4 = e11) & (v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2
% 14.10/2.60 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e23 | v1 = e22 | v1 = e20
% 14.10/2.60 | v1 = e21) & (v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21))
% 14.10/2.60
% 14.10/2.60 (function-axioms)
% 14.10/2.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3,
% 14.10/2.61 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.10/2.61 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) =
% 14.10/2.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) =
% 14.10/2.61 v1) | ~ (h(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.10/2.61 v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0))
% 14.10/2.61
% 14.10/2.61 Further assumptions not needed in the proof:
% 14.10/2.61 --------------------------------------------
% 14.10/2.61 ax1, ax3
% 14.10/2.61
% 14.10/2.61 Those formulas are unsatisfiable:
% 14.10/2.61 ---------------------------------
% 14.10/2.61
% 14.10/2.61 Begin of proof
% 14.10/2.61 |
% 14.10/2.61 | ALPHA: (ax2) implies:
% 14.10/2.61 | (1) ~ (e23 = e20)
% 14.10/2.61 |
% 14.10/2.61 | ALPHA: (ax4) implies:
% 14.10/2.61 | (2) op1(e11, e11) = e10
% 14.10/2.61 | (3) op1(e10, e10) = e10
% 14.10/2.61 | (4) op1(e12, e12) = e10
% 14.10/2.61 | (5) op1(e13, e13) = e10
% 14.10/2.61 |
% 14.10/2.61 | ALPHA: (ax5) implies:
% 14.10/2.61 | (6) op2(e21, e21) = e23
% 14.10/2.61 | (7) op2(e20, e23) = e23
% 14.10/2.61 | (8) op2(e22, e22) = e23
% 14.10/2.61 | (9) op2(e23, e20) = e23
% 14.10/2.61 | (10) op2(e23, e23) = e20
% 14.10/2.61 |
% 14.10/2.61 | ALPHA: (co1) implies:
% 14.10/2.62 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 14.10/2.62 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 14.10/2.62 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 14.10/2.62 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 14.10/2.62 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i]
% 14.10/2.62 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28:
% 14.10/2.62 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ?
% 14.10/2.62 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i]
% 14.10/2.62 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42:
% 14.10/2.62 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ?
% 14.10/2.62 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i]
% 14.10/2.62 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56:
% 14.10/2.62 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ?
% 14.10/2.62 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i]
% 14.10/2.62 | : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70:
% 14.10/2.62 | $i] : ? [v71: $i] : (h(v38) = v39 & h(v36) = v37 & h(v34) = v35 &
% 14.10/2.62 | h(v32) = v33 & h(v30) = v31 & h(v28) = v29 & h(v26) = v27 & h(v24) =
% 14.10/2.62 | v25 & h(v22) = v23 & h(v20) = v21 & h(v18) = v19 & h(v16) = v17 &
% 14.10/2.62 | h(v14) = v15 & h(v12) = v13 & h(v10) = v11 & h(v8) = v9 & h(v7) =
% 14.10/2.62 | e23 & h(v6) = e22 & h(v5) = e21 & h(v4) = e20 & h(e13) = v3 & h(e12)
% 14.10/2.62 | = v2 & h(e10) = v0 & h(e11) = v1 & j(v70) = v71 & j(v68) = v69 &
% 14.10/2.62 | j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & j(v60) = v61 & j(v58) =
% 14.10/2.62 | v59 & j(v56) = v57 & j(v54) = v55 & j(v52) = v53 & j(v50) = v51 &
% 14.10/2.62 | j(v48) = v49 & j(v46) = v47 & j(v44) = v45 & j(v42) = v43 & j(v40) =
% 14.10/2.62 | v41 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e23)
% 14.10/2.62 | = v7 & j(e22) = v6 & j(e20) = v4 & j(e21) = v5 & op2(v3, v3) = v39 &
% 14.10/2.62 | op2(v3, v2) = v37 & op2(v3, v1) = v35 & op2(v3, v0) = v33 & op2(v2,
% 14.10/2.62 | v3) = v31 & op2(v2, v2) = v29 & op2(v2, v1) = v27 & op2(v2, v0) =
% 14.10/2.62 | v25 & op2(v1, v3) = v23 & op2(v1, v2) = v21 & op2(v1, v1) = v19 &
% 14.10/2.62 | op2(v1, v0) = v17 & op2(v0, v3) = v15 & op2(v0, v2) = v13 & op2(v0,
% 14.10/2.62 | v1) = v11 & op2(v0, v0) = v9 & op2(e23, e23) = v70 & op2(e23, e22)
% 14.10/2.62 | = v68 & op2(e23, e20) = v64 & op2(e23, e21) = v66 & op2(e22, e23) =
% 14.10/2.62 | v62 & op2(e22, e22) = v60 & op2(e22, e20) = v56 & op2(e22, e21) =
% 14.10/2.62 | v58 & op2(e20, e23) = v46 & op2(e20, e22) = v44 & op2(e20, e20) =
% 14.10/2.62 | v40 & op2(e20, e21) = v42 & op2(e21, e23) = v54 & op2(e21, e22) =
% 14.10/2.62 | v52 & op2(e21, e20) = v48 & op2(e21, e21) = v50 & op1(v7, v7) = v71
% 14.10/2.62 | & op1(v7, v6) = v69 & op1(v7, v5) = v67 & op1(v7, v4) = v65 &
% 14.10/2.62 | op1(v6, v7) = v63 & op1(v6, v6) = v61 & op1(v6, v5) = v59 & op1(v6,
% 14.10/2.62 | v4) = v57 & op1(v5, v7) = v55 & op1(v5, v6) = v53 & op1(v5, v5) =
% 14.10/2.62 | v51 & op1(v5, v4) = v49 & op1(v4, v7) = v47 & op1(v4, v6) = v45 &
% 14.10/2.62 | op1(v4, v5) = v43 & op1(v4, v4) = v41 & op1(e13, e13) = v38 &
% 14.10/2.62 | op1(e13, e12) = v36 & op1(e13, e10) = v32 & op1(e13, e11) = v34 &
% 14.10/2.62 | op1(e12, e13) = v30 & op1(e12, e12) = v28 & op1(e12, e10) = v24 &
% 14.10/2.62 | op1(e12, e11) = v26 & op1(e10, e13) = v14 & op1(e10, e12) = v12 &
% 14.10/2.62 | op1(e10, e10) = v8 & op1(e10, e11) = v10 & op1(e11, e13) = v22 &
% 14.10/2.62 | op1(e11, e12) = v20 & op1(e11, e10) = v16 & op1(e11, e11) = v18 &
% 14.10/2.62 | $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65)
% 14.10/2.62 | & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) &
% 14.10/2.62 | $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52)
% 14.10/2.62 | & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) &
% 14.10/2.62 | $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39)
% 14.10/2.62 | & $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) &
% 14.10/2.62 | $i(v32) & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26)
% 14.10/2.62 | & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 14.10/2.62 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13)
% 14.10/2.62 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 14.10/2.62 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v7 = e13 | v7
% 14.10/2.62 | = e12 | v7 = e10 | v7 = e11) & (v6 = e13 | v6 = e12 | v6 = e10 |
% 14.10/2.62 | v6 = e11) & (v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 =
% 14.10/2.62 | e13 | v4 = e12 | v4 = e10 | v4 = e11) & (v3 = e23 | v3 = e22 | v3
% 14.10/2.62 | = e20 | v3 = e21) & (v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) &
% 14.10/2.62 | (v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e23 | v0 = e22 |
% 14.10/2.62 | v0 = e20 | v0 = e21))
% 14.10/2.62 |
% 14.10/2.62 | ALPHA: (function-axioms) implies:
% 14.10/2.62 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) |
% 14.10/2.62 | ~ (j(v2) = v0))
% 14.10/2.62 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) |
% 14.10/2.62 | ~ (h(v2) = v0))
% 14.10/2.63 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.10/2.63 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0))
% 14.10/2.63 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.10/2.63 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 14.10/2.63 |
% 14.10/2.63 | DELTA: instantiating (11) with fresh symbols all_4_0, all_4_1, all_4_2,
% 14.10/2.63 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 14.10/2.63 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16,
% 14.10/2.63 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23,
% 14.10/2.63 | all_4_24, all_4_25, all_4_26, all_4_27, all_4_28, all_4_29, all_4_30,
% 14.10/2.63 | all_4_31, all_4_32, all_4_33, all_4_34, all_4_35, all_4_36, all_4_37,
% 14.10/2.63 | all_4_38, all_4_39, all_4_40, all_4_41, all_4_42, all_4_43, all_4_44,
% 14.10/2.63 | all_4_45, all_4_46, all_4_47, all_4_48, all_4_49, all_4_50, all_4_51,
% 14.10/2.63 | all_4_52, all_4_53, all_4_54, all_4_55, all_4_56, all_4_57, all_4_58,
% 14.10/2.63 | all_4_59, all_4_60, all_4_61, all_4_62, all_4_63, all_4_64, all_4_65,
% 14.10/2.63 | all_4_66, all_4_67, all_4_68, all_4_69, all_4_70, all_4_71 gives:
% 14.10/2.63 | (16) h(all_4_33) = all_4_32 & h(all_4_35) = all_4_34 & h(all_4_37) =
% 14.10/2.63 | all_4_36 & h(all_4_39) = all_4_38 & h(all_4_41) = all_4_40 &
% 14.10/2.63 | h(all_4_43) = all_4_42 & h(all_4_45) = all_4_44 & h(all_4_47) =
% 14.10/2.63 | all_4_46 & h(all_4_49) = all_4_48 & h(all_4_51) = all_4_50 &
% 14.10/2.63 | h(all_4_53) = all_4_52 & h(all_4_55) = all_4_54 & h(all_4_57) =
% 14.10/2.63 | all_4_56 & h(all_4_59) = all_4_58 & h(all_4_61) = all_4_60 &
% 14.10/2.63 | h(all_4_63) = all_4_62 & h(all_4_64) = e23 & h(all_4_65) = e22 &
% 14.10/2.63 | h(all_4_66) = e21 & h(all_4_67) = e20 & h(e13) = all_4_68 & h(e12) =
% 14.10/2.63 | all_4_69 & h(e10) = all_4_71 & h(e11) = all_4_70 & j(all_4_1) =
% 14.51/2.63 | all_4_0 & j(all_4_3) = all_4_2 & j(all_4_5) = all_4_4 & j(all_4_7) =
% 14.51/2.63 | all_4_6 & j(all_4_9) = all_4_8 & j(all_4_11) = all_4_10 & j(all_4_13)
% 14.51/2.63 | = all_4_12 & j(all_4_15) = all_4_14 & j(all_4_17) = all_4_16 &
% 14.51/2.63 | j(all_4_19) = all_4_18 & j(all_4_21) = all_4_20 & j(all_4_23) =
% 14.51/2.63 | all_4_22 & j(all_4_25) = all_4_24 & j(all_4_27) = all_4_26 &
% 14.51/2.63 | j(all_4_29) = all_4_28 & j(all_4_31) = all_4_30 & j(all_4_68) = e13 &
% 14.51/2.63 | j(all_4_69) = e12 & j(all_4_70) = e11 & j(all_4_71) = e10 & j(e23) =
% 14.51/2.64 | all_4_64 & j(e22) = all_4_65 & j(e20) = all_4_67 & j(e21) = all_4_66 &
% 14.51/2.64 | op2(all_4_68, all_4_68) = all_4_32 & op2(all_4_68, all_4_69) =
% 14.51/2.64 | all_4_34 & op2(all_4_68, all_4_70) = all_4_36 & op2(all_4_68,
% 14.51/2.64 | all_4_71) = all_4_38 & op2(all_4_69, all_4_68) = all_4_40 &
% 14.51/2.64 | op2(all_4_69, all_4_69) = all_4_42 & op2(all_4_69, all_4_70) =
% 14.51/2.64 | all_4_44 & op2(all_4_69, all_4_71) = all_4_46 & op2(all_4_70,
% 14.51/2.64 | all_4_68) = all_4_48 & op2(all_4_70, all_4_69) = all_4_50 &
% 14.51/2.64 | op2(all_4_70, all_4_70) = all_4_52 & op2(all_4_70, all_4_71) =
% 14.51/2.64 | all_4_54 & op2(all_4_71, all_4_68) = all_4_56 & op2(all_4_71,
% 14.51/2.64 | all_4_69) = all_4_58 & op2(all_4_71, all_4_70) = all_4_60 &
% 14.51/2.64 | op2(all_4_71, all_4_71) = all_4_62 & op2(e23, e23) = all_4_1 &
% 14.51/2.64 | op2(e23, e22) = all_4_3 & op2(e23, e20) = all_4_7 & op2(e23, e21) =
% 14.51/2.64 | all_4_5 & op2(e22, e23) = all_4_9 & op2(e22, e22) = all_4_11 &
% 14.51/2.64 | op2(e22, e20) = all_4_15 & op2(e22, e21) = all_4_13 & op2(e20, e23) =
% 14.51/2.64 | all_4_25 & op2(e20, e22) = all_4_27 & op2(e20, e20) = all_4_31 &
% 14.51/2.64 | op2(e20, e21) = all_4_29 & op2(e21, e23) = all_4_17 & op2(e21, e22) =
% 14.51/2.64 | all_4_19 & op2(e21, e20) = all_4_23 & op2(e21, e21) = all_4_21 &
% 14.51/2.64 | op1(all_4_64, all_4_64) = all_4_0 & op1(all_4_64, all_4_65) = all_4_2
% 14.51/2.64 | & op1(all_4_64, all_4_66) = all_4_4 & op1(all_4_64, all_4_67) =
% 14.51/2.64 | all_4_6 & op1(all_4_65, all_4_64) = all_4_8 & op1(all_4_65, all_4_65)
% 14.51/2.64 | = all_4_10 & op1(all_4_65, all_4_66) = all_4_12 & op1(all_4_65,
% 14.51/2.64 | all_4_67) = all_4_14 & op1(all_4_66, all_4_64) = all_4_16 &
% 14.51/2.64 | op1(all_4_66, all_4_65) = all_4_18 & op1(all_4_66, all_4_66) =
% 14.51/2.64 | all_4_20 & op1(all_4_66, all_4_67) = all_4_22 & op1(all_4_67,
% 14.51/2.64 | all_4_64) = all_4_24 & op1(all_4_67, all_4_65) = all_4_26 &
% 14.51/2.64 | op1(all_4_67, all_4_66) = all_4_28 & op1(all_4_67, all_4_67) =
% 14.51/2.64 | all_4_30 & op1(e13, e13) = all_4_33 & op1(e13, e12) = all_4_35 &
% 14.51/2.64 | op1(e13, e10) = all_4_39 & op1(e13, e11) = all_4_37 & op1(e12, e13) =
% 14.51/2.64 | all_4_41 & op1(e12, e12) = all_4_43 & op1(e12, e10) = all_4_47 &
% 14.51/2.64 | op1(e12, e11) = all_4_45 & op1(e10, e13) = all_4_57 & op1(e10, e12) =
% 14.51/2.64 | all_4_59 & op1(e10, e10) = all_4_63 & op1(e10, e11) = all_4_61 &
% 14.51/2.64 | op1(e11, e13) = all_4_49 & op1(e11, e12) = all_4_51 & op1(e11, e10) =
% 14.51/2.64 | all_4_55 & op1(e11, e11) = all_4_53 & $i(all_4_0) & $i(all_4_1) &
% 14.51/2.64 | $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) &
% 14.51/2.64 | $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & $i(all_4_11)
% 14.51/2.64 | & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & $i(all_4_15) &
% 14.51/2.64 | $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & $i(all_4_19) &
% 14.51/2.64 | $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & $i(all_4_23) &
% 14.51/2.64 | $i(all_4_24) & $i(all_4_25) & $i(all_4_26) & $i(all_4_27) &
% 14.51/2.64 | $i(all_4_28) & $i(all_4_29) & $i(all_4_30) & $i(all_4_31) &
% 14.51/2.64 | $i(all_4_32) & $i(all_4_33) & $i(all_4_34) & $i(all_4_35) &
% 14.51/2.64 | $i(all_4_36) & $i(all_4_37) & $i(all_4_38) & $i(all_4_39) &
% 14.51/2.64 | $i(all_4_40) & $i(all_4_41) & $i(all_4_42) & $i(all_4_43) &
% 14.51/2.64 | $i(all_4_44) & $i(all_4_45) & $i(all_4_46) & $i(all_4_47) &
% 14.51/2.64 | $i(all_4_48) & $i(all_4_49) & $i(all_4_50) & $i(all_4_51) &
% 14.51/2.64 | $i(all_4_52) & $i(all_4_53) & $i(all_4_54) & $i(all_4_55) &
% 14.51/2.64 | $i(all_4_56) & $i(all_4_57) & $i(all_4_58) & $i(all_4_59) &
% 14.51/2.64 | $i(all_4_60) & $i(all_4_61) & $i(all_4_62) & $i(all_4_63) &
% 14.51/2.64 | $i(all_4_64) & $i(all_4_65) & $i(all_4_66) & $i(all_4_67) &
% 14.51/2.64 | $i(all_4_68) & $i(all_4_69) & $i(all_4_70) & $i(all_4_71) & (all_4_64
% 14.51/2.64 | = e13 | all_4_64 = e12 | all_4_64 = e10 | all_4_64 = e11) &
% 14.51/2.64 | (all_4_65 = e13 | all_4_65 = e12 | all_4_65 = e10 | all_4_65 = e11) &
% 14.51/2.64 | (all_4_66 = e13 | all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11) &
% 14.51/2.64 | (all_4_67 = e13 | all_4_67 = e12 | all_4_67 = e10 | all_4_67 = e11) &
% 14.51/2.64 | (all_4_68 = e23 | all_4_68 = e22 | all_4_68 = e20 | all_4_68 = e21) &
% 14.51/2.64 | (all_4_69 = e23 | all_4_69 = e22 | all_4_69 = e20 | all_4_69 = e21) &
% 14.51/2.64 | (all_4_70 = e23 | all_4_70 = e22 | all_4_70 = e20 | all_4_70 = e21) &
% 14.51/2.64 | (all_4_71 = e23 | all_4_71 = e22 | all_4_71 = e20 | all_4_71 = e21)
% 14.51/2.64 |
% 14.51/2.64 | ALPHA: (16) implies:
% 14.51/2.64 | (17) op1(e11, e11) = all_4_53
% 14.51/2.64 | (18) op1(e10, e10) = all_4_63
% 14.51/2.64 | (19) op1(e12, e12) = all_4_43
% 14.51/2.64 | (20) op1(e13, e13) = all_4_33
% 14.51/2.64 | (21) op1(all_4_66, all_4_66) = all_4_20
% 14.51/2.64 | (22) op2(e21, e21) = all_4_21
% 14.51/2.64 | (23) op2(e20, e23) = all_4_25
% 14.51/2.64 | (24) op2(e22, e22) = all_4_11
% 14.51/2.64 | (25) op2(e23, e20) = all_4_7
% 14.51/2.64 | (26) op2(e23, e23) = all_4_1
% 14.51/2.64 | (27) op2(all_4_71, all_4_71) = all_4_62
% 14.51/2.64 | (28) j(e23) = all_4_64
% 14.51/2.64 | (29) j(all_4_25) = all_4_24
% 14.51/2.64 | (30) j(all_4_21) = all_4_20
% 14.51/2.64 | (31) j(all_4_11) = all_4_10
% 14.51/2.64 | (32) j(all_4_7) = all_4_6
% 14.51/2.64 | (33) h(e10) = all_4_71
% 14.51/2.64 | (34) h(all_4_66) = e21
% 14.51/2.64 | (35) h(all_4_64) = e23
% 14.51/2.64 | (36) h(all_4_63) = all_4_62
% 14.51/2.64 | (37) h(all_4_53) = all_4_52
% 14.51/2.64 | (38) h(all_4_43) = all_4_42
% 14.51/2.64 | (39) h(all_4_33) = all_4_32
% 14.51/2.64 | (40) all_4_71 = e23 | all_4_71 = e22 | all_4_71 = e20 | all_4_71 = e21
% 14.51/2.64 | (41) all_4_66 = e13 | all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11
% 14.51/2.64 |
% 14.51/2.64 | GROUND_INST: instantiating (14) with e10, all_4_53, e11, e11, simplifying with
% 14.51/2.64 | (2), (17) gives:
% 14.51/2.64 | (42) all_4_53 = e10
% 14.51/2.64 |
% 14.51/2.64 | GROUND_INST: instantiating (14) with e10, all_4_63, e10, e10, simplifying with
% 14.51/2.64 | (3), (18) gives:
% 14.51/2.64 | (43) all_4_63 = e10
% 14.51/2.64 |
% 14.51/2.64 | GROUND_INST: instantiating (14) with e10, all_4_43, e12, e12, simplifying with
% 14.51/2.64 | (4), (19) gives:
% 14.51/2.64 | (44) all_4_43 = e10
% 14.51/2.64 |
% 14.51/2.64 | GROUND_INST: instantiating (14) with e10, all_4_33, e13, e13, simplifying with
% 14.51/2.64 | (5), (20) gives:
% 14.51/2.64 | (45) all_4_33 = e10
% 14.51/2.64 |
% 14.51/2.64 | GROUND_INST: instantiating (15) with e23, all_4_21, e21, e21, simplifying with
% 14.51/2.64 | (6), (22) gives:
% 14.51/2.65 | (46) all_4_21 = e23
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (15) with e23, all_4_25, e23, e20, simplifying with
% 14.51/2.65 | (7), (23) gives:
% 14.51/2.65 | (47) all_4_25 = e23
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (15) with e23, all_4_11, e22, e22, simplifying with
% 14.51/2.65 | (8), (24) gives:
% 14.51/2.65 | (48) all_4_11 = e23
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (15) with e23, all_4_7, e20, e23, simplifying with
% 14.51/2.65 | (9), (25) gives:
% 14.51/2.65 | (49) all_4_7 = e23
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (15) with e20, all_4_1, e23, e23, simplifying with
% 14.51/2.65 | (10), (26) gives:
% 14.51/2.65 | (50) all_4_1 = e20
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (39), (45) imply:
% 14.51/2.65 | (51) h(e10) = all_4_32
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (38), (44) imply:
% 14.51/2.65 | (52) h(e10) = all_4_42
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (37), (42) imply:
% 14.51/2.65 | (53) h(e10) = all_4_52
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (36), (43) imply:
% 14.51/2.65 | (54) h(e10) = all_4_62
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (32), (49) imply:
% 14.51/2.65 | (55) j(e23) = all_4_6
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (31), (48) imply:
% 14.51/2.65 | (56) j(e23) = all_4_10
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (30), (46) imply:
% 14.51/2.65 | (57) j(e23) = all_4_20
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (29), (47) imply:
% 14.51/2.65 | (58) j(e23) = all_4_24
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (12) with all_4_64, all_4_6, e23, simplifying with
% 14.51/2.65 | (28), (55) gives:
% 14.51/2.65 | (59) all_4_6 = all_4_64
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (12) with all_4_10, all_4_6, e23, simplifying with
% 14.51/2.65 | (55), (56) gives:
% 14.51/2.65 | (60) all_4_6 = all_4_10
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (12) with all_4_20, all_4_6, e23, simplifying with
% 14.51/2.65 | (55), (57) gives:
% 14.51/2.65 | (61) all_4_6 = all_4_20
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (12) with all_4_24, all_4_6, e23, simplifying with
% 14.51/2.65 | (55), (58) gives:
% 14.51/2.65 | (62) all_4_6 = all_4_24
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (13) with all_4_52, all_4_42, e10, simplifying with
% 14.51/2.65 | (52), (53) gives:
% 14.51/2.65 | (63) all_4_42 = all_4_52
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (13) with all_4_62, all_4_42, e10, simplifying with
% 14.51/2.65 | (52), (54) gives:
% 14.51/2.65 | (64) all_4_42 = all_4_62
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (13) with all_4_71, all_4_32, e10, simplifying with
% 14.51/2.65 | (33), (51) gives:
% 14.51/2.65 | (65) all_4_32 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | GROUND_INST: instantiating (13) with all_4_42, all_4_32, e10, simplifying with
% 14.51/2.65 | (51), (52) gives:
% 14.51/2.65 | (66) all_4_32 = all_4_42
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (59), (60) imply:
% 14.51/2.65 | (67) all_4_10 = all_4_64
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (60), (62) imply:
% 14.51/2.65 | (68) all_4_10 = all_4_24
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (60), (61) imply:
% 14.51/2.65 | (69) all_4_10 = all_4_20
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (68), (69) imply:
% 14.51/2.65 | (70) all_4_20 = all_4_24
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (67), (69) imply:
% 14.51/2.65 | (71) all_4_20 = all_4_64
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (70), (71) imply:
% 14.51/2.65 | (72) all_4_24 = all_4_64
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (65), (66) imply:
% 14.51/2.65 | (73) all_4_42 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | SIMP: (73) implies:
% 14.51/2.65 | (74) all_4_42 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (63), (74) imply:
% 14.51/2.65 | (75) all_4_52 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (63), (64) imply:
% 14.51/2.65 | (76) all_4_52 = all_4_62
% 14.51/2.65 |
% 14.51/2.65 | COMBINE_EQS: (75), (76) imply:
% 14.51/2.65 | (77) all_4_62 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | SIMP: (77) implies:
% 14.51/2.65 | (78) all_4_62 = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (27), (78) imply:
% 14.51/2.65 | (79) op2(all_4_71, all_4_71) = all_4_71
% 14.51/2.65 |
% 14.51/2.65 | REDUCE: (21), (71) imply:
% 14.51/2.65 | (80) op1(all_4_66, all_4_66) = all_4_64
% 14.51/2.65 |
% 14.51/2.65 | BETA: splitting (41) gives:
% 14.51/2.65 |
% 14.51/2.65 | Case 1:
% 14.51/2.65 | |
% 14.51/2.65 | | (81) all_4_66 = e13
% 14.51/2.65 | |
% 14.51/2.66 | | REDUCE: (80), (81) imply:
% 14.51/2.66 | | (82) op1(e13, e13) = all_4_64
% 14.51/2.66 | |
% 14.51/2.66 | | GROUND_INST: instantiating (14) with e10, all_4_64, e13, e13, simplifying
% 14.51/2.66 | | with (5), (82) gives:
% 14.51/2.66 | | (83) all_4_64 = e10
% 14.51/2.66 | |
% 14.51/2.66 | | REDUCE: (35), (83) imply:
% 14.51/2.66 | | (84) h(e10) = e23
% 14.51/2.66 | |
% 14.51/2.66 | | GROUND_INST: instantiating (13) with all_4_71, e23, e10, simplifying with
% 14.51/2.66 | | (33), (84) gives:
% 14.51/2.66 | | (85) all_4_71 = e23
% 14.51/2.66 | |
% 14.51/2.66 | | REDUCE: (79), (85) imply:
% 14.51/2.66 | | (86) op2(e23, e23) = e23
% 14.51/2.66 | |
% 14.51/2.66 | | GROUND_INST: instantiating (15) with e20, e23, e23, e23, simplifying with
% 14.51/2.66 | | (10), (86) gives:
% 14.51/2.66 | | (87) e23 = e20
% 14.51/2.66 | |
% 14.51/2.66 | | REDUCE: (1), (87) imply:
% 14.51/2.66 | | (88) $false
% 14.51/2.66 | |
% 14.51/2.66 | | CLOSE: (88) is inconsistent.
% 14.51/2.66 | |
% 14.51/2.66 | Case 2:
% 14.51/2.66 | |
% 14.51/2.66 | | (89) all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11
% 14.51/2.66 | |
% 14.51/2.66 | | BETA: splitting (40) gives:
% 14.51/2.66 | |
% 14.51/2.66 | | Case 1:
% 14.51/2.66 | | |
% 14.51/2.66 | | | (90) all_4_71 = e23
% 14.51/2.66 | | |
% 14.51/2.66 | | | REDUCE: (79), (90) imply:
% 14.51/2.66 | | | (91) op2(e23, e23) = e23
% 14.51/2.66 | | |
% 14.51/2.66 | | | GROUND_INST: instantiating (15) with e20, e23, e23, e23, simplifying with
% 14.51/2.66 | | | (10), (91) gives:
% 14.51/2.66 | | | (92) e23 = e20
% 14.51/2.66 | | |
% 14.51/2.66 | | | REDUCE: (1), (92) imply:
% 14.51/2.66 | | | (93) $false
% 14.51/2.66 | | |
% 14.51/2.66 | | | CLOSE: (93) is inconsistent.
% 14.51/2.66 | | |
% 14.51/2.66 | | Case 2:
% 14.51/2.66 | | |
% 14.51/2.66 | | | (94) ~ (all_4_71 = e23)
% 14.51/2.66 | | |
% 14.51/2.66 | | | BETA: splitting (89) gives:
% 14.51/2.66 | | |
% 14.51/2.66 | | | Case 1:
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | (95) all_4_66 = e12
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | REDUCE: (80), (95) imply:
% 14.51/2.66 | | | | (96) op1(e12, e12) = all_4_64
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e12, e12,
% 14.51/2.66 | | | | simplifying with (4), (96) gives:
% 14.51/2.66 | | | | (97) all_4_64 = e10
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | REF_CLOSE: (13), (33), (35), (94), (97) are inconsistent by sub-proof
% 14.51/2.66 | | | | #1.
% 14.51/2.66 | | | |
% 14.51/2.66 | | | Case 2:
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | (98) all_4_66 = e10 | all_4_66 = e11
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | BETA: splitting (98) gives:
% 14.51/2.66 | | | |
% 14.51/2.66 | | | | Case 1:
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | (99) all_4_66 = e10
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (34), (99) imply:
% 14.51/2.66 | | | | | (100) h(e10) = e21
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (80), (99) imply:
% 14.51/2.66 | | | | | (101) op1(e10, e10) = all_4_64
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e10, e10,
% 14.51/2.66 | | | | | simplifying with (3), (101) gives:
% 14.51/2.66 | | | | | (102) all_4_64 = e10
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | GROUND_INST: instantiating (13) with all_4_71, e21, e10, simplifying
% 14.51/2.66 | | | | | with (33), (100) gives:
% 14.51/2.66 | | | | | (103) all_4_71 = e21
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (94), (103) imply:
% 14.51/2.66 | | | | | (104) ~ (e23 = e21)
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | SIMP: (104) implies:
% 14.51/2.66 | | | | | (105) ~ (e23 = e21)
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (35), (102) imply:
% 14.51/2.66 | | | | | (106) h(e10) = e23
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | GROUND_INST: instantiating (13) with e21, e23, e10, simplifying with
% 14.51/2.66 | | | | | (100), (106) gives:
% 14.51/2.66 | | | | | (107) e23 = e21
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (105), (107) imply:
% 14.51/2.66 | | | | | (108) $false
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | CLOSE: (108) is inconsistent.
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | Case 2:
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | (109) all_4_66 = e11
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REDUCE: (80), (109) imply:
% 14.51/2.66 | | | | | (110) op1(e11, e11) = all_4_64
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e11, e11,
% 14.51/2.66 | | | | | simplifying with (2), (110) gives:
% 14.51/2.66 | | | | | (111) all_4_64 = e10
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | | REF_CLOSE: (13), (33), (35), (94), (111) are inconsistent by sub-proof
% 14.51/2.66 | | | | | #1.
% 14.51/2.66 | | | | |
% 14.51/2.66 | | | | End of split
% 14.51/2.66 | | | |
% 14.51/2.66 | | | End of split
% 14.51/2.66 | | |
% 14.51/2.66 | | End of split
% 14.51/2.66 | |
% 14.51/2.66 | End of split
% 14.51/2.66 |
% 14.51/2.66 End of proof
% 14.51/2.67
% 14.51/2.67 Sub-proof #1 shows that the following formulas are inconsistent:
% 14.51/2.67 ----------------------------------------------------------------
% 14.51/2.67 (1) ~ (all_4_71 = e23)
% 14.51/2.67 (2) h(e10) = all_4_71
% 14.51/2.67 (3) h(all_4_64) = e23
% 14.51/2.67 (4) all_4_64 = e10
% 14.51/2.67 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | ~
% 14.51/2.67 (h(v2) = v0))
% 14.51/2.67
% 14.51/2.67 Begin of proof
% 14.51/2.67 |
% 14.51/2.67 | REDUCE: (3), (4) imply:
% 14.51/2.67 | (6) h(e10) = e23
% 14.51/2.67 |
% 14.51/2.67 | GROUND_INST: instantiating (5) with all_4_71, e23, e10, simplifying with (2),
% 14.51/2.67 | (6) gives:
% 14.51/2.67 | (7) all_4_71 = e23
% 14.51/2.67 |
% 14.51/2.67 | REDUCE: (1), (7) imply:
% 14.51/2.67 | (8) $false
% 14.51/2.67 |
% 14.51/2.67 | CLOSE: (8) is inconsistent.
% 14.51/2.67 |
% 14.51/2.67 End of proof
% 14.51/2.67 % SZS output end Proof for theBenchmark
% 14.51/2.67
% 14.51/2.67 2111ms
%------------------------------------------------------------------------------