%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG184+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 : n008.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 16:39:41 EDT 2023 % Result : Theorem 17.41s 3.24s % Output : Proof 26.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : ALG184+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n008.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Mon Aug 28 04:00:32 EDT 2023 % 0.11/0.31 % CPUTime : % 0.16/0.59 ________ _____ % 0.16/0.59 ___ __ \_________(_)________________________________ % 0.16/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.59 % 0.16/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.59 (2023-06-19) % 0.16/0.59 % 0.16/0.59 (c) Philipp Rümmer, 2009-2023 % 0.16/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.59 Amanda Stjerna. % 0.16/0.59 Free software under BSD-3-Clause. % 0.16/0.59 % 0.16/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.59 % 0.16/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.61 Running up to 7 provers in parallel. % 0.16/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.27 Prover 4: Preprocessing ... % 3.51/1.27 Prover 1: Preprocessing ... % 4.05/1.33 Prover 2: Preprocessing ... % 4.05/1.33 Prover 5: Preprocessing ... % 4.05/1.33 Prover 0: Preprocessing ... % 4.05/1.33 Prover 6: Preprocessing ... % 4.05/1.35 Prover 3: Preprocessing ... % 8.85/1.99 Prover 2: Constructing countermodel ... % 8.85/2.00 Prover 1: Constructing countermodel ... % 9.13/2.03 Prover 4: Constructing countermodel ... % 9.33/2.06 Prover 0: Constructing countermodel ... % 9.33/2.07 Prover 6: Constructing countermodel ... % 9.33/2.08 Prover 3: Constructing countermodel ... % 12.05/2.48 Prover 5: Constructing countermodel ... % 17.41/3.22 Prover 0: proved (2607ms) % 17.41/3.22 % 17.41/3.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.41/3.24 % 17.41/3.24 Prover 6: stopped % 17.41/3.24 Prover 2: stopped % 17.78/3.25 Prover 5: stopped % 17.84/3.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.84/3.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.84/3.27 Prover 3: stopped % 17.84/3.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.84/3.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.84/3.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.65/3.36 Prover 8: Preprocessing ... % 18.65/3.38 Prover 10: Preprocessing ... % 18.65/3.43 Prover 7: Preprocessing ... % 19.28/3.47 Prover 11: Preprocessing ... % 19.60/3.50 Prover 13: Preprocessing ... % 20.02/3.57 Prover 10: Constructing countermodel ... % 20.02/3.58 Prover 8: Constructing countermodel ... % 20.02/3.58 Prover 7: Constructing countermodel ... % 20.02/3.63 Prover 11: Constructing countermodel ... % 21.85/3.87 Prover 13: Constructing countermodel ... % 23.22/4.03 Prover 4: Found proof (size 246) % 23.22/4.03 Prover 4: proved (3409ms) % 23.22/4.03 Prover 7: stopped % 23.22/4.03 Prover 10: stopped % 23.22/4.03 Prover 13: stopped % 23.22/4.03 Prover 11: stopped % 23.22/4.03 Prover 1: stopped % 23.22/4.04 Prover 8: stopped % 23.22/4.04 % 23.22/4.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.22/4.04 % 24.31/4.22 % SZS output start Proof for theBenchmark % 24.31/4.22 Assumptions after simplification: % 24.31/4.23 --------------------------------- % 24.31/4.23 % 24.31/4.23 (ax1) % 24.31/4.24 ~ (e14 = e13) & ~ (e14 = e12) & ~ (e14 = e10) & ~ (e14 = e11) & ~ (e13 = % 24.31/4.24 e12) & ~ (e13 = e10) & ~ (e13 = e11) & ~ (e12 = e10) & ~ (e12 = e11) & % 24.31/4.24 ~ (e10 = e11) & $i(e14) & $i(e13) & $i(e12) & $i(e10) & $i(e11) % 24.31/4.24 % 24.31/4.24 (ax4) % 24.68/4.29 op1(e14, e14) = e10 & op1(e14, e13) = e14 & op1(e14, e12) = e11 & op1(e14, % 24.68/4.29 e10) = e12 & op1(e14, e11) = e13 & op1(e13, e14) = e11 & op1(e13, e13) = e12 % 24.68/4.29 & op1(e13, e12) = e14 & op1(e13, e10) = e13 & op1(e13, e11) = e10 & op1(e12, % 24.68/4.29 e14) = e12 & op1(e12, e13) = e10 & op1(e12, e12) = e13 & op1(e12, e10) = e11 % 24.68/4.29 & op1(e12, e11) = e14 & op1(e10, e14) = e13 & op1(e10, e13) = e11 & op1(e10, % 24.68/4.29 e12) = e10 & op1(e10, e10) = e14 & op1(e10, e11) = e12 & op1(e11, e14) = e14 % 24.68/4.29 & op1(e11, e13) = e13 & op1(e11, e12) = e12 & op1(e11, e10) = e10 & op1(e11, % 24.68/4.29 e11) = e11 & $i(e14) & $i(e13) & $i(e12) & $i(e10) & $i(e11) % 24.68/4.29 % 24.68/4.29 (ax5) % 24.68/4.30 op2(e24, e24) = e24 & op2(e24, e23) = e21 & op2(e24, e22) = e20 & op2(e24, % 24.68/4.30 e20) = e23 & op2(e24, e21) = e22 & op2(e23, e24) = e22 & op2(e23, e23) = e23 % 24.68/4.30 & op2(e23, e22) = e21 & op2(e23, e20) = e24 & op2(e23, e21) = e20 & op2(e22, % 24.68/4.30 e24) = e23 & op2(e22, e23) = e20 & op2(e22, e22) = e22 & op2(e22, e20) = e21 % 24.68/4.30 & op2(e22, e21) = e24 & op2(e20, e24) = e21 & op2(e20, e23) = e22 & op2(e20, % 24.68/4.30 e22) = e24 & op2(e20, e20) = e20 & op2(e20, e21) = e23 & op2(e21, e24) = e20 % 24.68/4.30 & op2(e21, e23) = e24 & op2(e21, e22) = e23 & op2(e21, e20) = e22 & op2(e21, % 24.68/4.30 e21) = e21 & $i(e24) & $i(e23) & $i(e22) & $i(e20) & $i(e21) % 24.68/4.30 % 24.68/4.30 (co1) % 24.68/4.34 $i(e24) & $i(e23) & $i(e22) & $i(e20) & $i(e21) & $i(e14) & $i(e13) & $i(e12) % 24.68/4.34 & $i(e10) & $i(e11) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 24.68/4.34 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: % 24.68/4.34 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 24.68/4.34 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 24.68/4.34 $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: % 24.68/4.34 $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: % 24.68/4.34 $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: % 24.68/4.34 $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] : ? [v38: $i] : ? [v39: % 24.68/4.34 $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: $i] : ? [v43: $i] : ? [v44: % 24.68/4.34 $i] : ? [v45: $i] : ? [v46: $i] : ? [v47: $i] : ? [v48: $i] : ? [v49: % 24.68/4.34 $i] : ? [v50: $i] : ? [v51: $i] : ? [v52: $i] : ? [v53: $i] : ? [v54: % 24.68/4.34 $i] : ? [v55: $i] : ? [v56: $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: % 24.68/4.34 $i] : ? [v60: $i] : ? [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: % 24.68/4.34 $i] : ? [v65: $i] : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: % 24.68/4.34 $i] : ? [v70: $i] : ? [v71: $i] : ? [v72: $i] : ? [v73: $i] : ? [v74: % 24.68/4.34 $i] : ? [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: $i] : ? [v79: % 24.68/4.34 $i] : ? [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? [v83: $i] : ? [v84: % 24.68/4.34 $i] : ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? [v88: $i] : ? [v89: % 24.68/4.34 $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? [v93: $i] : ? [v94: % 24.68/4.34 $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? [v98: $i] : ? [v99: % 24.68/4.34 $i] : ? [v100: $i] : ? [v101: $i] : ? [v102: $i] : ? [v103: $i] : ? % 24.68/4.34 [v104: $i] : ? [v105: $i] : ? [v106: $i] : ? [v107: $i] : ? [v108: $i] : % 24.68/4.34 ? [v109: $i] : (h(v58) = v59 & h(v56) = v57 & h(v54) = v55 & h(v52) = v53 & % 24.68/4.34 h(v50) = v51 & h(v48) = v49 & h(v46) = v47 & h(v44) = v45 & h(v42) = v43 & % 24.68/4.34 h(v40) = v41 & h(v38) = v39 & h(v36) = v37 & h(v34) = v35 & h(v32) = v33 & % 24.68/4.35 h(v30) = v31 & h(v28) = v29 & h(v26) = v27 & h(v24) = v25 & h(v22) = v23 & % 24.68/4.35 h(v20) = v21 & h(v18) = v19 & h(v16) = v17 & h(v14) = v15 & h(v12) = v13 & % 24.68/4.35 h(v10) = v11 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 & h(v5) % 24.68/4.35 = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 % 24.68/4.35 & j(v108) = v109 & j(v106) = v107 & j(v104) = v105 & j(v102) = v103 & % 24.68/4.35 j(v100) = v101 & j(v98) = v99 & j(v96) = v97 & j(v94) = v95 & j(v92) = v93 & % 24.68/4.35 j(v90) = v91 & j(v88) = v89 & j(v86) = v87 & j(v84) = v85 & j(v82) = v83 & % 24.68/4.35 j(v80) = v81 & j(v78) = v79 & j(v76) = v77 & j(v74) = v75 & j(v72) = v73 & % 24.68/4.35 j(v70) = v71 & j(v68) = v69 & j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & % 24.68/4.35 j(v60) = v61 & j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) % 24.68/4.35 = e10 & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = v6 % 24.68/4.35 & op2(v4, v4) = v59 & op2(v4, v3) = v57 & op2(v4, v2) = v55 & op2(v4, v1) = % 24.68/4.35 v53 & op2(v4, v0) = v51 & op2(v3, v4) = v49 & op2(v3, v3) = v47 & op2(v3, % 24.68/4.35 v2) = v45 & op2(v3, v1) = v43 & op2(v3, v0) = v41 & op2(v2, v4) = v39 & % 24.68/4.35 op2(v2, v3) = v37 & op2(v2, v2) = v35 & op2(v2, v1) = v33 & op2(v2, v0) = % 24.68/4.35 v31 & op2(v1, v4) = v29 & op2(v1, v3) = v27 & op2(v1, v2) = v25 & op2(v1, % 24.68/4.35 v1) = v23 & op2(v1, v0) = v21 & op2(v0, v4) = v19 & op2(v0, v3) = v17 & % 24.68/4.35 op2(v0, v2) = v15 & op2(v0, v1) = v13 & op2(v0, v0) = v11 & op2(e24, e24) = % 24.68/4.35 v108 & op2(e24, e23) = v106 & op2(e24, e22) = v104 & op2(e24, e20) = v100 & % 24.68/4.35 op2(e24, e21) = v102 & op2(e23, e24) = v98 & op2(e23, e23) = v96 & op2(e23, % 24.68/4.35 e22) = v94 & op2(e23, e20) = v90 & op2(e23, e21) = v92 & op2(e22, e24) = % 24.68/4.35 v88 & op2(e22, e23) = v86 & op2(e22, e22) = v84 & op2(e22, e20) = v80 & % 24.68/4.35 op2(e22, e21) = v82 & op2(e20, e24) = v68 & op2(e20, e23) = v66 & op2(e20, % 24.68/4.35 e22) = v64 & op2(e20, e20) = v60 & op2(e20, e21) = v62 & op2(e21, e24) = % 24.68/4.35 v78 & op2(e21, e23) = v76 & op2(e21, e22) = v74 & op2(e21, e20) = v70 & % 24.68/4.35 op2(e21, e21) = v72 & op1(v9, v9) = v109 & op1(v9, v8) = v107 & op1(v9, v7) % 24.68/4.35 = v105 & op1(v9, v6) = v103 & op1(v9, v5) = v101 & op1(v8, v9) = v99 & % 24.68/4.35 op1(v8, v8) = v97 & op1(v8, v7) = v95 & op1(v8, v6) = v93 & op1(v8, v5) = % 24.68/4.35 v91 & op1(v7, v9) = v89 & op1(v7, v8) = v87 & op1(v7, v7) = v85 & op1(v7, % 24.68/4.35 v6) = v83 & op1(v7, v5) = v81 & op1(v6, v9) = v79 & op1(v6, v8) = v77 & % 24.68/4.35 op1(v6, v7) = v75 & op1(v6, v6) = v73 & op1(v6, v5) = v71 & op1(v5, v9) = % 24.68/4.35 v69 & op1(v5, v8) = v67 & op1(v5, v7) = v65 & op1(v5, v6) = v63 & op1(v5, % 24.68/4.35 v5) = v61 & op1(e14, e14) = v58 & op1(e14, e13) = v56 & op1(e14, e12) = % 24.68/4.35 v54 & op1(e14, e10) = v50 & op1(e14, e11) = v52 & op1(e13, e14) = v48 & % 24.68/4.35 op1(e13, e13) = v46 & op1(e13, e12) = v44 & op1(e13, e10) = v40 & op1(e13, % 24.68/4.35 e11) = v42 & op1(e12, e14) = v38 & op1(e12, e13) = v36 & op1(e12, e12) = % 24.68/4.35 v34 & op1(e12, e10) = v30 & op1(e12, e11) = v32 & op1(e10, e14) = v18 & % 24.68/4.35 op1(e10, e13) = v16 & op1(e10, e12) = v14 & op1(e10, e10) = v10 & op1(e10, % 24.68/4.35 e11) = v12 & op1(e11, e14) = v28 & op1(e11, e13) = v26 & op1(e11, e12) = % 24.68/4.35 v24 & op1(e11, e10) = v20 & op1(e11, e11) = v22 & $i(v109) & $i(v108) & % 24.68/4.35 $i(v107) & $i(v106) & $i(v105) & $i(v104) & $i(v103) & $i(v102) & $i(v101) & % 24.68/4.35 $i(v100) & $i(v99) & $i(v98) & $i(v97) & $i(v96) & $i(v95) & $i(v94) & % 24.68/4.35 $i(v93) & $i(v92) & $i(v91) & $i(v90) & $i(v89) & $i(v88) & $i(v87) & % 24.68/4.35 $i(v86) & $i(v85) & $i(v84) & $i(v83) & $i(v82) & $i(v81) & $i(v80) & % 24.68/4.35 $i(v79) & $i(v78) & $i(v77) & $i(v76) & $i(v75) & $i(v74) & $i(v73) & % 24.68/4.35 $i(v72) & $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & % 24.68/4.35 $i(v65) & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & % 24.68/4.35 $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) & % 24.68/4.35 $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & $i(v45) & % 24.68/4.35 $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) & $i(v38) & % 24.68/4.35 $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & $i(v32) & $i(v31) & % 24.68/4.35 $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & % 24.68/4.35 $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & % 24.68/4.35 $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) % 24.68/4.35 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 24.68/4.35 $i(v0) & (v9 = e14 | v9 = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 % 24.68/4.35 | v8 = e13 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = % 24.68/4.35 e12 | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = e10 | % 24.68/4.35 v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = % 24.68/4.35 e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & (v3 = e24 | v3 = e23 | % 24.68/4.35 v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | v2 = e23 | v2 = e22 | v2 = % 24.68/4.35 e20 | v2 = e21) & (v1 = e24 | v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & % 24.68/4.35 (v0 = e24 | v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21)) % 24.68/4.35 % 24.68/4.35 (function-axioms) % 24.68/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3, % 24.68/4.35 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 24.68/4.36 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = % 24.68/4.36 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = % 24.68/4.36 v1) | ~ (h(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 24.68/4.36 v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 24.68/4.36 % 24.68/4.36 Further assumptions not needed in the proof: % 24.68/4.36 -------------------------------------------- % 24.68/4.36 ax2, ax3 % 24.68/4.36 % 24.68/4.36 Those formulas are unsatisfiable: % 24.68/4.36 --------------------------------- % 24.68/4.36 % 24.68/4.36 Begin of proof % 24.68/4.36 | % 24.68/4.36 | ALPHA: (ax1) implies: % 24.68/4.36 | (1) ~ (e14 = e10) % 24.68/4.36 | % 24.68/4.36 | ALPHA: (ax4) implies: % 24.68/4.36 | (2) op1(e11, e14) = e14 % 24.68/4.36 | (3) op1(e10, e10) = e14 % 24.68/4.36 | (4) op1(e12, e11) = e14 % 24.68/4.36 | (5) op1(e13, e12) = e14 % 24.68/4.36 | (6) op1(e14, e13) = e14 % 24.68/4.36 | (7) op1(e14, e14) = e10 % 24.68/4.36 | % 24.68/4.36 | ALPHA: (ax5) implies: % 24.68/4.36 | (8) op2(e21, e21) = e21 % 24.68/4.37 | (9) op2(e21, e20) = e22 % 24.68/4.37 | (10) op2(e21, e22) = e23 % 24.68/4.37 | (11) op2(e21, e23) = e24 % 24.68/4.37 | (12) op2(e21, e24) = e20 % 24.68/4.37 | (13) op2(e20, e21) = e23 % 24.68/4.37 | (14) op2(e20, e20) = e20 % 24.68/4.37 | (15) op2(e20, e22) = e24 % 24.68/4.37 | (16) op2(e20, e23) = e22 % 24.68/4.37 | (17) op2(e20, e24) = e21 % 24.68/4.37 | (18) op2(e22, e21) = e24 % 24.68/4.37 | (19) op2(e22, e20) = e21 % 24.68/4.37 | (20) op2(e22, e22) = e22 % 24.68/4.37 | (21) op2(e22, e23) = e20 % 24.68/4.37 | (22) op2(e22, e24) = e23 % 24.68/4.37 | (23) op2(e23, e21) = e20 % 24.68/4.37 | (24) op2(e23, e20) = e24 % 24.68/4.37 | (25) op2(e23, e22) = e21 % 24.68/4.37 | (26) op2(e23, e23) = e23 % 24.68/4.37 | (27) op2(e23, e24) = e22 % 24.68/4.37 | (28) op2(e24, e21) = e22 % 24.68/4.37 | (29) op2(e24, e20) = e23 % 24.68/4.37 | (30) op2(e24, e22) = e20 % 24.68/4.37 | (31) op2(e24, e23) = e21 % 24.68/4.37 | (32) op2(e24, e24) = e24 % 24.68/4.37 | % 24.68/4.37 | ALPHA: (co1) implies: % 25.11/4.40 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 25.11/4.40 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 25.11/4.40 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 25.11/4.40 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 25.11/4.40 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 25.11/4.40 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 25.11/4.40 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 25.11/4.40 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] % 25.11/4.40 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: % 25.11/4.40 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? % 25.11/4.40 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] % 25.11/4.40 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: % 25.11/4.40 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? % 25.11/4.41 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] % 25.11/4.41 | : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: % 25.11/4.41 | $i] : ? [v71: $i] : ? [v72: $i] : ? [v73: $i] : ? [v74: $i] : ? % 25.11/4.41 | [v75: $i] : ? [v76: $i] : ? [v77: $i] : ? [v78: $i] : ? [v79: $i] % 25.11/4.41 | : ? [v80: $i] : ? [v81: $i] : ? [v82: $i] : ? [v83: $i] : ? [v84: % 25.11/4.41 | $i] : ? [v85: $i] : ? [v86: $i] : ? [v87: $i] : ? [v88: $i] : ? % 25.11/4.41 | [v89: $i] : ? [v90: $i] : ? [v91: $i] : ? [v92: $i] : ? [v93: $i] % 25.11/4.41 | : ? [v94: $i] : ? [v95: $i] : ? [v96: $i] : ? [v97: $i] : ? [v98: % 25.11/4.41 | $i] : ? [v99: $i] : ? [v100: $i] : ? [v101: $i] : ? [v102: $i] : % 25.11/4.41 | ? [v103: $i] : ? [v104: $i] : ? [v105: $i] : ? [v106: $i] : ? % 25.11/4.41 | [v107: $i] : ? [v108: $i] : ? [v109: $i] : (h(v58) = v59 & h(v56) = % 25.11/4.41 | v57 & h(v54) = v55 & h(v52) = v53 & h(v50) = v51 & h(v48) = v49 & % 25.11/4.41 | h(v46) = v47 & h(v44) = v45 & h(v42) = v43 & h(v40) = v41 & h(v38) = % 25.11/4.41 | v39 & h(v36) = v37 & h(v34) = v35 & h(v32) = v33 & h(v30) = v31 & % 25.11/4.41 | h(v28) = v29 & h(v26) = v27 & h(v24) = v25 & h(v22) = v23 & h(v20) = % 25.11/4.41 | v21 & h(v18) = v19 & h(v16) = v17 & h(v14) = v15 & h(v12) = v13 & % 25.11/4.41 | h(v10) = v11 & h(v9) = e24 & h(v8) = e23 & h(v7) = e22 & h(v6) = e21 % 25.11/4.41 | & h(v5) = e20 & h(e14) = v4 & h(e13) = v3 & h(e12) = v2 & h(e10) = % 25.11/4.41 | v0 & h(e11) = v1 & j(v108) = v109 & j(v106) = v107 & j(v104) = v105 % 25.11/4.41 | & j(v102) = v103 & j(v100) = v101 & j(v98) = v99 & j(v96) = v97 & % 25.11/4.41 | j(v94) = v95 & j(v92) = v93 & j(v90) = v91 & j(v88) = v89 & j(v86) = % 25.11/4.41 | v87 & j(v84) = v85 & j(v82) = v83 & j(v80) = v81 & j(v78) = v79 & % 25.11/4.41 | j(v76) = v77 & j(v74) = v75 & j(v72) = v73 & j(v70) = v71 & j(v68) = % 25.11/4.41 | v69 & j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & j(v60) = v61 & % 25.11/4.41 | j(v4) = e14 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 % 25.11/4.41 | & j(e24) = v9 & j(e23) = v8 & j(e22) = v7 & j(e20) = v5 & j(e21) = % 25.11/4.41 | v6 & op2(v4, v4) = v59 & op2(v4, v3) = v57 & op2(v4, v2) = v55 & % 25.11/4.41 | op2(v4, v1) = v53 & op2(v4, v0) = v51 & op2(v3, v4) = v49 & op2(v3, % 25.11/4.41 | v3) = v47 & op2(v3, v2) = v45 & op2(v3, v1) = v43 & op2(v3, v0) = % 25.11/4.41 | v41 & op2(v2, v4) = v39 & op2(v2, v3) = v37 & op2(v2, v2) = v35 & % 25.11/4.41 | op2(v2, v1) = v33 & op2(v2, v0) = v31 & op2(v1, v4) = v29 & op2(v1, % 25.11/4.41 | v3) = v27 & op2(v1, v2) = v25 & op2(v1, v1) = v23 & op2(v1, v0) = % 25.11/4.41 | v21 & op2(v0, v4) = v19 & op2(v0, v3) = v17 & op2(v0, v2) = v15 & % 25.11/4.41 | op2(v0, v1) = v13 & op2(v0, v0) = v11 & op2(e24, e24) = v108 & % 25.11/4.41 | op2(e24, e23) = v106 & op2(e24, e22) = v104 & op2(e24, e20) = v100 & % 25.11/4.41 | op2(e24, e21) = v102 & op2(e23, e24) = v98 & op2(e23, e23) = v96 & % 25.11/4.41 | op2(e23, e22) = v94 & op2(e23, e20) = v90 & op2(e23, e21) = v92 & % 25.11/4.41 | op2(e22, e24) = v88 & op2(e22, e23) = v86 & op2(e22, e22) = v84 & % 25.11/4.41 | op2(e22, e20) = v80 & op2(e22, e21) = v82 & op2(e20, e24) = v68 & % 25.11/4.41 | op2(e20, e23) = v66 & op2(e20, e22) = v64 & op2(e20, e20) = v60 & % 25.11/4.41 | op2(e20, e21) = v62 & op2(e21, e24) = v78 & op2(e21, e23) = v76 & % 25.11/4.41 | op2(e21, e22) = v74 & op2(e21, e20) = v70 & op2(e21, e21) = v72 & % 25.11/4.41 | op1(v9, v9) = v109 & op1(v9, v8) = v107 & op1(v9, v7) = v105 & % 25.11/4.41 | op1(v9, v6) = v103 & op1(v9, v5) = v101 & op1(v8, v9) = v99 & % 25.11/4.41 | op1(v8, v8) = v97 & op1(v8, v7) = v95 & op1(v8, v6) = v93 & op1(v8, % 25.11/4.41 | v5) = v91 & op1(v7, v9) = v89 & op1(v7, v8) = v87 & op1(v7, v7) = % 25.11/4.41 | v85 & op1(v7, v6) = v83 & op1(v7, v5) = v81 & op1(v6, v9) = v79 & % 25.11/4.41 | op1(v6, v8) = v77 & op1(v6, v7) = v75 & op1(v6, v6) = v73 & op1(v6, % 25.11/4.41 | v5) = v71 & op1(v5, v9) = v69 & op1(v5, v8) = v67 & op1(v5, v7) = % 25.11/4.41 | v65 & op1(v5, v6) = v63 & op1(v5, v5) = v61 & op1(e14, e14) = v58 & % 25.11/4.41 | op1(e14, e13) = v56 & op1(e14, e12) = v54 & op1(e14, e10) = v50 & % 25.11/4.41 | op1(e14, e11) = v52 & op1(e13, e14) = v48 & op1(e13, e13) = v46 & % 25.11/4.41 | op1(e13, e12) = v44 & op1(e13, e10) = v40 & op1(e13, e11) = v42 & % 25.11/4.41 | op1(e12, e14) = v38 & op1(e12, e13) = v36 & op1(e12, e12) = v34 & % 25.11/4.41 | op1(e12, e10) = v30 & op1(e12, e11) = v32 & op1(e10, e14) = v18 & % 25.11/4.41 | op1(e10, e13) = v16 & op1(e10, e12) = v14 & op1(e10, e10) = v10 & % 25.11/4.41 | op1(e10, e11) = v12 & op1(e11, e14) = v28 & op1(e11, e13) = v26 & % 25.11/4.41 | op1(e11, e12) = v24 & op1(e11, e10) = v20 & op1(e11, e11) = v22 & % 25.11/4.41 | $i(v109) & $i(v108) & $i(v107) & $i(v106) & $i(v105) & $i(v104) & % 25.11/4.41 | $i(v103) & $i(v102) & $i(v101) & $i(v100) & $i(v99) & $i(v98) & % 25.11/4.41 | $i(v97) & $i(v96) & $i(v95) & $i(v94) & $i(v93) & $i(v92) & $i(v91) % 25.11/4.42 | & $i(v90) & $i(v89) & $i(v88) & $i(v87) & $i(v86) & $i(v85) & % 25.11/4.42 | $i(v84) & $i(v83) & $i(v82) & $i(v81) & $i(v80) & $i(v79) & $i(v78) % 25.11/4.42 | & $i(v77) & $i(v76) & $i(v75) & $i(v74) & $i(v73) & $i(v72) & % 25.11/4.42 | $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) % 25.11/4.42 | & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & % 25.11/4.42 | $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) % 25.11/4.42 | & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & % 25.11/4.42 | $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) % 25.11/4.42 | & $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & % 25.11/4.42 | $i(v32) & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) % 25.11/4.42 | & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 25.11/4.42 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 25.11/4.42 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 25.11/4.42 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v9 = e14 | v9 % 25.11/4.42 | = e13 | v9 = e12 | v9 = e10 | v9 = e11) & (v8 = e14 | v8 = e13 | % 25.11/4.42 | v8 = e12 | v8 = e10 | v8 = e11) & (v7 = e14 | v7 = e13 | v7 = e12 % 25.11/4.42 | | v7 = e10 | v7 = e11) & (v6 = e14 | v6 = e13 | v6 = e12 | v6 = % 25.11/4.42 | e10 | v6 = e11) & (v5 = e14 | v5 = e13 | v5 = e12 | v5 = e10 | v5 % 25.11/4.42 | = e11) & (v4 = e24 | v4 = e23 | v4 = e22 | v4 = e20 | v4 = e21) & % 25.11/4.42 | (v3 = e24 | v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 = e24 | % 25.11/4.42 | v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e24 | v1 = e23 % 25.11/4.42 | | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e24 | v0 = e23 | v0 = % 25.11/4.42 | e22 | v0 = e20 | v0 = e21)) % 25.11/4.42 | % 25.11/4.42 | ALPHA: (function-axioms) implies: % 25.11/4.42 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) | % 25.11/4.42 | ~ (j(v2) = v0)) % 25.11/4.42 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | % 25.11/4.42 | ~ (h(v2) = v0)) % 25.11/4.42 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.11/4.42 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 25.11/4.42 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.11/4.42 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 25.11/4.42 | % 25.11/4.42 | DELTA: instantiating (33) with fresh symbols all_4_0, all_4_1, all_4_2, % 25.11/4.42 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 25.11/4.42 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 25.11/4.42 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 25.11/4.42 | all_4_24, all_4_25, all_4_26, all_4_27, all_4_28, all_4_29, all_4_30, % 25.11/4.42 | all_4_31, all_4_32, all_4_33, all_4_34, all_4_35, all_4_36, all_4_37, % 25.11/4.42 | all_4_38, all_4_39, all_4_40, all_4_41, all_4_42, all_4_43, all_4_44, % 25.11/4.43 | all_4_45, all_4_46, all_4_47, all_4_48, all_4_49, all_4_50, all_4_51, % 25.11/4.43 | all_4_52, all_4_53, all_4_54, all_4_55, all_4_56, all_4_57, all_4_58, % 25.11/4.43 | all_4_59, all_4_60, all_4_61, all_4_62, all_4_63, all_4_64, all_4_65, % 25.11/4.43 | all_4_66, all_4_67, all_4_68, all_4_69, all_4_70, all_4_71, all_4_72, % 25.11/4.43 | all_4_73, all_4_74, all_4_75, all_4_76, all_4_77, all_4_78, all_4_79, % 25.11/4.43 | all_4_80, all_4_81, all_4_82, all_4_83, all_4_84, all_4_85, all_4_86, % 25.11/4.43 | all_4_87, all_4_88, all_4_89, all_4_90, all_4_91, all_4_92, all_4_93, % 25.11/4.43 | all_4_94, all_4_95, all_4_96, all_4_97, all_4_98, all_4_99, all_4_100, % 25.11/4.43 | all_4_101, all_4_102, all_4_103, all_4_104, all_4_105, all_4_106, % 25.11/4.43 | all_4_107, all_4_108, all_4_109 gives: % 25.11/4.44 | (38) h(all_4_51) = all_4_50 & h(all_4_53) = all_4_52 & h(all_4_55) = % 25.11/4.44 | all_4_54 & h(all_4_57) = all_4_56 & h(all_4_59) = all_4_58 & % 25.11/4.44 | h(all_4_61) = all_4_60 & h(all_4_63) = all_4_62 & h(all_4_65) = % 25.11/4.44 | all_4_64 & h(all_4_67) = all_4_66 & h(all_4_69) = all_4_68 & % 25.11/4.44 | h(all_4_71) = all_4_70 & h(all_4_73) = all_4_72 & h(all_4_75) = % 25.11/4.44 | all_4_74 & h(all_4_77) = all_4_76 & h(all_4_79) = all_4_78 & % 25.11/4.44 | h(all_4_81) = all_4_80 & h(all_4_83) = all_4_82 & h(all_4_85) = % 25.11/4.44 | all_4_84 & h(all_4_87) = all_4_86 & h(all_4_89) = all_4_88 & % 25.11/4.44 | h(all_4_91) = all_4_90 & h(all_4_93) = all_4_92 & h(all_4_95) = % 25.11/4.45 | all_4_94 & h(all_4_97) = all_4_96 & h(all_4_99) = all_4_98 & % 25.11/4.45 | h(all_4_100) = e24 & h(all_4_101) = e23 & h(all_4_102) = e22 & % 25.11/4.45 | h(all_4_103) = e21 & h(all_4_104) = e20 & h(e14) = all_4_105 & h(e13) % 25.11/4.45 | = all_4_106 & h(e12) = all_4_107 & h(e10) = all_4_109 & h(e11) = % 25.11/4.45 | all_4_108 & j(all_4_1) = all_4_0 & j(all_4_3) = all_4_2 & j(all_4_5) = % 25.11/4.45 | all_4_4 & j(all_4_7) = all_4_6 & j(all_4_9) = all_4_8 & j(all_4_11) = % 25.11/4.45 | all_4_10 & j(all_4_13) = all_4_12 & j(all_4_15) = all_4_14 & % 25.11/4.45 | j(all_4_17) = all_4_16 & j(all_4_19) = all_4_18 & j(all_4_21) = % 25.11/4.45 | all_4_20 & j(all_4_23) = all_4_22 & j(all_4_25) = all_4_24 & % 25.11/4.45 | j(all_4_27) = all_4_26 & j(all_4_29) = all_4_28 & j(all_4_31) = % 25.11/4.45 | all_4_30 & j(all_4_33) = all_4_32 & j(all_4_35) = all_4_34 & % 25.11/4.45 | j(all_4_37) = all_4_36 & j(all_4_39) = all_4_38 & j(all_4_41) = % 25.11/4.45 | all_4_40 & j(all_4_43) = all_4_42 & j(all_4_45) = all_4_44 & % 25.11/4.45 | j(all_4_47) = all_4_46 & j(all_4_49) = all_4_48 & j(all_4_105) = e14 & % 25.11/4.45 | j(all_4_106) = e13 & j(all_4_107) = e12 & j(all_4_108) = e11 & % 25.11/4.45 | j(all_4_109) = e10 & j(e24) = all_4_100 & j(e23) = all_4_101 & j(e22) % 25.11/4.45 | = all_4_102 & j(e20) = all_4_104 & j(e21) = all_4_103 & op2(all_4_105, % 25.11/4.45 | all_4_105) = all_4_50 & op2(all_4_105, all_4_106) = all_4_52 & % 25.11/4.45 | op2(all_4_105, all_4_107) = all_4_54 & op2(all_4_105, all_4_108) = % 25.11/4.45 | all_4_56 & op2(all_4_105, all_4_109) = all_4_58 & op2(all_4_106, % 25.11/4.45 | all_4_105) = all_4_60 & op2(all_4_106, all_4_106) = all_4_62 & % 25.11/4.45 | op2(all_4_106, all_4_107) = all_4_64 & op2(all_4_106, all_4_108) = % 25.11/4.45 | all_4_66 & op2(all_4_106, all_4_109) = all_4_68 & op2(all_4_107, % 25.11/4.45 | all_4_105) = all_4_70 & op2(all_4_107, all_4_106) = all_4_72 & % 25.11/4.45 | op2(all_4_107, all_4_107) = all_4_74 & op2(all_4_107, all_4_108) = % 25.11/4.45 | all_4_76 & op2(all_4_107, all_4_109) = all_4_78 & op2(all_4_108, % 25.11/4.45 | all_4_105) = all_4_80 & op2(all_4_108, all_4_106) = all_4_82 & % 25.11/4.45 | op2(all_4_108, all_4_107) = all_4_84 & op2(all_4_108, all_4_108) = % 25.11/4.45 | all_4_86 & op2(all_4_108, all_4_109) = all_4_88 & op2(all_4_109, % 25.11/4.45 | all_4_105) = all_4_90 & op2(all_4_109, all_4_106) = all_4_92 & % 25.11/4.45 | op2(all_4_109, all_4_107) = all_4_94 & op2(all_4_109, all_4_108) = % 25.11/4.45 | all_4_96 & op2(all_4_109, all_4_109) = all_4_98 & op2(e24, e24) = % 25.11/4.45 | all_4_1 & op2(e24, e23) = all_4_3 & op2(e24, e22) = all_4_5 & op2(e24, % 25.11/4.45 | e20) = all_4_9 & op2(e24, e21) = all_4_7 & op2(e23, e24) = all_4_11 % 25.11/4.45 | & op2(e23, e23) = all_4_13 & op2(e23, e22) = all_4_15 & op2(e23, e20) % 25.11/4.45 | = all_4_19 & op2(e23, e21) = all_4_17 & op2(e22, e24) = all_4_21 & % 25.11/4.45 | op2(e22, e23) = all_4_23 & op2(e22, e22) = all_4_25 & op2(e22, e20) = % 25.11/4.45 | all_4_29 & op2(e22, e21) = all_4_27 & op2(e20, e24) = all_4_41 & % 25.11/4.45 | op2(e20, e23) = all_4_43 & op2(e20, e22) = all_4_45 & op2(e20, e20) = % 25.11/4.45 | all_4_49 & op2(e20, e21) = all_4_47 & op2(e21, e24) = all_4_31 & % 25.11/4.45 | op2(e21, e23) = all_4_33 & op2(e21, e22) = all_4_35 & op2(e21, e20) = % 25.11/4.45 | all_4_39 & op2(e21, e21) = all_4_37 & op1(all_4_100, all_4_100) = % 25.11/4.45 | all_4_0 & op1(all_4_100, all_4_101) = all_4_2 & op1(all_4_100, % 25.11/4.45 | all_4_102) = all_4_4 & op1(all_4_100, all_4_103) = all_4_6 & % 25.11/4.45 | op1(all_4_100, all_4_104) = all_4_8 & op1(all_4_101, all_4_100) = % 25.11/4.45 | all_4_10 & op1(all_4_101, all_4_101) = all_4_12 & op1(all_4_101, % 25.11/4.45 | all_4_102) = all_4_14 & op1(all_4_101, all_4_103) = all_4_16 & % 25.11/4.45 | op1(all_4_101, all_4_104) = all_4_18 & op1(all_4_102, all_4_100) = % 25.11/4.45 | all_4_20 & op1(all_4_102, all_4_101) = all_4_22 & op1(all_4_102, % 25.11/4.45 | all_4_102) = all_4_24 & op1(all_4_102, all_4_103) = all_4_26 & % 25.11/4.45 | op1(all_4_102, all_4_104) = all_4_28 & op1(all_4_103, all_4_100) = % 25.11/4.45 | all_4_30 & op1(all_4_103, all_4_101) = all_4_32 & op1(all_4_103, % 25.11/4.45 | all_4_102) = all_4_34 & op1(all_4_103, all_4_103) = all_4_36 & % 25.11/4.45 | op1(all_4_103, all_4_104) = all_4_38 & op1(all_4_104, all_4_100) = % 25.11/4.45 | all_4_40 & op1(all_4_104, all_4_101) = all_4_42 & op1(all_4_104, % 25.11/4.45 | all_4_102) = all_4_44 & op1(all_4_104, all_4_103) = all_4_46 & % 25.11/4.45 | op1(all_4_104, all_4_104) = all_4_48 & op1(e14, e14) = all_4_51 & % 25.11/4.45 | op1(e14, e13) = all_4_53 & op1(e14, e12) = all_4_55 & op1(e14, e10) = % 25.11/4.45 | all_4_59 & op1(e14, e11) = all_4_57 & op1(e13, e14) = all_4_61 & % 25.11/4.45 | op1(e13, e13) = all_4_63 & op1(e13, e12) = all_4_65 & op1(e13, e10) = % 25.11/4.45 | all_4_69 & op1(e13, e11) = all_4_67 & op1(e12, e14) = all_4_71 & % 25.11/4.45 | op1(e12, e13) = all_4_73 & op1(e12, e12) = all_4_75 & op1(e12, e10) = % 25.11/4.45 | all_4_79 & op1(e12, e11) = all_4_77 & op1(e10, e14) = all_4_91 & % 25.11/4.45 | op1(e10, e13) = all_4_93 & op1(e10, e12) = all_4_95 & op1(e10, e10) = % 25.11/4.45 | all_4_99 & op1(e10, e11) = all_4_97 & op1(e11, e14) = all_4_81 & % 25.11/4.45 | op1(e11, e13) = all_4_83 & op1(e11, e12) = all_4_85 & op1(e11, e10) = % 25.11/4.45 | all_4_89 & op1(e11, e11) = all_4_87 & $i(all_4_0) & $i(all_4_1) & % 25.11/4.45 | $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & % 25.11/4.45 | $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & $i(all_4_11) % 25.11/4.45 | & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & % 25.11/4.45 | $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & % 25.11/4.45 | $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & % 25.11/4.45 | $i(all_4_24) & $i(all_4_25) & $i(all_4_26) & $i(all_4_27) & % 25.11/4.45 | $i(all_4_28) & $i(all_4_29) & $i(all_4_30) & $i(all_4_31) & % 25.11/4.45 | $i(all_4_32) & $i(all_4_33) & $i(all_4_34) & $i(all_4_35) & % 25.11/4.45 | $i(all_4_36) & $i(all_4_37) & $i(all_4_38) & $i(all_4_39) & % 25.11/4.45 | $i(all_4_40) & $i(all_4_41) & $i(all_4_42) & $i(all_4_43) & % 25.11/4.45 | $i(all_4_44) & $i(all_4_45) & $i(all_4_46) & $i(all_4_47) & % 25.11/4.45 | $i(all_4_48) & $i(all_4_49) & $i(all_4_50) & $i(all_4_51) & % 25.11/4.45 | $i(all_4_52) & $i(all_4_53) & $i(all_4_54) & $i(all_4_55) & % 25.11/4.45 | $i(all_4_56) & $i(all_4_57) & $i(all_4_58) & $i(all_4_59) & % 25.11/4.45 | $i(all_4_60) & $i(all_4_61) & $i(all_4_62) & $i(all_4_63) & % 25.11/4.45 | $i(all_4_64) & $i(all_4_65) & $i(all_4_66) & $i(all_4_67) & % 25.11/4.45 | $i(all_4_68) & $i(all_4_69) & $i(all_4_70) & $i(all_4_71) & % 25.11/4.45 | $i(all_4_72) & $i(all_4_73) & $i(all_4_74) & $i(all_4_75) & % 25.11/4.45 | $i(all_4_76) & $i(all_4_77) & $i(all_4_78) & $i(all_4_79) & % 25.11/4.45 | $i(all_4_80) & $i(all_4_81) & $i(all_4_82) & $i(all_4_83) & % 25.11/4.45 | $i(all_4_84) & $i(all_4_85) & $i(all_4_86) & $i(all_4_87) & % 25.11/4.45 | $i(all_4_88) & $i(all_4_89) & $i(all_4_90) & $i(all_4_91) & % 25.11/4.45 | $i(all_4_92) & $i(all_4_93) & $i(all_4_94) & $i(all_4_95) & % 25.11/4.45 | $i(all_4_96) & $i(all_4_97) & $i(all_4_98) & $i(all_4_99) & % 25.11/4.45 | $i(all_4_100) & $i(all_4_101) & $i(all_4_102) & $i(all_4_103) & % 25.11/4.45 | $i(all_4_104) & $i(all_4_105) & $i(all_4_106) & $i(all_4_107) & % 25.11/4.45 | $i(all_4_108) & $i(all_4_109) & (all_4_100 = e14 | all_4_100 = e13 | % 25.11/4.45 | all_4_100 = e12 | all_4_100 = e10 | all_4_100 = e11) & (all_4_101 = % 25.11/4.45 | e14 | all_4_101 = e13 | all_4_101 = e12 | all_4_101 = e10 | % 25.11/4.46 | all_4_101 = e11) & (all_4_102 = e14 | all_4_102 = e13 | all_4_102 = % 25.11/4.46 | e12 | all_4_102 = e10 | all_4_102 = e11) & (all_4_103 = e14 | % 25.11/4.46 | all_4_103 = e13 | all_4_103 = e12 | all_4_103 = e10 | all_4_103 = % 25.11/4.46 | e11) & (all_4_104 = e14 | all_4_104 = e13 | all_4_104 = e12 | % 25.11/4.46 | all_4_104 = e10 | all_4_104 = e11) & (all_4_105 = e24 | all_4_105 = % 25.11/4.46 | e23 | all_4_105 = e22 | all_4_105 = e20 | all_4_105 = e21) & % 25.11/4.46 | (all_4_106 = e24 | all_4_106 = e23 | all_4_106 = e22 | all_4_106 = e20 % 25.11/4.46 | | all_4_106 = e21) & (all_4_107 = e24 | all_4_107 = e23 | all_4_107 % 25.11/4.46 | = e22 | all_4_107 = e20 | all_4_107 = e21) & (all_4_108 = e24 | % 25.11/4.46 | all_4_108 = e23 | all_4_108 = e22 | all_4_108 = e20 | all_4_108 = % 25.11/4.46 | e21) & (all_4_109 = e24 | all_4_109 = e23 | all_4_109 = e22 | % 25.11/4.46 | all_4_109 = e20 | all_4_109 = e21) % 25.11/4.46 | % 25.11/4.46 | ALPHA: (38) implies: % 25.11/4.46 | (39) op1(e11, e14) = all_4_81 % 25.11/4.46 | (40) op1(e10, e10) = all_4_99 % 25.11/4.46 | (41) op1(e12, e11) = all_4_77 % 25.11/4.46 | (42) op1(e13, e12) = all_4_65 % 25.11/4.46 | (43) op1(e14, e13) = all_4_53 % 25.11/4.46 | (44) op1(e14, e14) = all_4_51 % 25.11/4.46 | (45) op1(all_4_104, all_4_104) = all_4_48 % 25.11/4.46 | (46) op1(all_4_103, all_4_103) = all_4_36 % 25.11/4.46 | (47) op1(all_4_102, all_4_102) = all_4_24 % 25.11/4.46 | (48) op1(all_4_101, all_4_101) = all_4_12 % 25.11/4.46 | (49) op2(e21, e21) = all_4_37 % 25.11/4.46 | (50) op2(e21, e20) = all_4_39 % 25.11/4.46 | (51) op2(e21, e22) = all_4_35 % 25.11/4.46 | (52) op2(e21, e23) = all_4_33 % 25.11/4.46 | (53) op2(e21, e24) = all_4_31 % 25.11/4.46 | (54) op2(e20, e21) = all_4_47 % 25.11/4.46 | (55) op2(e20, e20) = all_4_49 % 25.11/4.46 | (56) op2(e20, e22) = all_4_45 % 25.11/4.47 | (57) op2(e20, e23) = all_4_43 % 25.11/4.47 | (58) op2(e20, e24) = all_4_41 % 25.11/4.47 | (59) op2(e22, e21) = all_4_27 % 25.11/4.47 | (60) op2(e22, e20) = all_4_29 % 25.11/4.47 | (61) op2(e22, e22) = all_4_25 % 25.11/4.47 | (62) op2(e22, e23) = all_4_23 % 25.11/4.47 | (63) op2(e22, e24) = all_4_21 % 25.11/4.47 | (64) op2(e23, e21) = all_4_17 % 25.11/4.47 | (65) op2(e23, e20) = all_4_19 % 25.11/4.47 | (66) op2(e23, e22) = all_4_15 % 25.11/4.47 | (67) op2(e23, e23) = all_4_13 % 25.11/4.47 | (68) op2(e23, e24) = all_4_11 % 25.11/4.47 | (69) op2(e24, e21) = all_4_7 % 25.11/4.47 | (70) op2(e24, e20) = all_4_9 % 25.11/4.47 | (71) op2(e24, e22) = all_4_5 % 25.11/4.47 | (72) op2(e24, e23) = all_4_3 % 25.11/4.47 | (73) op2(e24, e24) = all_4_1 % 25.11/4.47 | (74) op2(all_4_109, all_4_109) = all_4_98 % 25.11/4.47 | (75) j(e21) = all_4_103 % 25.11/4.47 | (76) j(e20) = all_4_104 % 25.11/4.47 | (77) j(e22) = all_4_102 % 25.11/4.47 | (78) j(e23) = all_4_101 % 25.11/4.47 | (79) j(e24) = all_4_100 % 25.11/4.47 | (80) j(all_4_109) = e10 % 25.11/4.47 | (81) j(all_4_105) = e14 % 25.11/4.47 | (82) j(all_4_49) = all_4_48 % 25.11/4.47 | (83) j(all_4_47) = all_4_46 % 25.11/4.47 | (84) j(all_4_45) = all_4_44 % 25.11/4.47 | (85) j(all_4_43) = all_4_42 % 25.11/4.47 | (86) j(all_4_41) = all_4_40 % 25.11/4.47 | (87) j(all_4_39) = all_4_38 % 25.11/4.47 | (88) j(all_4_37) = all_4_36 % 25.11/4.47 | (89) j(all_4_35) = all_4_34 % 25.11/4.47 | (90) j(all_4_33) = all_4_32 % 25.11/4.47 | (91) j(all_4_31) = all_4_30 % 25.11/4.47 | (92) j(all_4_29) = all_4_28 % 25.11/4.47 | (93) j(all_4_27) = all_4_26 % 25.11/4.47 | (94) j(all_4_25) = all_4_24 % 25.11/4.48 | (95) j(all_4_23) = all_4_22 % 25.11/4.48 | (96) j(all_4_21) = all_4_20 % 25.11/4.48 | (97) j(all_4_19) = all_4_18 % 25.11/4.48 | (98) j(all_4_17) = all_4_16 % 25.11/4.48 | (99) j(all_4_15) = all_4_14 % 25.11/4.48 | (100) j(all_4_13) = all_4_12 % 25.11/4.48 | (101) j(all_4_11) = all_4_10 % 25.11/4.48 | (102) j(all_4_9) = all_4_8 % 25.11/4.48 | (103) j(all_4_7) = all_4_6 % 25.11/4.48 | (104) j(all_4_5) = all_4_4 % 25.11/4.48 | (105) j(all_4_3) = all_4_2 % 25.11/4.48 | (106) j(all_4_1) = all_4_0 % 25.11/4.48 | (107) h(e14) = all_4_105 % 25.11/4.48 | (108) h(all_4_99) = all_4_98 % 25.11/4.48 | (109) h(all_4_81) = all_4_80 % 25.11/4.48 | (110) h(all_4_77) = all_4_76 % 25.11/4.48 | (111) h(all_4_65) = all_4_64 % 25.11/4.48 | (112) h(all_4_53) = all_4_52 % 25.11/4.48 | (113) all_4_109 = e24 | all_4_109 = e23 | all_4_109 = e22 | all_4_109 = e20 % 25.11/4.48 | | all_4_109 = e21 % 25.11/4.48 | (114) all_4_104 = e14 | all_4_104 = e13 | all_4_104 = e12 | all_4_104 = e10 % 25.11/4.48 | | all_4_104 = e11 % 25.11/4.48 | (115) all_4_103 = e14 | all_4_103 = e13 | all_4_103 = e12 | all_4_103 = e10 % 25.11/4.48 | | all_4_103 = e11 % 25.11/4.48 | (116) all_4_102 = e14 | all_4_102 = e13 | all_4_102 = e12 | all_4_102 = e10 % 25.11/4.48 | | all_4_102 = e11 % 25.11/4.48 | (117) all_4_101 = e14 | all_4_101 = e13 | all_4_101 = e12 | all_4_101 = e10 % 25.11/4.48 | | all_4_101 = e11 % 25.11/4.48 | % 25.11/4.48 | GROUND_INST: instantiating (36) with e14, all_4_81, e14, e11, simplifying with % 25.11/4.48 | (2), (39) gives: % 25.11/4.48 | (118) all_4_81 = e14 % 25.11/4.48 | % 25.11/4.48 | GROUND_INST: instantiating (36) with e14, all_4_99, e10, e10, simplifying with % 25.11/4.48 | (3), (40) gives: % 25.11/4.48 | (119) all_4_99 = e14 % 25.11/4.48 | % 25.11/4.48 | GROUND_INST: instantiating (36) with e14, all_4_77, e11, e12, simplifying with % 25.11/4.48 | (4), (41) gives: % 25.11/4.49 | (120) all_4_77 = e14 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (36) with e14, all_4_65, e12, e13, simplifying with % 25.11/4.49 | (5), (42) gives: % 25.11/4.49 | (121) all_4_65 = e14 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (36) with e14, all_4_53, e13, e14, simplifying with % 25.11/4.49 | (6), (43) gives: % 25.11/4.49 | (122) all_4_53 = e14 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (36) with e10, all_4_51, e14, e14, simplifying with % 25.11/4.49 | (7), (44) gives: % 25.11/4.49 | (123) all_4_51 = e10 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e21, all_4_37, e21, e21, simplifying with % 25.11/4.49 | (8), (49) gives: % 25.11/4.49 | (124) all_4_37 = e21 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e22, all_4_39, e20, e21, simplifying with % 25.11/4.49 | (9), (50) gives: % 25.11/4.49 | (125) all_4_39 = e22 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e23, all_4_35, e22, e21, simplifying with % 25.11/4.49 | (10), (51) gives: % 25.11/4.49 | (126) all_4_35 = e23 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e24, all_4_33, e23, e21, simplifying with % 25.11/4.49 | (11), (52) gives: % 25.11/4.49 | (127) all_4_33 = e24 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e20, all_4_31, e24, e21, simplifying with % 25.11/4.49 | (12), (53) gives: % 25.11/4.49 | (128) all_4_31 = e20 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e23, all_4_47, e21, e20, simplifying with % 25.11/4.49 | (13), (54) gives: % 25.11/4.49 | (129) all_4_47 = e23 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e20, all_4_49, e20, e20, simplifying with % 25.11/4.49 | (14), (55) gives: % 25.11/4.49 | (130) all_4_49 = e20 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e24, all_4_45, e22, e20, simplifying with % 25.11/4.49 | (15), (56) gives: % 25.11/4.49 | (131) all_4_45 = e24 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e22, all_4_43, e23, e20, simplifying with % 25.11/4.49 | (16), (57) gives: % 25.11/4.49 | (132) all_4_43 = e22 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e21, all_4_41, e24, e20, simplifying with % 25.11/4.49 | (17), (58) gives: % 25.11/4.49 | (133) all_4_41 = e21 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e24, all_4_27, e21, e22, simplifying with % 25.11/4.49 | (18), (59) gives: % 25.11/4.49 | (134) all_4_27 = e24 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e21, all_4_29, e20, e22, simplifying with % 25.11/4.49 | (19), (60) gives: % 25.11/4.49 | (135) all_4_29 = e21 % 25.11/4.49 | % 25.11/4.49 | GROUND_INST: instantiating (37) with e22, all_4_25, e22, e22, simplifying with % 25.11/4.49 | (20), (61) gives: % 25.11/4.50 | (136) all_4_25 = e22 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e20, all_4_23, e23, e22, simplifying with % 25.11/4.50 | (21), (62) gives: % 25.11/4.50 | (137) all_4_23 = e20 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e23, all_4_21, e24, e22, simplifying with % 25.11/4.50 | (22), (63) gives: % 25.11/4.50 | (138) all_4_21 = e23 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e20, all_4_17, e21, e23, simplifying with % 25.11/4.50 | (23), (64) gives: % 25.11/4.50 | (139) all_4_17 = e20 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e24, all_4_19, e20, e23, simplifying with % 25.11/4.50 | (24), (65) gives: % 25.11/4.50 | (140) all_4_19 = e24 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e21, all_4_15, e22, e23, simplifying with % 25.11/4.50 | (25), (66) gives: % 25.11/4.50 | (141) all_4_15 = e21 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e23, all_4_13, e23, e23, simplifying with % 25.11/4.50 | (26), (67) gives: % 25.11/4.50 | (142) all_4_13 = e23 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e22, all_4_11, e24, e23, simplifying with % 25.11/4.50 | (27), (68) gives: % 25.11/4.50 | (143) all_4_11 = e22 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e22, all_4_7, e21, e24, simplifying with % 25.11/4.50 | (28), (69) gives: % 25.11/4.50 | (144) all_4_7 = e22 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e23, all_4_9, e20, e24, simplifying with % 25.11/4.50 | (29), (70) gives: % 25.11/4.50 | (145) all_4_9 = e23 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e20, all_4_5, e22, e24, simplifying with % 25.11/4.50 | (30), (71) gives: % 25.11/4.50 | (146) all_4_5 = e20 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e21, all_4_3, e23, e24, simplifying with % 25.11/4.50 | (31), (72) gives: % 25.11/4.50 | (147) all_4_3 = e21 % 25.11/4.50 | % 25.11/4.50 | GROUND_INST: instantiating (37) with e24, all_4_1, e24, e24, simplifying with % 25.11/4.50 | (32), (73) gives: % 25.11/4.50 | (148) all_4_1 = e24 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (112), (122) imply: % 25.11/4.50 | (149) h(e14) = all_4_52 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (111), (121) imply: % 25.11/4.50 | (150) h(e14) = all_4_64 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (110), (120) imply: % 25.11/4.50 | (151) h(e14) = all_4_76 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (109), (118) imply: % 25.11/4.50 | (152) h(e14) = all_4_80 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (108), (119) imply: % 25.11/4.50 | (153) h(e14) = all_4_98 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (106), (148) imply: % 25.11/4.50 | (154) j(e24) = all_4_0 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (105), (147) imply: % 25.11/4.50 | (155) j(e21) = all_4_2 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (104), (146) imply: % 25.11/4.50 | (156) j(e20) = all_4_4 % 25.11/4.50 | % 25.11/4.50 | REDUCE: (103), (144) imply: % 25.11/4.51 | (157) j(e22) = all_4_6 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (102), (145) imply: % 25.11/4.51 | (158) j(e23) = all_4_8 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (101), (143) imply: % 25.11/4.51 | (159) j(e22) = all_4_10 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (100), (142) imply: % 25.11/4.51 | (160) j(e23) = all_4_12 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (99), (141) imply: % 25.11/4.51 | (161) j(e21) = all_4_14 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (98), (139) imply: % 25.11/4.51 | (162) j(e20) = all_4_16 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (97), (140) imply: % 25.11/4.51 | (163) j(e24) = all_4_18 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (96), (138) imply: % 25.11/4.51 | (164) j(e23) = all_4_20 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (95), (137) imply: % 25.11/4.51 | (165) j(e20) = all_4_22 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (94), (136) imply: % 25.11/4.51 | (166) j(e22) = all_4_24 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (93), (134) imply: % 25.11/4.51 | (167) j(e24) = all_4_26 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (92), (135) imply: % 25.11/4.51 | (168) j(e21) = all_4_28 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (91), (128) imply: % 25.11/4.51 | (169) j(e20) = all_4_30 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (90), (127) imply: % 25.11/4.51 | (170) j(e24) = all_4_32 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (89), (126) imply: % 25.11/4.51 | (171) j(e23) = all_4_34 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (88), (124) imply: % 25.11/4.51 | (172) j(e21) = all_4_36 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (87), (125) imply: % 25.11/4.51 | (173) j(e22) = all_4_38 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (86), (133) imply: % 25.11/4.51 | (174) j(e21) = all_4_40 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (85), (132) imply: % 25.11/4.51 | (175) j(e22) = all_4_42 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (84), (131) imply: % 25.11/4.51 | (176) j(e24) = all_4_44 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (83), (129) imply: % 25.11/4.51 | (177) j(e23) = all_4_46 % 25.11/4.51 | % 25.11/4.51 | REDUCE: (82), (130) imply: % 25.11/4.51 | (178) j(e20) = all_4_48 % 25.11/4.51 | % 25.11/4.51 | GROUND_INST: instantiating (34) with all_4_103, all_4_14, e21, simplifying % 25.11/4.51 | with (75), (161) gives: % 25.11/4.51 | (179) all_4_14 = all_4_103 % 25.11/4.51 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_28, all_4_14, e21, simplifying with % 25.11/4.52 | (161), (168) gives: % 25.11/4.52 | (180) all_4_14 = all_4_28 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_36, all_4_14, e21, simplifying with % 25.11/4.52 | (161), (172) gives: % 25.11/4.52 | (181) all_4_14 = all_4_36 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_28, all_4_2, e21, simplifying with % 25.11/4.52 | (155), (168) gives: % 25.11/4.52 | (182) all_4_2 = all_4_28 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_40, all_4_2, e21, simplifying with % 25.11/4.52 | (155), (174) gives: % 25.11/4.52 | (183) all_4_2 = all_4_40 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_104, all_4_22, e20, simplifying % 25.11/4.52 | with (76), (165) gives: % 25.11/4.52 | (184) all_4_22 = all_4_104 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_30, all_4_22, e20, simplifying with % 25.11/4.52 | (165), (169) gives: % 25.11/4.52 | (185) all_4_22 = all_4_30 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_16, all_4_4, e20, simplifying with % 25.11/4.52 | (156), (162) gives: % 25.11/4.52 | (186) all_4_4 = all_4_16 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_22, all_4_4, e20, simplifying with % 25.11/4.52 | (156), (165) gives: % 25.11/4.52 | (187) all_4_4 = all_4_22 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_48, all_4_4, e20, simplifying with % 25.11/4.52 | (156), (178) gives: % 25.11/4.52 | (188) all_4_4 = all_4_48 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_102, all_4_10, e22, simplifying % 25.11/4.52 | with (77), (159) gives: % 25.11/4.52 | (189) all_4_10 = all_4_102 % 25.11/4.52 | % 25.11/4.52 | GROUND_INST: instantiating (34) with all_4_24, all_4_10, e22, simplifying with % 25.11/4.52 | (159), (166) gives: % 25.11/4.52 | (190) all_4_10 = all_4_24 % 25.11/4.52 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_38, all_4_10, e22, simplifying with % 25.11/4.53 | (159), (173) gives: % 25.11/4.53 | (191) all_4_10 = all_4_38 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_24, all_4_6, e22, simplifying with % 25.11/4.53 | (157), (166) gives: % 25.11/4.53 | (192) all_4_6 = all_4_24 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_42, all_4_6, e22, simplifying with % 25.11/4.53 | (157), (175) gives: % 25.11/4.53 | (193) all_4_6 = all_4_42 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_101, all_4_20, e23, simplifying % 25.11/4.53 | with (78), (164) gives: % 25.11/4.53 | (194) all_4_20 = all_4_101 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_34, all_4_20, e23, simplifying with % 25.11/4.53 | (164), (171) gives: % 25.11/4.53 | (195) all_4_20 = all_4_34 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_20, all_4_12, e23, simplifying with % 25.11/4.53 | (160), (164) gives: % 25.11/4.53 | (196) all_4_12 = all_4_20 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_12, all_4_8, e23, simplifying with % 25.11/4.53 | (158), (160) gives: % 25.11/4.53 | (197) all_4_8 = all_4_12 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_46, all_4_8, e23, simplifying with % 25.11/4.53 | (158), (177) gives: % 25.11/4.53 | (198) all_4_8 = all_4_46 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_100, all_4_26, e24, simplifying % 25.11/4.53 | with (79), (167) gives: % 25.11/4.53 | (199) all_4_26 = all_4_100 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_32, all_4_26, e24, simplifying with % 25.11/4.53 | (167), (170) gives: % 25.11/4.53 | (200) all_4_26 = all_4_32 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_18, all_4_0, e24, simplifying with % 25.11/4.53 | (154), (163) gives: % 25.11/4.53 | (201) all_4_0 = all_4_18 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_32, all_4_0, e24, simplifying with % 25.11/4.53 | (154), (170) gives: % 25.11/4.53 | (202) all_4_0 = all_4_32 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (34) with all_4_44, all_4_0, e24, simplifying with % 25.11/4.53 | (154), (176) gives: % 25.11/4.53 | (203) all_4_0 = all_4_44 % 25.11/4.53 | % 25.11/4.53 | GROUND_INST: instantiating (35) with all_4_105, all_4_80, e14, simplifying % 25.11/4.53 | with (107), (152) gives: % 25.11/4.53 | (204) all_4_80 = all_4_105 % 25.11/4.53 | % 25.11/4.54 | GROUND_INST: instantiating (35) with all_4_80, all_4_76, e14, simplifying with % 25.11/4.54 | (151), (152) gives: % 25.11/4.54 | (205) all_4_76 = all_4_80 % 25.11/4.54 | % 25.11/4.54 | GROUND_INST: instantiating (35) with all_4_76, all_4_64, e14, simplifying with % 25.11/4.54 | (150), (151) gives: % 25.11/4.54 | (206) all_4_64 = all_4_76 % 25.11/4.54 | % 25.11/4.54 | GROUND_INST: instantiating (35) with all_4_64, all_4_52, e14, simplifying with % 25.11/4.54 | (149), (150) gives: % 25.11/4.54 | (207) all_4_52 = all_4_64 % 25.11/4.54 | % 25.11/4.54 | GROUND_INST: instantiating (35) with all_4_98, all_4_52, e14, simplifying with % 25.11/4.54 | (149), (153) gives: % 25.11/4.54 | (208) all_4_52 = all_4_98 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (201), (203) imply: % 25.11/4.54 | (209) all_4_18 = all_4_44 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (201), (202) imply: % 25.11/4.54 | (210) all_4_18 = all_4_32 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (182), (183) imply: % 25.11/4.54 | (211) all_4_28 = all_4_40 % 25.11/4.54 | % 25.11/4.54 | SIMP: (211) implies: % 25.11/4.54 | (212) all_4_28 = all_4_40 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (186), (188) imply: % 25.11/4.54 | (213) all_4_16 = all_4_48 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (186), (187) imply: % 25.11/4.54 | (214) all_4_16 = all_4_22 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (192), (193) imply: % 25.11/4.54 | (215) all_4_24 = all_4_42 % 25.11/4.54 | % 25.11/4.54 | SIMP: (215) implies: % 25.11/4.54 | (216) all_4_24 = all_4_42 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (197), (198) imply: % 25.11/4.54 | (217) all_4_12 = all_4_46 % 25.11/4.54 | % 25.11/4.54 | SIMP: (217) implies: % 25.11/4.54 | (218) all_4_12 = all_4_46 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (190), (191) imply: % 25.11/4.54 | (219) all_4_24 = all_4_38 % 25.11/4.54 | % 25.11/4.54 | SIMP: (219) implies: % 25.11/4.54 | (220) all_4_24 = all_4_38 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (189), (191) imply: % 25.11/4.54 | (221) all_4_38 = all_4_102 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (196), (218) imply: % 25.11/4.54 | (222) all_4_20 = all_4_46 % 25.11/4.54 | % 25.11/4.54 | SIMP: (222) implies: % 25.11/4.54 | (223) all_4_20 = all_4_46 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (180), (181) imply: % 25.11/4.54 | (224) all_4_28 = all_4_36 % 25.11/4.54 | % 25.11/4.54 | SIMP: (224) implies: % 25.11/4.54 | (225) all_4_28 = all_4_36 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (179), (181) imply: % 25.11/4.54 | (226) all_4_36 = all_4_103 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (213), (214) imply: % 25.11/4.54 | (227) all_4_22 = all_4_48 % 25.11/4.54 | % 25.11/4.54 | SIMP: (227) implies: % 25.11/4.54 | (228) all_4_22 = all_4_48 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (209), (210) imply: % 25.11/4.54 | (229) all_4_32 = all_4_44 % 25.11/4.54 | % 25.11/4.54 | SIMP: (229) implies: % 25.11/4.54 | (230) all_4_32 = all_4_44 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (194), (195) imply: % 25.11/4.54 | (231) all_4_34 = all_4_101 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (195), (223) imply: % 25.11/4.54 | (232) all_4_34 = all_4_46 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (184), (185) imply: % 25.11/4.54 | (233) all_4_30 = all_4_104 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (185), (228) imply: % 25.11/4.54 | (234) all_4_30 = all_4_48 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (216), (220) imply: % 25.11/4.54 | (235) all_4_38 = all_4_42 % 25.11/4.54 | % 25.11/4.54 | SIMP: (235) implies: % 25.11/4.54 | (236) all_4_38 = all_4_42 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (199), (200) imply: % 25.11/4.54 | (237) all_4_32 = all_4_100 % 25.11/4.54 | % 25.11/4.54 | SIMP: (237) implies: % 25.11/4.54 | (238) all_4_32 = all_4_100 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (212), (225) imply: % 25.11/4.54 | (239) all_4_36 = all_4_40 % 25.11/4.54 | % 25.11/4.54 | SIMP: (239) implies: % 25.11/4.54 | (240) all_4_36 = all_4_40 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (233), (234) imply: % 25.11/4.54 | (241) all_4_48 = all_4_104 % 25.11/4.54 | % 25.11/4.54 | COMBINE_EQS: (230), (238) imply: % 25.11/4.54 | (242) all_4_44 = all_4_100 % 25.11/4.55 | % 25.11/4.55 | SIMP: (242) implies: % 25.11/4.55 | (243) all_4_44 = all_4_100 % 25.11/4.55 | % 25.11/4.55 | COMBINE_EQS: (231), (232) imply: % 25.11/4.55 | (244) all_4_46 = all_4_101 % 25.11/4.55 | % 25.11/4.55 | COMBINE_EQS: (226), (240) imply: % 25.11/4.55 | (245) all_4_40 = all_4_103 % 25.11/4.55 | % 25.11/4.55 | SIMP: (245) implies: % 25.11/4.55 | (246) all_4_40 = all_4_103 % 25.11/4.55 | % 25.11/4.55 | COMBINE_EQS: (221), (236) imply: % 25.11/4.55 | (247) all_4_42 = all_4_102 % 25.11/4.55 | % 25.11/4.55 | COMBINE_EQS: (207), (208) imply: % 25.11/4.55 | (248) all_4_64 = all_4_98 % 25.11/4.55 | % 25.11/4.55 | SIMP: (248) implies: % 25.11/4.55 | (249) all_4_64 = all_4_98 % 25.11/4.55 | % 25.11/4.55 | COMBINE_EQS: (206), (249) imply: % 25.11/4.55 | (250) all_4_76 = all_4_98 % 25.11/4.55 | % 25.11/4.55 | SIMP: (250) implies: % 25.11/4.55 | (251) all_4_76 = all_4_98 % 25.41/4.56 | % 25.41/4.56 | COMBINE_EQS: (205), (251) imply: % 25.41/4.56 | (252) all_4_80 = all_4_98 % 25.41/4.56 | % 25.41/4.56 | SIMP: (252) implies: % 25.41/4.56 | (253) all_4_80 = all_4_98 % 25.41/4.56 | % 25.41/4.56 | COMBINE_EQS: (204), (253) imply: % 25.41/4.56 | (254) all_4_98 = all_4_105 % 25.41/4.56 | % 25.41/4.56 | COMBINE_EQS: (216), (247) imply: % 25.41/4.56 | (255) all_4_24 = all_4_102 % 25.41/4.56 | % 25.41/4.56 | COMBINE_EQS: (218), (244) imply: % 25.41/4.56 | (256) all_4_12 = all_4_101 % 25.41/4.56 | % 25.41/4.56 | REDUCE: (74), (254) imply: % 25.41/4.56 | (257) op2(all_4_109, all_4_109) = all_4_105 % 25.41/4.56 | % 25.41/4.56 | REDUCE: (48), (256) imply: % 25.41/4.56 | (258) op1(all_4_101, all_4_101) = all_4_101 % 25.41/4.56 | % 25.41/4.56 | REDUCE: (47), (255) imply: % 25.41/4.56 | (259) op1(all_4_102, all_4_102) = all_4_102 % 25.41/4.56 | % 25.41/4.56 | REDUCE: (46), (226) imply: % 25.41/4.56 | (260) op1(all_4_103, all_4_103) = all_4_103 % 25.41/4.56 | % 25.41/4.56 | REDUCE: (45), (241) imply: % 25.41/4.56 | (261) op1(all_4_104, all_4_104) = all_4_104 % 25.41/4.56 | % 25.41/4.56 | BETA: splitting (113) gives: % 25.41/4.56 | % 25.41/4.56 | Case 1: % 25.41/4.56 | | % 25.41/4.56 | | (262) all_4_109 = e24 % 25.41/4.56 | | % 25.41/4.56 | | REDUCE: (80), (262) imply: % 25.41/4.56 | | (263) j(e24) = e10 % 25.41/4.56 | | % 25.41/4.56 | | REDUCE: (257), (262) imply: % 25.41/4.56 | | (264) op2(e24, e24) = all_4_105 % 25.41/4.56 | | % 25.41/4.56 | | GROUND_INST: instantiating (37) with e24, all_4_105, e24, e24, simplifying % 25.41/4.56 | | with (32), (264) gives: % 25.41/4.56 | | (265) all_4_105 = e24 % 25.41/4.56 | | % 25.41/4.56 | | GROUND_INST: instantiating (34) with all_4_100, e10, e24, simplifying with % 25.41/4.56 | | (79), (263) gives: % 25.41/4.56 | | (266) all_4_100 = e10 % 25.41/4.56 | | % 25.41/4.56 | | REDUCE: (81), (265) imply: % 25.41/4.56 | | (267) j(e24) = e14 % 25.41/4.56 | | % 25.41/4.56 | | GROUND_INST: instantiating (34) with e10, e14, e24, simplifying with (263), % 25.41/4.56 | | (267) gives: % 25.41/4.56 | | (268) e14 = e10 % 25.41/4.56 | | % 25.41/4.56 | | REDUCE: (1), (268) imply: % 25.41/4.56 | | (269) $false % 25.41/4.56 | | % 25.41/4.56 | | CLOSE: (269) is inconsistent. % 25.41/4.56 | | % 25.41/4.56 | Case 2: % 25.41/4.56 | | % 25.41/4.56 | | (270) all_4_109 = e23 | all_4_109 = e22 | all_4_109 = e20 | all_4_109 = % 25.41/4.56 | | e21 % 25.41/4.56 | | % 25.41/4.56 | | BETA: splitting (116) gives: % 25.41/4.56 | | % 25.41/4.56 | | Case 1: % 25.41/4.56 | | | % 25.41/4.56 | | | (271) all_4_102 = e14 % 25.41/4.56 | | | % 25.41/4.56 | | | REDUCE: (259), (271) imply: % 25.41/4.56 | | | (272) op1(e14, e14) = e14 % 25.41/4.56 | | | % 25.41/4.56 | | | REF_CLOSE: (1), (7), (36), (272) are inconsistent by sub-proof #1. % 25.41/4.56 | | | % 25.41/4.56 | | Case 2: % 25.41/4.56 | | | % 25.41/4.56 | | | (273) ~ (all_4_102 = e14) % 25.41/4.56 | | | % 25.41/4.56 | | | BETA: splitting (117) gives: % 25.41/4.56 | | | % 25.41/4.56 | | | Case 1: % 25.41/4.56 | | | | % 25.41/4.56 | | | | (274) all_4_101 = e14 % 25.41/4.57 | | | | % 25.41/4.57 | | | | REDUCE: (258), (274) imply: % 25.41/4.57 | | | | (275) op1(e14, e14) = e14 % 25.41/4.57 | | | | % 25.41/4.57 | | | | REF_CLOSE: (1), (7), (36), (275) are inconsistent by sub-proof #1. % 25.41/4.57 | | | | % 25.41/4.57 | | | Case 2: % 25.41/4.57 | | | | % 25.41/4.57 | | | | (276) ~ (all_4_101 = e14) % 25.41/4.57 | | | | % 25.41/4.57 | | | | BETA: splitting (114) gives: % 25.41/4.57 | | | | % 25.41/4.57 | | | | Case 1: % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | (277) all_4_104 = e14 % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | REDUCE: (261), (277) imply: % 25.41/4.57 | | | | | (278) op1(e14, e14) = e14 % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | GROUND_INST: instantiating (36) with e10, e14, e14, e14, simplifying % 25.41/4.57 | | | | | with (7), (278) gives: % 25.41/4.57 | | | | | (279) e14 = e10 % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | REDUCE: (1), (279) imply: % 25.41/4.57 | | | | | (280) $false % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | CLOSE: (280) is inconsistent. % 25.41/4.57 | | | | | % 25.41/4.57 | | | | Case 2: % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | (281) ~ (all_4_104 = e14) % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | BETA: splitting (115) gives: % 25.41/4.57 | | | | | % 25.41/4.57 | | | | | Case 1: % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | (282) all_4_103 = e14 % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | REDUCE: (260), (282) imply: % 25.41/4.57 | | | | | | (283) op1(e14, e14) = e14 % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | REF_CLOSE: (1), (7), (36), (283) are inconsistent by sub-proof #1. % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | Case 2: % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | (284) ~ (all_4_103 = e14) % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | BETA: splitting (270) gives: % 25.41/4.57 | | | | | | % 25.41/4.57 | | | | | | Case 1: % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | (285) all_4_109 = e23 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | REDUCE: (80), (285) imply: % 25.41/4.57 | | | | | | | (286) j(e23) = e10 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | REDUCE: (257), (285) imply: % 25.41/4.57 | | | | | | | (287) op2(e23, e23) = all_4_105 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | GROUND_INST: instantiating (37) with e23, all_4_105, e23, e23, % 25.41/4.57 | | | | | | | simplifying with (26), (287) gives: % 25.41/4.57 | | | | | | | (288) all_4_105 = e23 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | GROUND_INST: instantiating (34) with all_4_101, e10, e23, % 25.41/4.57 | | | | | | | simplifying with (78), (286) gives: % 25.41/4.57 | | | | | | | (289) all_4_101 = e10 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | REDUCE: (276), (289) imply: % 25.41/4.57 | | | | | | | (290) ~ (e14 = e10) % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | REDUCE: (81), (288) imply: % 25.41/4.57 | | | | | | | (291) j(e23) = e14 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | GROUND_INST: instantiating (34) with e10, e14, e23, simplifying % 25.41/4.57 | | | | | | | with (286), (291) gives: % 25.41/4.57 | | | | | | | (292) e14 = e10 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | REDUCE: (1), (292) imply: % 25.41/4.57 | | | | | | | (293) $false % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | CLOSE: (293) is inconsistent. % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | Case 2: % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | (294) all_4_109 = e22 | all_4_109 = e20 | all_4_109 = e21 % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | BETA: splitting (294) gives: % 25.41/4.57 | | | | | | | % 25.41/4.57 | | | | | | | Case 1: % 25.41/4.57 | | | | | | | | % 25.41/4.57 | | | | | | | | (295) all_4_109 = e22 % 25.41/4.57 | | | | | | | | % 25.41/4.57 | | | | | | | | REDUCE: (80), (295) imply: % 25.41/4.57 | | | | | | | | (296) j(e22) = e10 % 25.41/4.57 | | | | | | | | % 25.41/4.57 | | | | | | | | REDUCE: (257), (295) imply: % 25.41/4.57 | | | | | | | | (297) op2(e22, e22) = all_4_105 % 25.41/4.57 | | | | | | | | % 25.41/4.57 | | | | | | | | GROUND_INST: instantiating (37) with e22, all_4_105, e22, e22, % 25.41/4.57 | | | | | | | | simplifying with (20), (297) gives: % 25.41/4.58 | | | | | | | | (298) all_4_105 = e22 % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | GROUND_INST: instantiating (34) with all_4_102, e10, e22, % 25.41/4.58 | | | | | | | | simplifying with (77), (296) gives: % 25.41/4.58 | | | | | | | | (299) all_4_102 = e10 % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | REDUCE: (273), (299) imply: % 25.41/4.58 | | | | | | | | (300) ~ (e14 = e10) % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | REDUCE: (81), (298) imply: % 25.41/4.58 | | | | | | | | (301) j(e22) = e14 % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | GROUND_INST: instantiating (34) with e10, e14, e22, simplifying % 25.41/4.58 | | | | | | | | with (296), (301) gives: % 25.41/4.58 | | | | | | | | (302) e14 = e10 % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | REDUCE: (1), (302) imply: % 25.41/4.58 | | | | | | | | (303) $false % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | CLOSE: (303) is inconsistent. % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | Case 2: % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | (304) all_4_109 = e20 | all_4_109 = e21 % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | BETA: splitting (304) gives: % 25.41/4.58 | | | | | | | | % 25.41/4.58 | | | | | | | | Case 1: % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | (305) all_4_109 = e20 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | REDUCE: (80), (305) imply: % 25.41/4.58 | | | | | | | | | (306) j(e20) = e10 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | REDUCE: (257), (305) imply: % 25.41/4.58 | | | | | | | | | (307) op2(e20, e20) = all_4_105 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | GROUND_INST: instantiating (37) with e20, all_4_105, e20, e20, % 25.41/4.58 | | | | | | | | | simplifying with (14), (307) gives: % 25.41/4.58 | | | | | | | | | (308) all_4_105 = e20 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | GROUND_INST: instantiating (34) with all_4_104, e10, e20, % 25.41/4.58 | | | | | | | | | simplifying with (76), (306) gives: % 25.41/4.58 | | | | | | | | | (309) all_4_104 = e10 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | REDUCE: (281), (309) imply: % 25.41/4.58 | | | | | | | | | (310) ~ (e14 = e10) % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | REDUCE: (81), (308) imply: % 25.41/4.58 | | | | | | | | | (311) j(e20) = e14 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | GROUND_INST: instantiating (34) with e10, e14, e20, simplifying % 25.41/4.58 | | | | | | | | | with (306), (311) gives: % 25.41/4.58 | | | | | | | | | (312) e14 = e10 % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | REDUCE: (1), (312) imply: % 25.41/4.58 | | | | | | | | | (313) $false % 25.41/4.58 | | | | | | | | | % 25.41/4.58 | | | | | | | | | CLOSE: (313) is inconsistent. % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | Case 2: % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | | (314) all_4_109 = e21 % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | | REDUCE: (80), (314) imply: % 25.99/4.58 | | | | | | | | | (315) j(e21) = e10 % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | | REDUCE: (257), (314) imply: % 25.99/4.58 | | | | | | | | | (316) op2(e21, e21) = all_4_105 % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | | GROUND_INST: instantiating (37) with e21, all_4_105, e21, e21, % 25.99/4.58 | | | | | | | | | simplifying with (8), (316) gives: % 25.99/4.58 | | | | | | | | | (317) all_4_105 = e21 % 25.99/4.58 | | | | | | | | | % 25.99/4.58 | | | | | | | | | GROUND_INST: instantiating (34) with all_4_103, e10, e21, % 25.99/4.58 | | | | | | | | | simplifying with (75), (315) gives: % 25.99/4.59 | | | | | | | | | (318) all_4_103 = e10 % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | | REDUCE: (284), (318) imply: % 25.99/4.59 | | | | | | | | | (319) ~ (e14 = e10) % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | | REDUCE: (81), (317) imply: % 25.99/4.59 | | | | | | | | | (320) j(e21) = e14 % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | | GROUND_INST: instantiating (34) with e10, e14, e21, simplifying % 25.99/4.59 | | | | | | | | | with (315), (320) gives: % 25.99/4.59 | | | | | | | | | (321) e14 = e10 % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | | REDUCE: (1), (321) imply: % 25.99/4.59 | | | | | | | | | (322) $false % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | | CLOSE: (322) is inconsistent. % 25.99/4.59 | | | | | | | | | % 25.99/4.59 | | | | | | | | End of split % 25.99/4.59 | | | | | | | | % 25.99/4.59 | | | | | | | End of split % 25.99/4.59 | | | | | | | % 25.99/4.59 | | | | | | End of split % 25.99/4.59 | | | | | | % 25.99/4.59 | | | | | End of split % 25.99/4.59 | | | | | % 25.99/4.59 | | | | End of split % 25.99/4.59 | | | | % 25.99/4.59 | | | End of split % 25.99/4.59 | | | % 25.99/4.59 | | End of split % 25.99/4.59 | | % 25.99/4.59 | End of split % 26.04/4.60 | % 26.04/4.60 End of proof % 26.04/4.60 % 26.04/4.60 Sub-proof #1 shows that the following formulas are inconsistent: % 26.04/4.60 ---------------------------------------------------------------- % 26.04/4.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.04/4.60 (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 26.04/4.60 (2) op1(e14, e14) = e14 % 26.04/4.60 (3) op1(e14, e14) = e10 % 26.04/4.60 (4) ~ (e14 = e10) % 26.04/4.60 % 26.04/4.60 Begin of proof % 26.04/4.60 | % 26.04/4.60 | GROUND_INST: instantiating (1) with e10, e14, e14, e14, simplifying with (2), % 26.04/4.60 | (3) gives: % 26.04/4.60 | (5) e14 = e10 % 26.04/4.60 | % 26.04/4.60 | REDUCE: (4), (5) imply: % 26.04/4.60 | (6) $false % 26.04/4.60 | % 26.04/4.60 | CLOSE: (6) is inconsistent. % 26.04/4.60 | % 26.04/4.60 End of proof % 26.04/4.60 % SZS output end Proof for theBenchmark % 26.04/4.60 % 26.04/4.60 4000ms %------------------------------------------------------------------------------