%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG042+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 : n009.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 16:35:49 EDT 2023 % Result : Theorem 8.95s 1.89s % Output : Proof 13.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ALG042+1 : TPTP v8.1.2. Released v2.7.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 04:16:35 EDT 2023 % 0.12/0.34 % CPUTime : % 0.49/0.59 ________ _____ % 0.49/0.59 ___ __ \_________(_)________________________________ % 0.49/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.49/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.49/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.49/0.59 % 0.49/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.49/0.60 (2023-06-19) % 0.49/0.60 % 0.49/0.60 (c) Philipp Rümmer, 2009-2023 % 0.49/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.49/0.60 Amanda Stjerna. % 0.49/0.60 Free software under BSD-3-Clause. % 0.49/0.60 % 0.49/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.49/0.60 % 0.49/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.49/0.61 Running up to 7 provers in parallel. % 0.49/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.49/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.49/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.49/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.49/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.49/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.49/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.98/1.07 Prover 4: Preprocessing ... % 2.98/1.07 Prover 1: Preprocessing ... % 3.07/1.10 Prover 0: Preprocessing ... % 3.07/1.10 Prover 5: Preprocessing ... % 3.07/1.10 Prover 3: Preprocessing ... % 3.07/1.10 Prover 2: Preprocessing ... % 3.07/1.10 Prover 6: Preprocessing ... % 5.67/1.43 Prover 4: Constructing countermodel ... % 5.67/1.43 Prover 6: Constructing countermodel ... % 5.67/1.43 Prover 0: Constructing countermodel ... % 5.67/1.43 Prover 1: Constructing countermodel ... % 5.67/1.44 Prover 3: Constructing countermodel ... % 5.67/1.44 Prover 2: Constructing countermodel ... % 6.82/1.60 Prover 5: Constructing countermodel ... % 8.95/1.89 Prover 0: proved (1274ms) % 8.95/1.89 % 8.95/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.95/1.89 % 8.95/1.90 Prover 5: stopped % 8.95/1.90 Prover 6: stopped % 8.95/1.90 Prover 2: stopped % 8.95/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.95/1.90 Prover 3: stopped % 8.95/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.95/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.95/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.95/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.68/2.00 Prover 8: Preprocessing ... % 9.68/2.01 Prover 7: Preprocessing ... % 9.68/2.02 Prover 13: Preprocessing ... % 9.68/2.02 Prover 10: Preprocessing ... % 9.68/2.03 Prover 11: Preprocessing ... % 10.27/2.11 Prover 10: Constructing countermodel ... % 10.27/2.11 Prover 11: Constructing countermodel ... % 10.27/2.12 Prover 8: Constructing countermodel ... % 10.68/2.15 Prover 7: Constructing countermodel ... % 10.68/2.17 Prover 13: Constructing countermodel ... % 12.39/2.38 Prover 1: Found proof (size 96) % 12.39/2.38 Prover 1: proved (1764ms) % 12.39/2.38 Prover 13: stopped % 12.39/2.38 Prover 11: stopped % 12.39/2.38 Prover 4: stopped % 12.39/2.38 Prover 7: stopped % 12.39/2.38 Prover 10: stopped % 12.39/2.38 Prover 8: stopped % 12.39/2.38 % 12.39/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.39/2.38 % 12.39/2.40 % SZS output start Proof for theBenchmark % 12.39/2.41 Assumptions after simplification: % 12.39/2.41 --------------------------------- % 12.39/2.41 % 12.39/2.41 (ax2) % 12.83/2.41 ~ (e23 = e22) & ~ (e23 = e20) & ~ (e23 = e21) & ~ (e22 = e20) & ~ (e22 = % 12.83/2.41 e21) & ~ (e20 = e21) & $i(e23) & $i(e22) & $i(e20) & $i(e21) % 12.83/2.41 % 12.83/2.41 (ax4) % 12.83/2.44 op1(e13, e13) = e10 & op1(e13, e12) = e11 & op1(e13, e10) = e13 & op1(e13, % 12.83/2.44 e11) = e12 & op1(e12, e13) = e11 & op1(e12, e12) = e10 & op1(e12, e10) = e12 % 12.83/2.44 & op1(e12, e11) = e13 & op1(e10, e13) = e13 & op1(e10, e12) = e12 & op1(e10, % 12.83/2.44 e10) = e10 & op1(e10, e11) = e11 & op1(e11, e13) = e12 & op1(e11, e12) = e13 % 12.83/2.44 & op1(e11, e10) = e11 & op1(e11, e11) = e10 & $i(e13) & $i(e12) & $i(e10) & % 12.83/2.44 $i(e11) % 12.83/2.44 % 12.83/2.44 (ax5) % 12.83/2.44 op2(e23, e23) = e20 & op2(e23, e22) = e21 & op2(e23, e20) = e23 & op2(e23, % 12.83/2.44 e21) = e22 & op2(e22, e23) = e21 & op2(e22, e22) = e23 & op2(e22, e20) = e22 % 12.83/2.44 & op2(e22, e21) = e20 & op2(e20, e23) = e23 & op2(e20, e22) = e22 & op2(e20, % 12.83/2.44 e20) = e20 & op2(e20, e21) = e21 & op2(e21, e23) = e22 & op2(e21, e22) = e20 % 12.83/2.44 & op2(e21, e20) = e21 & op2(e21, e21) = e23 & $i(e23) & $i(e22) & $i(e20) & % 12.83/2.44 $i(e21) % 12.83/2.44 % 12.83/2.44 (co1) % 12.83/2.46 $i(e23) & $i(e22) & $i(e20) & $i(e21) & $i(e13) & $i(e12) & $i(e10) & $i(e11) % 12.83/2.46 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 12.83/2.46 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: % 12.83/2.46 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: % 12.83/2.46 $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ? [v20: % 12.83/2.46 $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: % 12.83/2.46 $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: % 12.83/2.46 $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ? [v35: % 12.83/2.46 $i] : ? [v36: $i] : ? [v37: $i] : ? [v38: $i] : ? [v39: $i] : ? [v40: % 12.83/2.46 $i] : ? [v41: $i] : ? [v42: $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: % 12.83/2.46 $i] : ? [v46: $i] : ? [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: % 12.83/2.46 $i] : ? [v51: $i] : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: % 12.83/2.46 $i] : ? [v56: $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: % 12.83/2.46 $i] : ? [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: % 12.83/2.46 $i] : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: % 12.83/2.46 $i] : ? [v71: $i] : (h(v38) = v39 & h(v36) = v37 & h(v34) = v35 & h(v32) = % 12.83/2.46 v33 & h(v30) = v31 & h(v28) = v29 & h(v26) = v27 & h(v24) = v25 & h(v22) = % 12.83/2.46 v23 & h(v20) = v21 & h(v18) = v19 & h(v16) = v17 & h(v14) = v15 & h(v12) = % 12.83/2.46 v13 & h(v10) = v11 & h(v8) = v9 & h(v7) = e23 & h(v6) = e22 & h(v5) = e21 & % 12.83/2.46 h(v4) = e20 & h(e13) = v3 & h(e12) = v2 & h(e10) = v0 & h(e11) = v1 & j(v70) % 12.83/2.46 = v71 & j(v68) = v69 & j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & j(v60) = % 12.83/2.46 v61 & j(v58) = v59 & j(v56) = v57 & j(v54) = v55 & j(v52) = v53 & j(v50) = % 12.83/2.46 v51 & j(v48) = v49 & j(v46) = v47 & j(v44) = v45 & j(v42) = v43 & j(v40) = % 12.83/2.46 v41 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e23) = v7 & % 12.83/2.46 j(e22) = v6 & j(e20) = v4 & j(e21) = v5 & op2(v3, v3) = v39 & op2(v3, v2) = % 12.83/2.46 v37 & op2(v3, v1) = v35 & op2(v3, v0) = v33 & op2(v2, v3) = v31 & op2(v2, % 12.83/2.46 v2) = v29 & op2(v2, v1) = v27 & op2(v2, v0) = v25 & op2(v1, v3) = v23 & % 12.83/2.46 op2(v1, v2) = v21 & op2(v1, v1) = v19 & op2(v1, v0) = v17 & op2(v0, v3) = % 12.83/2.46 v15 & op2(v0, v2) = v13 & op2(v0, v1) = v11 & op2(v0, v0) = v9 & op2(e23, % 12.83/2.46 e23) = v70 & op2(e23, e22) = v68 & op2(e23, e20) = v64 & op2(e23, e21) = % 12.83/2.46 v66 & op2(e22, e23) = v62 & op2(e22, e22) = v60 & op2(e22, e20) = v56 & % 12.83/2.46 op2(e22, e21) = v58 & op2(e20, e23) = v46 & op2(e20, e22) = v44 & op2(e20, % 12.83/2.46 e20) = v40 & op2(e20, e21) = v42 & op2(e21, e23) = v54 & op2(e21, e22) = % 12.83/2.46 v52 & op2(e21, e20) = v48 & op2(e21, e21) = v50 & op1(v7, v7) = v71 & % 12.83/2.46 op1(v7, v6) = v69 & op1(v7, v5) = v67 & op1(v7, v4) = v65 & op1(v6, v7) = % 12.83/2.46 v63 & op1(v6, v6) = v61 & op1(v6, v5) = v59 & op1(v6, v4) = v57 & op1(v5, % 12.83/2.46 v7) = v55 & op1(v5, v6) = v53 & op1(v5, v5) = v51 & op1(v5, v4) = v49 & % 12.83/2.46 op1(v4, v7) = v47 & op1(v4, v6) = v45 & op1(v4, v5) = v43 & op1(v4, v4) = % 12.83/2.46 v41 & op1(e13, e13) = v38 & op1(e13, e12) = v36 & op1(e13, e10) = v32 & % 12.83/2.46 op1(e13, e11) = v34 & op1(e12, e13) = v30 & op1(e12, e12) = v28 & op1(e12, % 12.83/2.46 e10) = v24 & op1(e12, e11) = v26 & op1(e10, e13) = v14 & op1(e10, e12) = % 12.83/2.46 v12 & op1(e10, e10) = v8 & op1(e10, e11) = v10 & op1(e11, e13) = v22 & % 12.83/2.46 op1(e11, e12) = v20 & op1(e11, e10) = v16 & op1(e11, e11) = v18 & $i(v71) & % 12.83/2.46 $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) & $i(v64) & % 12.83/2.46 $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & $i(v58) & $i(v57) & % 12.83/2.46 $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) & $i(v51) & $i(v50) & % 12.83/2.46 $i(v49) & $i(v48) & $i(v47) & $i(v46) & $i(v45) & $i(v44) & $i(v43) & % 12.83/2.46 $i(v42) & $i(v41) & $i(v40) & $i(v39) & $i(v38) & $i(v37) & $i(v36) & % 12.83/2.46 $i(v35) & $i(v34) & $i(v33) & $i(v32) & $i(v31) & $i(v30) & $i(v29) & % 12.83/2.46 $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) & $i(v22) & % 12.83/2.46 $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & % 12.83/2.46 $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 12.83/2.46 $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v7 = e13 | % 12.83/2.46 v7 = e12 | v7 = e10 | v7 = e11) & (v6 = e13 | v6 = e12 | v6 = e10 | v6 = % 12.83/2.46 e11) & (v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = e13 | v4 = e12 % 12.83/2.46 | v4 = e10 | v4 = e11) & (v3 = e23 | v3 = e22 | v3 = e20 | v3 = e21) & (v2 % 12.83/2.46 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & (v1 = e23 | v1 = e22 | v1 = e20 % 12.83/2.46 | v1 = e21) & (v0 = e23 | v0 = e22 | v0 = e20 | v0 = e21)) % 12.83/2.46 % 12.83/2.46 (function-axioms) % 13.09/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3, % 13.09/2.46 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 13.09/2.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = % 13.09/2.46 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = % 13.09/2.46 v1) | ~ (h(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 13.09/2.46 v0 | ~ (j(v2) = v1) | ~ (j(v2) = v0)) % 13.09/2.46 % 13.09/2.46 Further assumptions not needed in the proof: % 13.09/2.46 -------------------------------------------- % 13.09/2.46 ax1, ax3 % 13.09/2.46 % 13.09/2.46 Those formulas are unsatisfiable: % 13.09/2.46 --------------------------------- % 13.09/2.46 % 13.09/2.46 Begin of proof % 13.09/2.47 | % 13.09/2.47 | ALPHA: (ax2) implies: % 13.09/2.47 | (1) ~ (e23 = e20) % 13.09/2.47 | % 13.09/2.47 | ALPHA: (ax4) implies: % 13.09/2.47 | (2) op1(e11, e11) = e10 % 13.09/2.47 | (3) op1(e10, e10) = e10 % 13.09/2.47 | (4) op1(e12, e12) = e10 % 13.09/2.47 | (5) op1(e13, e13) = e10 % 13.09/2.47 | % 13.09/2.47 | ALPHA: (ax5) implies: % 13.09/2.47 | (6) op2(e21, e21) = e23 % 13.09/2.47 | (7) op2(e20, e23) = e23 % 13.09/2.47 | (8) op2(e22, e22) = e23 % 13.09/2.47 | (9) op2(e23, e20) = e23 % 13.09/2.47 | (10) op2(e23, e23) = e20 % 13.09/2.47 | % 13.09/2.47 | ALPHA: (co1) implies: % 13.09/2.48 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 13.09/2.48 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 13.09/2.48 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 13.09/2.48 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 13.09/2.48 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 13.09/2.48 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 13.09/2.48 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? % 13.09/2.48 | [v33: $i] : ? [v34: $i] : ? [v35: $i] : ? [v36: $i] : ? [v37: $i] % 13.09/2.48 | : ? [v38: $i] : ? [v39: $i] : ? [v40: $i] : ? [v41: $i] : ? [v42: % 13.09/2.48 | $i] : ? [v43: $i] : ? [v44: $i] : ? [v45: $i] : ? [v46: $i] : ? % 13.09/2.48 | [v47: $i] : ? [v48: $i] : ? [v49: $i] : ? [v50: $i] : ? [v51: $i] % 13.09/2.48 | : ? [v52: $i] : ? [v53: $i] : ? [v54: $i] : ? [v55: $i] : ? [v56: % 13.09/2.48 | $i] : ? [v57: $i] : ? [v58: $i] : ? [v59: $i] : ? [v60: $i] : ? % 13.09/2.48 | [v61: $i] : ? [v62: $i] : ? [v63: $i] : ? [v64: $i] : ? [v65: $i] % 13.09/2.48 | : ? [v66: $i] : ? [v67: $i] : ? [v68: $i] : ? [v69: $i] : ? [v70: % 13.09/2.48 | $i] : ? [v71: $i] : (h(v38) = v39 & h(v36) = v37 & h(v34) = v35 & % 13.09/2.48 | h(v32) = v33 & h(v30) = v31 & h(v28) = v29 & h(v26) = v27 & h(v24) = % 13.09/2.48 | v25 & h(v22) = v23 & h(v20) = v21 & h(v18) = v19 & h(v16) = v17 & % 13.09/2.48 | h(v14) = v15 & h(v12) = v13 & h(v10) = v11 & h(v8) = v9 & h(v7) = % 13.09/2.48 | e23 & h(v6) = e22 & h(v5) = e21 & h(v4) = e20 & h(e13) = v3 & h(e12) % 13.09/2.48 | = v2 & h(e10) = v0 & h(e11) = v1 & j(v70) = v71 & j(v68) = v69 & % 13.09/2.48 | j(v66) = v67 & j(v64) = v65 & j(v62) = v63 & j(v60) = v61 & j(v58) = % 13.09/2.48 | v59 & j(v56) = v57 & j(v54) = v55 & j(v52) = v53 & j(v50) = v51 & % 13.09/2.48 | j(v48) = v49 & j(v46) = v47 & j(v44) = v45 & j(v42) = v43 & j(v40) = % 13.09/2.48 | v41 & j(v3) = e13 & j(v2) = e12 & j(v1) = e11 & j(v0) = e10 & j(e23) % 13.09/2.48 | = v7 & j(e22) = v6 & j(e20) = v4 & j(e21) = v5 & op2(v3, v3) = v39 & % 13.09/2.48 | op2(v3, v2) = v37 & op2(v3, v1) = v35 & op2(v3, v0) = v33 & op2(v2, % 13.09/2.48 | v3) = v31 & op2(v2, v2) = v29 & op2(v2, v1) = v27 & op2(v2, v0) = % 13.09/2.48 | v25 & op2(v1, v3) = v23 & op2(v1, v2) = v21 & op2(v1, v1) = v19 & % 13.09/2.48 | op2(v1, v0) = v17 & op2(v0, v3) = v15 & op2(v0, v2) = v13 & op2(v0, % 13.09/2.48 | v1) = v11 & op2(v0, v0) = v9 & op2(e23, e23) = v70 & op2(e23, e22) % 13.09/2.48 | = v68 & op2(e23, e20) = v64 & op2(e23, e21) = v66 & op2(e22, e23) = % 13.09/2.48 | v62 & op2(e22, e22) = v60 & op2(e22, e20) = v56 & op2(e22, e21) = % 13.09/2.48 | v58 & op2(e20, e23) = v46 & op2(e20, e22) = v44 & op2(e20, e20) = % 13.09/2.48 | v40 & op2(e20, e21) = v42 & op2(e21, e23) = v54 & op2(e21, e22) = % 13.09/2.48 | v52 & op2(e21, e20) = v48 & op2(e21, e21) = v50 & op1(v7, v7) = v71 % 13.09/2.48 | & op1(v7, v6) = v69 & op1(v7, v5) = v67 & op1(v7, v4) = v65 & % 13.09/2.48 | op1(v6, v7) = v63 & op1(v6, v6) = v61 & op1(v6, v5) = v59 & op1(v6, % 13.09/2.48 | v4) = v57 & op1(v5, v7) = v55 & op1(v5, v6) = v53 & op1(v5, v5) = % 13.09/2.48 | v51 & op1(v5, v4) = v49 & op1(v4, v7) = v47 & op1(v4, v6) = v45 & % 13.09/2.48 | op1(v4, v5) = v43 & op1(v4, v4) = v41 & op1(e13, e13) = v38 & % 13.09/2.48 | op1(e13, e12) = v36 & op1(e13, e10) = v32 & op1(e13, e11) = v34 & % 13.09/2.48 | op1(e12, e13) = v30 & op1(e12, e12) = v28 & op1(e12, e10) = v24 & % 13.09/2.48 | op1(e12, e11) = v26 & op1(e10, e13) = v14 & op1(e10, e12) = v12 & % 13.09/2.48 | op1(e10, e10) = v8 & op1(e10, e11) = v10 & op1(e11, e13) = v22 & % 13.09/2.48 | op1(e11, e12) = v20 & op1(e11, e10) = v16 & op1(e11, e11) = v18 & % 13.09/2.48 | $i(v71) & $i(v70) & $i(v69) & $i(v68) & $i(v67) & $i(v66) & $i(v65) % 13.09/2.48 | & $i(v64) & $i(v63) & $i(v62) & $i(v61) & $i(v60) & $i(v59) & % 13.09/2.48 | $i(v58) & $i(v57) & $i(v56) & $i(v55) & $i(v54) & $i(v53) & $i(v52) % 13.09/2.48 | & $i(v51) & $i(v50) & $i(v49) & $i(v48) & $i(v47) & $i(v46) & % 13.09/2.48 | $i(v45) & $i(v44) & $i(v43) & $i(v42) & $i(v41) & $i(v40) & $i(v39) % 13.09/2.48 | & $i(v38) & $i(v37) & $i(v36) & $i(v35) & $i(v34) & $i(v33) & % 13.09/2.48 | $i(v32) & $i(v31) & $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) % 13.09/2.48 | & $i(v25) & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 13.09/2.48 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 13.09/2.48 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 13.09/2.48 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v7 = e13 | v7 % 13.09/2.48 | = e12 | v7 = e10 | v7 = e11) & (v6 = e13 | v6 = e12 | v6 = e10 | % 13.09/2.48 | v6 = e11) & (v5 = e13 | v5 = e12 | v5 = e10 | v5 = e11) & (v4 = % 13.09/2.48 | e13 | v4 = e12 | v4 = e10 | v4 = e11) & (v3 = e23 | v3 = e22 | v3 % 13.09/2.48 | = e20 | v3 = e21) & (v2 = e23 | v2 = e22 | v2 = e20 | v2 = e21) & % 13.09/2.48 | (v1 = e23 | v1 = e22 | v1 = e20 | v1 = e21) & (v0 = e23 | v0 = e22 | % 13.09/2.48 | v0 = e20 | v0 = e21)) % 13.09/2.48 | % 13.09/2.48 | ALPHA: (function-axioms) implies: % 13.09/2.48 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) | % 13.09/2.48 | ~ (j(v2) = v0)) % 13.09/2.48 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | % 13.09/2.48 | ~ (h(v2) = v0)) % 13.09/2.48 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.09/2.48 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 13.09/2.49 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.09/2.49 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 13.09/2.49 | % 13.09/2.49 | DELTA: instantiating (11) with fresh symbols all_4_0, all_4_1, all_4_2, % 13.09/2.49 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9, % 13.09/2.49 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16, % 13.09/2.49 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23, % 13.09/2.49 | all_4_24, all_4_25, all_4_26, all_4_27, all_4_28, all_4_29, all_4_30, % 13.09/2.49 | all_4_31, all_4_32, all_4_33, all_4_34, all_4_35, all_4_36, all_4_37, % 13.09/2.49 | all_4_38, all_4_39, all_4_40, all_4_41, all_4_42, all_4_43, all_4_44, % 13.09/2.49 | all_4_45, all_4_46, all_4_47, all_4_48, all_4_49, all_4_50, all_4_51, % 13.09/2.49 | all_4_52, all_4_53, all_4_54, all_4_55, all_4_56, all_4_57, all_4_58, % 13.09/2.49 | all_4_59, all_4_60, all_4_61, all_4_62, all_4_63, all_4_64, all_4_65, % 13.09/2.49 | all_4_66, all_4_67, all_4_68, all_4_69, all_4_70, all_4_71 gives: % 13.09/2.49 | (16) h(all_4_33) = all_4_32 & h(all_4_35) = all_4_34 & h(all_4_37) = % 13.09/2.49 | all_4_36 & h(all_4_39) = all_4_38 & h(all_4_41) = all_4_40 & % 13.09/2.49 | h(all_4_43) = all_4_42 & h(all_4_45) = all_4_44 & h(all_4_47) = % 13.09/2.49 | all_4_46 & h(all_4_49) = all_4_48 & h(all_4_51) = all_4_50 & % 13.09/2.49 | h(all_4_53) = all_4_52 & h(all_4_55) = all_4_54 & h(all_4_57) = % 13.09/2.49 | all_4_56 & h(all_4_59) = all_4_58 & h(all_4_61) = all_4_60 & % 13.09/2.49 | h(all_4_63) = all_4_62 & h(all_4_64) = e23 & h(all_4_65) = e22 & % 13.09/2.49 | h(all_4_66) = e21 & h(all_4_67) = e20 & h(e13) = all_4_68 & h(e12) = % 13.09/2.49 | all_4_69 & h(e10) = all_4_71 & h(e11) = all_4_70 & j(all_4_1) = % 13.09/2.49 | all_4_0 & j(all_4_3) = all_4_2 & j(all_4_5) = all_4_4 & j(all_4_7) = % 13.09/2.49 | all_4_6 & j(all_4_9) = all_4_8 & j(all_4_11) = all_4_10 & j(all_4_13) % 13.09/2.49 | = all_4_12 & j(all_4_15) = all_4_14 & j(all_4_17) = all_4_16 & % 13.09/2.49 | j(all_4_19) = all_4_18 & j(all_4_21) = all_4_20 & j(all_4_23) = % 13.09/2.49 | all_4_22 & j(all_4_25) = all_4_24 & j(all_4_27) = all_4_26 & % 13.09/2.49 | j(all_4_29) = all_4_28 & j(all_4_31) = all_4_30 & j(all_4_68) = e13 & % 13.09/2.49 | j(all_4_69) = e12 & j(all_4_70) = e11 & j(all_4_71) = e10 & j(e23) = % 13.09/2.49 | all_4_64 & j(e22) = all_4_65 & j(e20) = all_4_67 & j(e21) = all_4_66 & % 13.09/2.49 | op2(all_4_68, all_4_68) = all_4_32 & op2(all_4_68, all_4_69) = % 13.09/2.49 | all_4_34 & op2(all_4_68, all_4_70) = all_4_36 & op2(all_4_68, % 13.09/2.49 | all_4_71) = all_4_38 & op2(all_4_69, all_4_68) = all_4_40 & % 13.09/2.49 | op2(all_4_69, all_4_69) = all_4_42 & op2(all_4_69, all_4_70) = % 13.09/2.49 | all_4_44 & op2(all_4_69, all_4_71) = all_4_46 & op2(all_4_70, % 13.09/2.49 | all_4_68) = all_4_48 & op2(all_4_70, all_4_69) = all_4_50 & % 13.09/2.49 | op2(all_4_70, all_4_70) = all_4_52 & op2(all_4_70, all_4_71) = % 13.09/2.50 | all_4_54 & op2(all_4_71, all_4_68) = all_4_56 & op2(all_4_71, % 13.09/2.50 | all_4_69) = all_4_58 & op2(all_4_71, all_4_70) = all_4_60 & % 13.09/2.50 | op2(all_4_71, all_4_71) = all_4_62 & op2(e23, e23) = all_4_1 & % 13.09/2.50 | op2(e23, e22) = all_4_3 & op2(e23, e20) = all_4_7 & op2(e23, e21) = % 13.09/2.50 | all_4_5 & op2(e22, e23) = all_4_9 & op2(e22, e22) = all_4_11 & % 13.09/2.50 | op2(e22, e20) = all_4_15 & op2(e22, e21) = all_4_13 & op2(e20, e23) = % 13.09/2.50 | all_4_25 & op2(e20, e22) = all_4_27 & op2(e20, e20) = all_4_31 & % 13.09/2.50 | op2(e20, e21) = all_4_29 & op2(e21, e23) = all_4_17 & op2(e21, e22) = % 13.09/2.50 | all_4_19 & op2(e21, e20) = all_4_23 & op2(e21, e21) = all_4_21 & % 13.09/2.50 | op1(all_4_64, all_4_64) = all_4_0 & op1(all_4_64, all_4_65) = all_4_2 % 13.09/2.50 | & op1(all_4_64, all_4_66) = all_4_4 & op1(all_4_64, all_4_67) = % 13.09/2.50 | all_4_6 & op1(all_4_65, all_4_64) = all_4_8 & op1(all_4_65, all_4_65) % 13.09/2.50 | = all_4_10 & op1(all_4_65, all_4_66) = all_4_12 & op1(all_4_65, % 13.09/2.50 | all_4_67) = all_4_14 & op1(all_4_66, all_4_64) = all_4_16 & % 13.09/2.50 | op1(all_4_66, all_4_65) = all_4_18 & op1(all_4_66, all_4_66) = % 13.09/2.50 | all_4_20 & op1(all_4_66, all_4_67) = all_4_22 & op1(all_4_67, % 13.09/2.50 | all_4_64) = all_4_24 & op1(all_4_67, all_4_65) = all_4_26 & % 13.09/2.50 | op1(all_4_67, all_4_66) = all_4_28 & op1(all_4_67, all_4_67) = % 13.09/2.50 | all_4_30 & op1(e13, e13) = all_4_33 & op1(e13, e12) = all_4_35 & % 13.09/2.50 | op1(e13, e10) = all_4_39 & op1(e13, e11) = all_4_37 & op1(e12, e13) = % 13.09/2.50 | all_4_41 & op1(e12, e12) = all_4_43 & op1(e12, e10) = all_4_47 & % 13.09/2.50 | op1(e12, e11) = all_4_45 & op1(e10, e13) = all_4_57 & op1(e10, e12) = % 13.09/2.50 | all_4_59 & op1(e10, e10) = all_4_63 & op1(e10, e11) = all_4_61 & % 13.09/2.50 | op1(e11, e13) = all_4_49 & op1(e11, e12) = all_4_51 & op1(e11, e10) = % 13.09/2.50 | all_4_55 & op1(e11, e11) = all_4_53 & $i(all_4_0) & $i(all_4_1) & % 13.09/2.50 | $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) & % 13.09/2.50 | $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & $i(all_4_11) % 13.09/2.50 | & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & $i(all_4_15) & % 13.09/2.50 | $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & $i(all_4_19) & % 13.09/2.50 | $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & $i(all_4_23) & % 13.09/2.50 | $i(all_4_24) & $i(all_4_25) & $i(all_4_26) & $i(all_4_27) & % 13.09/2.50 | $i(all_4_28) & $i(all_4_29) & $i(all_4_30) & $i(all_4_31) & % 13.09/2.50 | $i(all_4_32) & $i(all_4_33) & $i(all_4_34) & $i(all_4_35) & % 13.09/2.50 | $i(all_4_36) & $i(all_4_37) & $i(all_4_38) & $i(all_4_39) & % 13.09/2.50 | $i(all_4_40) & $i(all_4_41) & $i(all_4_42) & $i(all_4_43) & % 13.09/2.50 | $i(all_4_44) & $i(all_4_45) & $i(all_4_46) & $i(all_4_47) & % 13.09/2.50 | $i(all_4_48) & $i(all_4_49) & $i(all_4_50) & $i(all_4_51) & % 13.09/2.50 | $i(all_4_52) & $i(all_4_53) & $i(all_4_54) & $i(all_4_55) & % 13.09/2.50 | $i(all_4_56) & $i(all_4_57) & $i(all_4_58) & $i(all_4_59) & % 13.09/2.50 | $i(all_4_60) & $i(all_4_61) & $i(all_4_62) & $i(all_4_63) & % 13.09/2.50 | $i(all_4_64) & $i(all_4_65) & $i(all_4_66) & $i(all_4_67) & % 13.09/2.50 | $i(all_4_68) & $i(all_4_69) & $i(all_4_70) & $i(all_4_71) & (all_4_64 % 13.09/2.50 | = e13 | all_4_64 = e12 | all_4_64 = e10 | all_4_64 = e11) & % 13.09/2.50 | (all_4_65 = e13 | all_4_65 = e12 | all_4_65 = e10 | all_4_65 = e11) & % 13.09/2.50 | (all_4_66 = e13 | all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11) & % 13.09/2.50 | (all_4_67 = e13 | all_4_67 = e12 | all_4_67 = e10 | all_4_67 = e11) & % 13.09/2.50 | (all_4_68 = e23 | all_4_68 = e22 | all_4_68 = e20 | all_4_68 = e21) & % 13.09/2.50 | (all_4_69 = e23 | all_4_69 = e22 | all_4_69 = e20 | all_4_69 = e21) & % 13.09/2.50 | (all_4_70 = e23 | all_4_70 = e22 | all_4_70 = e20 | all_4_70 = e21) & % 13.09/2.50 | (all_4_71 = e23 | all_4_71 = e22 | all_4_71 = e20 | all_4_71 = e21) % 13.09/2.50 | % 13.09/2.50 | ALPHA: (16) implies: % 13.09/2.50 | (17) op1(e11, e11) = all_4_53 % 13.09/2.50 | (18) op1(e10, e10) = all_4_63 % 13.09/2.50 | (19) op1(e12, e12) = all_4_43 % 13.09/2.50 | (20) op1(e13, e13) = all_4_33 % 13.09/2.50 | (21) op1(all_4_66, all_4_66) = all_4_20 % 13.09/2.50 | (22) op2(e21, e21) = all_4_21 % 13.09/2.50 | (23) op2(e20, e23) = all_4_25 % 13.09/2.50 | (24) op2(e22, e22) = all_4_11 % 13.09/2.50 | (25) op2(e23, e20) = all_4_7 % 13.09/2.50 | (26) op2(e23, e23) = all_4_1 % 13.09/2.50 | (27) op2(all_4_71, all_4_71) = all_4_62 % 13.09/2.50 | (28) j(e23) = all_4_64 % 13.09/2.50 | (29) j(all_4_25) = all_4_24 % 13.09/2.50 | (30) j(all_4_21) = all_4_20 % 13.09/2.50 | (31) j(all_4_11) = all_4_10 % 13.09/2.50 | (32) j(all_4_7) = all_4_6 % 13.09/2.50 | (33) h(e10) = all_4_71 % 13.09/2.50 | (34) h(all_4_66) = e21 % 13.09/2.50 | (35) h(all_4_64) = e23 % 13.09/2.50 | (36) h(all_4_63) = all_4_62 % 13.09/2.50 | (37) h(all_4_53) = all_4_52 % 13.09/2.50 | (38) h(all_4_43) = all_4_42 % 13.09/2.50 | (39) h(all_4_33) = all_4_32 % 13.09/2.50 | (40) all_4_71 = e23 | all_4_71 = e22 | all_4_71 = e20 | all_4_71 = e21 % 13.09/2.50 | (41) all_4_66 = e13 | all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11 % 13.09/2.50 | % 13.09/2.50 | GROUND_INST: instantiating (14) with e10, all_4_53, e11, e11, simplifying with % 13.09/2.50 | (2), (17) gives: % 13.09/2.50 | (42) all_4_53 = e10 % 13.09/2.50 | % 13.09/2.50 | GROUND_INST: instantiating (14) with e10, all_4_63, e10, e10, simplifying with % 13.09/2.50 | (3), (18) gives: % 13.09/2.50 | (43) all_4_63 = e10 % 13.09/2.50 | % 13.09/2.50 | GROUND_INST: instantiating (14) with e10, all_4_43, e12, e12, simplifying with % 13.09/2.50 | (4), (19) gives: % 13.09/2.50 | (44) all_4_43 = e10 % 13.09/2.50 | % 13.09/2.50 | GROUND_INST: instantiating (14) with e10, all_4_33, e13, e13, simplifying with % 13.09/2.50 | (5), (20) gives: % 13.09/2.50 | (45) all_4_33 = e10 % 13.09/2.50 | % 13.09/2.51 | GROUND_INST: instantiating (15) with e23, all_4_21, e21, e21, simplifying with % 13.09/2.51 | (6), (22) gives: % 13.09/2.51 | (46) all_4_21 = e23 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (15) with e23, all_4_25, e23, e20, simplifying with % 13.09/2.51 | (7), (23) gives: % 13.09/2.51 | (47) all_4_25 = e23 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (15) with e23, all_4_11, e22, e22, simplifying with % 13.09/2.51 | (8), (24) gives: % 13.09/2.51 | (48) all_4_11 = e23 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (15) with e23, all_4_7, e20, e23, simplifying with % 13.09/2.51 | (9), (25) gives: % 13.09/2.51 | (49) all_4_7 = e23 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (15) with e20, all_4_1, e23, e23, simplifying with % 13.09/2.51 | (10), (26) gives: % 13.09/2.51 | (50) all_4_1 = e20 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (39), (45) imply: % 13.09/2.51 | (51) h(e10) = all_4_32 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (38), (44) imply: % 13.09/2.51 | (52) h(e10) = all_4_42 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (37), (42) imply: % 13.09/2.51 | (53) h(e10) = all_4_52 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (36), (43) imply: % 13.09/2.51 | (54) h(e10) = all_4_62 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (32), (49) imply: % 13.09/2.51 | (55) j(e23) = all_4_6 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (31), (48) imply: % 13.09/2.51 | (56) j(e23) = all_4_10 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (30), (46) imply: % 13.09/2.51 | (57) j(e23) = all_4_20 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (29), (47) imply: % 13.09/2.51 | (58) j(e23) = all_4_24 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (12) with all_4_64, all_4_6, e23, simplifying with % 13.09/2.51 | (28), (55) gives: % 13.09/2.51 | (59) all_4_6 = all_4_64 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (12) with all_4_10, all_4_6, e23, simplifying with % 13.09/2.51 | (55), (56) gives: % 13.09/2.51 | (60) all_4_6 = all_4_10 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (12) with all_4_20, all_4_6, e23, simplifying with % 13.09/2.51 | (55), (57) gives: % 13.09/2.51 | (61) all_4_6 = all_4_20 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (12) with all_4_24, all_4_6, e23, simplifying with % 13.09/2.51 | (55), (58) gives: % 13.09/2.51 | (62) all_4_6 = all_4_24 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (13) with all_4_52, all_4_42, e10, simplifying with % 13.09/2.51 | (52), (53) gives: % 13.09/2.51 | (63) all_4_42 = all_4_52 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (13) with all_4_62, all_4_42, e10, simplifying with % 13.09/2.51 | (52), (54) gives: % 13.09/2.51 | (64) all_4_42 = all_4_62 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (13) with all_4_71, all_4_32, e10, simplifying with % 13.09/2.51 | (33), (51) gives: % 13.09/2.51 | (65) all_4_32 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | GROUND_INST: instantiating (13) with all_4_42, all_4_32, e10, simplifying with % 13.09/2.51 | (51), (52) gives: % 13.09/2.51 | (66) all_4_32 = all_4_42 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (59), (60) imply: % 13.09/2.51 | (67) all_4_10 = all_4_64 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (60), (62) imply: % 13.09/2.51 | (68) all_4_10 = all_4_24 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (60), (61) imply: % 13.09/2.51 | (69) all_4_10 = all_4_20 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (68), (69) imply: % 13.09/2.51 | (70) all_4_20 = all_4_24 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (67), (69) imply: % 13.09/2.51 | (71) all_4_20 = all_4_64 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (70), (71) imply: % 13.09/2.51 | (72) all_4_24 = all_4_64 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (65), (66) imply: % 13.09/2.51 | (73) all_4_42 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | SIMP: (73) implies: % 13.09/2.51 | (74) all_4_42 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (63), (74) imply: % 13.09/2.51 | (75) all_4_52 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (63), (64) imply: % 13.09/2.51 | (76) all_4_52 = all_4_62 % 13.09/2.51 | % 13.09/2.51 | COMBINE_EQS: (75), (76) imply: % 13.09/2.51 | (77) all_4_62 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | SIMP: (77) implies: % 13.09/2.51 | (78) all_4_62 = all_4_71 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (27), (78) imply: % 13.09/2.51 | (79) op2(all_4_71, all_4_71) = all_4_71 % 13.09/2.51 | % 13.09/2.51 | REDUCE: (21), (71) imply: % 13.09/2.51 | (80) op1(all_4_66, all_4_66) = all_4_64 % 13.09/2.51 | % 13.09/2.51 | BETA: splitting (41) gives: % 13.09/2.51 | % 13.09/2.51 | Case 1: % 13.09/2.51 | | % 13.09/2.51 | | (81) all_4_66 = e13 % 13.09/2.52 | | % 13.09/2.52 | | REDUCE: (80), (81) imply: % 13.09/2.52 | | (82) op1(e13, e13) = all_4_64 % 13.09/2.52 | | % 13.09/2.52 | | GROUND_INST: instantiating (14) with e10, all_4_64, e13, e13, simplifying % 13.09/2.52 | | with (5), (82) gives: % 13.09/2.52 | | (83) all_4_64 = e10 % 13.09/2.52 | | % 13.09/2.52 | | REDUCE: (35), (83) imply: % 13.09/2.52 | | (84) h(e10) = e23 % 13.09/2.52 | | % 13.09/2.52 | | GROUND_INST: instantiating (13) with all_4_71, e23, e10, simplifying with % 13.09/2.52 | | (33), (84) gives: % 13.09/2.52 | | (85) all_4_71 = e23 % 13.09/2.52 | | % 13.09/2.52 | | REDUCE: (79), (85) imply: % 13.09/2.52 | | (86) op2(e23, e23) = e23 % 13.09/2.52 | | % 13.09/2.52 | | GROUND_INST: instantiating (15) with e20, e23, e23, e23, simplifying with % 13.09/2.52 | | (10), (86) gives: % 13.09/2.52 | | (87) e23 = e20 % 13.09/2.52 | | % 13.09/2.52 | | REDUCE: (1), (87) imply: % 13.09/2.52 | | (88) $false % 13.09/2.52 | | % 13.09/2.52 | | CLOSE: (88) is inconsistent. % 13.09/2.52 | | % 13.09/2.52 | Case 2: % 13.09/2.52 | | % 13.09/2.52 | | (89) all_4_66 = e12 | all_4_66 = e10 | all_4_66 = e11 % 13.09/2.52 | | % 13.09/2.52 | | BETA: splitting (40) gives: % 13.09/2.52 | | % 13.09/2.52 | | Case 1: % 13.09/2.52 | | | % 13.09/2.52 | | | (90) all_4_71 = e23 % 13.09/2.52 | | | % 13.09/2.52 | | | REDUCE: (79), (90) imply: % 13.09/2.52 | | | (91) op2(e23, e23) = e23 % 13.09/2.52 | | | % 13.09/2.52 | | | GROUND_INST: instantiating (15) with e20, e23, e23, e23, simplifying with % 13.09/2.52 | | | (10), (91) gives: % 13.09/2.52 | | | (92) e23 = e20 % 13.09/2.52 | | | % 13.09/2.52 | | | REDUCE: (1), (92) imply: % 13.09/2.52 | | | (93) $false % 13.09/2.52 | | | % 13.09/2.52 | | | CLOSE: (93) is inconsistent. % 13.09/2.52 | | | % 13.09/2.52 | | Case 2: % 13.09/2.52 | | | % 13.09/2.52 | | | (94) ~ (all_4_71 = e23) % 13.09/2.52 | | | % 13.09/2.52 | | | BETA: splitting (89) gives: % 13.09/2.52 | | | % 13.09/2.52 | | | Case 1: % 13.09/2.52 | | | | % 13.09/2.52 | | | | (95) all_4_66 = e12 % 13.09/2.52 | | | | % 13.09/2.52 | | | | REDUCE: (80), (95) imply: % 13.09/2.52 | | | | (96) op1(e12, e12) = all_4_64 % 13.09/2.52 | | | | % 13.09/2.52 | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e12, e12, % 13.09/2.52 | | | | simplifying with (4), (96) gives: % 13.09/2.52 | | | | (97) all_4_64 = e10 % 13.09/2.52 | | | | % 13.09/2.52 | | | | REF_CLOSE: (13), (33), (35), (94), (97) are inconsistent by sub-proof % 13.09/2.52 | | | | #1. % 13.09/2.52 | | | | % 13.09/2.52 | | | Case 2: % 13.09/2.52 | | | | % 13.09/2.52 | | | | (98) all_4_66 = e10 | all_4_66 = e11 % 13.09/2.52 | | | | % 13.09/2.52 | | | | BETA: splitting (98) gives: % 13.09/2.52 | | | | % 13.09/2.52 | | | | Case 1: % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | (99) all_4_66 = e10 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (34), (99) imply: % 13.09/2.52 | | | | | (100) h(e10) = e21 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (80), (99) imply: % 13.09/2.52 | | | | | (101) op1(e10, e10) = all_4_64 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e10, e10, % 13.09/2.52 | | | | | simplifying with (3), (101) gives: % 13.09/2.52 | | | | | (102) all_4_64 = e10 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | GROUND_INST: instantiating (13) with all_4_71, e21, e10, simplifying % 13.09/2.52 | | | | | with (33), (100) gives: % 13.09/2.52 | | | | | (103) all_4_71 = e21 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (94), (103) imply: % 13.09/2.52 | | | | | (104) ~ (e23 = e21) % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | SIMP: (104) implies: % 13.09/2.52 | | | | | (105) ~ (e23 = e21) % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (35), (102) imply: % 13.09/2.52 | | | | | (106) h(e10) = e23 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | GROUND_INST: instantiating (13) with e21, e23, e10, simplifying with % 13.09/2.52 | | | | | (100), (106) gives: % 13.09/2.52 | | | | | (107) e23 = e21 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (105), (107) imply: % 13.09/2.52 | | | | | (108) $false % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | CLOSE: (108) is inconsistent. % 13.09/2.52 | | | | | % 13.09/2.52 | | | | Case 2: % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | (109) all_4_66 = e11 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REDUCE: (80), (109) imply: % 13.09/2.52 | | | | | (110) op1(e11, e11) = all_4_64 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | GROUND_INST: instantiating (14) with e10, all_4_64, e11, e11, % 13.09/2.52 | | | | | simplifying with (2), (110) gives: % 13.09/2.52 | | | | | (111) all_4_64 = e10 % 13.09/2.52 | | | | | % 13.09/2.52 | | | | | REF_CLOSE: (13), (33), (35), (94), (111) are inconsistent by sub-proof % 13.09/2.52 | | | | | #1. % 13.09/2.52 | | | | | % 13.09/2.52 | | | | End of split % 13.09/2.52 | | | | % 13.09/2.53 | | | End of split % 13.09/2.53 | | | % 13.09/2.53 | | End of split % 13.09/2.53 | | % 13.09/2.53 | End of split % 13.09/2.53 | % 13.09/2.53 End of proof % 13.09/2.53 % 13.09/2.53 Sub-proof #1 shows that the following formulas are inconsistent: % 13.09/2.53 ---------------------------------------------------------------- % 13.09/2.53 (1) ~ (all_4_71 = e23) % 13.09/2.53 (2) all_4_64 = e10 % 13.09/2.53 (3) h(all_4_64) = e23 % 13.09/2.53 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | ~ % 13.09/2.53 (h(v2) = v0)) % 13.09/2.53 (5) h(e10) = all_4_71 % 13.09/2.53 % 13.09/2.53 Begin of proof % 13.09/2.53 | % 13.09/2.53 | REDUCE: (2), (3) imply: % 13.09/2.53 | (6) h(e10) = e23 % 13.09/2.53 | % 13.09/2.53 | GROUND_INST: instantiating (4) with all_4_71, e23, e10, simplifying with (5), % 13.09/2.53 | (6) gives: % 13.09/2.53 | (7) all_4_71 = e23 % 13.09/2.53 | % 13.09/2.53 | REDUCE: (1), (7) imply: % 13.09/2.53 | (8) $false % 13.09/2.53 | % 13.09/2.53 | CLOSE: (8) is inconsistent. % 13.09/2.53 | % 13.09/2.53 End of proof % 13.09/2.53 % SZS output end Proof for theBenchmark % 13.09/2.53 % 13.09/2.53 1931ms %------------------------------------------------------------------------------