%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG202+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 : n024.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 16:39:52 EDT 2023 % Result : Theorem 5.71s 1.56s % Output : Proof 9.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG202+1 : TPTP v8.1.2. Released v2.7.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Mon Aug 28 03:57:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.24/1.00 Prover 4: Preprocessing ... % 2.24/1.00 Prover 1: Preprocessing ... % 2.54/1.04 Prover 5: Preprocessing ... % 2.54/1.04 Prover 3: Preprocessing ... % 2.54/1.04 Prover 2: Preprocessing ... % 2.54/1.04 Prover 6: Preprocessing ... % 2.54/1.04 Prover 0: Preprocessing ... % 4.09/1.35 Prover 1: Constructing countermodel ... % 4.44/1.35 Prover 5: Constructing countermodel ... % 4.44/1.36 Prover 6: Proving ... % 4.44/1.36 Prover 3: Constructing countermodel ... % 4.89/1.39 Prover 2: Proving ... % 4.95/1.40 Prover 4: Constructing countermodel ... % 5.05/1.46 Prover 0: Proving ... % 5.05/1.50 Prover 3: gave up % 5.71/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.71/1.52 Prover 1: gave up % 5.71/1.54 Prover 7: Preprocessing ... % 5.71/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.71/1.55 Prover 8: Preprocessing ... % 5.71/1.56 Prover 5: proved (922ms) % 5.71/1.56 % 5.71/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.71/1.56 % 5.71/1.57 Prover 0: stopped % 5.71/1.58 Prover 2: stopped % 5.71/1.58 Prover 6: stopped % 5.71/1.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.71/1.58 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.36/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.36/1.59 Prover 10: Preprocessing ... % 6.36/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.36/1.61 Prover 11: Preprocessing ... % 6.36/1.61 Prover 16: Preprocessing ... % 6.36/1.62 Prover 13: Preprocessing ... % 6.36/1.63 Prover 7: Constructing countermodel ... % 6.36/1.64 Prover 8: Warning: ignoring some quantifiers % 6.36/1.64 Prover 8: Constructing countermodel ... % 6.36/1.65 Prover 10: Constructing countermodel ... % 6.36/1.65 Prover 7: gave up % 6.36/1.67 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 6.36/1.68 Prover 19: Preprocessing ... % 7.05/1.69 Prover 10: gave up % 7.10/1.70 Prover 16: Constructing countermodel ... % 7.27/1.72 Prover 13: Constructing countermodel ... % 7.27/1.73 Prover 11: Constructing countermodel ... % 7.27/1.76 Prover 19: Warning: ignoring some quantifiers % 7.27/1.77 Prover 19: Constructing countermodel ... % 9.15/1.99 Prover 13: Found proof (size 55) % 9.15/1.99 Prover 13: proved (401ms) % 9.15/1.99 Prover 19: stopped % 9.15/1.99 Prover 11: stopped % 9.15/1.99 Prover 16: stopped % 9.15/1.99 Prover 4: stopped % 9.15/1.99 Prover 8: stopped % 9.15/1.99 % 9.15/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.15/1.99 % 9.15/2.01 % SZS output start Proof for theBenchmark % 9.15/2.01 Assumptions after simplification: % 9.15/2.01 --------------------------------- % 9.15/2.01 % 9.15/2.01 (ax2) % 9.15/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~ $i(v1) | % 9.15/2.03 ~ $i(v0) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) & ! [v0: $i] : ! % 9.15/2.03 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sorti2(v1) | ~ sorti2(v0) | ? [v2: % 9.15/2.03 $i] : (op2(v0, v1) = v2 & $i(v2) & sorti2(v2))) % 9.15/2.03 % 9.15/2.04 (ax3) % 9.15/2.04 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (op1(v0, v0) = v1) | ~ $i(v0) | ~ % 9.15/2.04 sorti1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | op1(v0, v0) = v0) % 9.15/2.04 % 9.15/2.04 (ax4) % 9.15/2.04 ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & op2(v0, v0) = v1 & $i(v1) & $i(v0) % 9.15/2.04 & sorti2(v0)) % 9.15/2.04 % 9.15/2.04 (co1) % 9.15/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 9.15/2.05 (j(v2) = v3) | ~ (j(v0) = v1) | ~ (op1(v1, v3) = v4) | ~ $i(v2) | ~ % 9.15/2.05 $i(v0) | ~ sorti2(v2) | ~ sorti2(v0) | ? [v5: $i] : (j(v5) = v4 & op2(v0, % 9.15/2.05 v2) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 9.15/2.05 ! [v3: $i] : ! [v4: $i] : ( ~ (h(v2) = v3) | ~ (h(v0) = v1) | ~ (op2(v1, % 9.15/2.05 v3) = v4) | ~ $i(v2) | ~ $i(v0) | ~ sorti1(v2) | ~ sorti1(v0) | ? % 9.15/2.05 [v5: $i] : (h(v5) = v4 & op1(v0, v2) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] % 9.15/2.05 : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~ sorti2(v0) | h(v1) = v0) & % 9.15/2.05 ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~ sorti2(v0) | % 9.15/2.05 sorti1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ~ % 9.15/2.05 sorti1(v0) | j(v1) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ % 9.15/2.05 $i(v0) | ~ sorti1(v0) | sorti2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 9.15/2.05 sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & h(v1) = v0 & $i(v1))) & ! [v0: $i] % 9.15/2.05 : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & $i(v1) & % 9.15/2.05 sorti1(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : % 9.15/2.05 (j(v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti2(v2) | ? [v3: % 9.15/2.05 $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, % 9.15/2.05 v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) & ! [v0: % 9.15/2.05 $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (j(v1) = v0 & h(v0) = v1 & % 9.15/2.05 $i(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (h(v0) % 9.15/2.05 = v1 & $i(v1) & sorti2(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | % 9.15/2.05 ? [v1: $i] : (h(v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti1(v2) % 9.15/2.05 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & h(v2) = v5 & % 9.15/2.05 op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v3))))) % 9.15/2.05 % 9.15/2.05 (function-axioms) % 9.15/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3, % 9.15/2.05 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.15/2.05 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = % 9.15/2.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = % 9.15/2.05 v1) | ~ (j(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.15/2.05 v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) % 9.15/2.06 % 9.15/2.06 Further assumptions not needed in the proof: % 9.15/2.06 -------------------------------------------- % 9.15/2.06 ax1 % 9.15/2.06 % 9.15/2.06 Those formulas are unsatisfiable: % 9.15/2.06 --------------------------------- % 9.15/2.06 % 9.15/2.06 Begin of proof % 9.15/2.06 | % 9.15/2.06 | ALPHA: (ax2) implies: % 9.15/2.06 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sorti2(v1) | ~ % 9.15/2.06 | sorti2(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & $i(v2) & sorti2(v2))) % 9.15/2.06 | % 9.15/2.06 | ALPHA: (ax3) implies: % 9.15/2.06 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (op1(v0, v0) = v1) | ~ % 9.15/2.06 | $i(v0) | ~ sorti1(v0)) % 9.15/2.06 | % 9.15/2.06 | ALPHA: (co1) implies: % 9.66/2.06 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (h(v0) = v1 & % 9.66/2.06 | $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti1(v2) | ? [v3: $i] : % 9.66/2.06 | ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) % 9.66/2.06 | = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v3))))) % 9.66/2.06 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & % 9.66/2.06 | $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti2(v2) | ? [v3: $i] : % 9.66/2.06 | ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) % 9.66/2.06 | = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) % 9.66/2.06 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & % 9.66/2.06 | $i(v1) & sorti1(v1))) % 9.66/2.06 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & % 9.66/2.06 | h(v1) = v0 & $i(v1))) % 9.66/2.06 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~ % 9.66/2.06 | sorti2(v0) | h(v1) = v0) % 9.66/2.06 | % 9.66/2.06 | ALPHA: (function-axioms) implies: % 9.66/2.07 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | % 9.66/2.07 | ~ (h(v2) = v0)) % 9.66/2.07 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) | % 9.66/2.07 | ~ (j(v2) = v0)) % 9.66/2.07 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.66/2.07 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 9.66/2.07 | % 9.66/2.07 | DELTA: instantiating (ax4) with fresh symbols all_7_0, all_7_1 gives: % 9.66/2.07 | (11) ~ (all_7_0 = all_7_1) & op2(all_7_1, all_7_1) = all_7_0 & $i(all_7_0) % 9.66/2.07 | & $i(all_7_1) & sorti2(all_7_1) % 9.66/2.07 | % 9.66/2.07 | ALPHA: (11) implies: % 9.66/2.07 | (12) ~ (all_7_0 = all_7_1) % 9.66/2.07 | (13) sorti2(all_7_1) % 9.66/2.07 | (14) $i(all_7_1) % 9.66/2.07 | (15) op2(all_7_1, all_7_1) = all_7_0 % 9.66/2.07 | % 9.66/2.07 | GROUND_INST: instantiating (1) with all_7_1, all_7_1, simplifying with (13), % 9.66/2.07 | (14) gives: % 9.66/2.07 | (16) ? [v0: $i] : (op2(all_7_1, all_7_1) = v0 & $i(v0) & sorti2(v0)) % 9.66/2.07 | % 9.66/2.07 | GROUND_INST: instantiating (6) with all_7_1, simplifying with (13), (14) % 9.66/2.07 | gives: % 9.66/2.07 | (17) ? [v0: $i] : (j(all_7_1) = v0 & h(v0) = all_7_1 & $i(v0)) % 9.66/2.07 | % 9.66/2.07 | GROUND_INST: instantiating (5) with all_7_1, simplifying with (13), (14) % 9.66/2.07 | gives: % 9.66/2.07 | (18) ? [v0: $i] : (j(all_7_1) = v0 & $i(v0) & sorti1(v0)) % 9.66/2.07 | % 9.66/2.07 | GROUND_INST: instantiating (4) with all_7_1, simplifying with (13), (14) % 9.66/2.07 | gives: % 9.66/2.07 | (19) ? [v0: $i] : (j(all_7_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | % 9.66/2.07 | ~ sorti2(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) = % 9.66/2.07 | v3 & j(v1) = v4 & op2(all_7_1, v1) = v2 & op1(v0, v4) = v3 & % 9.66/2.07 | $i(v4) & $i(v3) & $i(v2)))) % 9.66/2.07 | % 9.66/2.07 | DELTA: instantiating (18) with fresh symbol all_15_0 gives: % 9.66/2.07 | (20) j(all_7_1) = all_15_0 & $i(all_15_0) & sorti1(all_15_0) % 9.66/2.07 | % 9.66/2.07 | ALPHA: (20) implies: % 9.66/2.07 | (21) sorti1(all_15_0) % 9.66/2.07 | (22) j(all_7_1) = all_15_0 % 9.66/2.07 | % 9.66/2.07 | DELTA: instantiating (17) with fresh symbol all_17_0 gives: % 9.66/2.07 | (23) j(all_7_1) = all_17_0 & h(all_17_0) = all_7_1 & $i(all_17_0) % 9.66/2.07 | % 9.66/2.07 | ALPHA: (23) implies: % 9.66/2.07 | (24) $i(all_17_0) % 9.66/2.07 | (25) h(all_17_0) = all_7_1 % 9.66/2.07 | (26) j(all_7_1) = all_17_0 % 9.66/2.07 | % 9.66/2.07 | DELTA: instantiating (16) with fresh symbol all_19_0 gives: % 9.66/2.07 | (27) op2(all_7_1, all_7_1) = all_19_0 & $i(all_19_0) & sorti2(all_19_0) % 9.66/2.07 | % 9.66/2.07 | ALPHA: (27) implies: % 9.66/2.08 | (28) sorti2(all_19_0) % 9.66/2.08 | (29) $i(all_19_0) % 9.66/2.08 | (30) op2(all_7_1, all_7_1) = all_19_0 % 9.66/2.08 | % 9.66/2.08 | DELTA: instantiating (19) with fresh symbol all_21_0 gives: % 9.66/2.08 | (31) j(all_7_1) = all_21_0 & $i(all_21_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 9.66/2.08 | sorti2(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & % 9.66/2.08 | j(v0) = v3 & op2(all_7_1, v0) = v1 & op1(all_21_0, v3) = v2 & % 9.66/2.08 | $i(v3) & $i(v2) & $i(v1))) % 9.66/2.08 | % 9.66/2.08 | ALPHA: (31) implies: % 9.66/2.08 | (32) j(all_7_1) = all_21_0 % 9.66/2.08 | (33) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : ? [v2: $i] : % 9.66/2.08 | ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_1, v0) = v1 & % 9.66/2.08 | op1(all_21_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1))) % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (33) with all_7_1, simplifying with (13), (14) % 9.66/2.08 | gives: % 9.66/2.08 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_1) = % 9.66/2.08 | v2 & op2(all_7_1, all_7_1) = v0 & op1(all_21_0, v2) = v1 & $i(v2) & % 9.66/2.08 | $i(v1) & $i(v0)) % 9.66/2.08 | % 9.66/2.08 | DELTA: instantiating (34) with fresh symbols all_24_0, all_24_1, all_24_2 % 9.66/2.08 | gives: % 9.66/2.08 | (35) j(all_24_2) = all_24_1 & j(all_7_1) = all_24_0 & op2(all_7_1, all_7_1) % 9.66/2.08 | = all_24_2 & op1(all_21_0, all_24_0) = all_24_1 & $i(all_24_0) & % 9.66/2.08 | $i(all_24_1) & $i(all_24_2) % 9.66/2.08 | % 9.66/2.08 | ALPHA: (35) implies: % 9.66/2.08 | (36) op1(all_21_0, all_24_0) = all_24_1 % 9.66/2.08 | (37) op2(all_7_1, all_7_1) = all_24_2 % 9.66/2.08 | (38) j(all_7_1) = all_24_0 % 9.66/2.08 | (39) j(all_24_2) = all_24_1 % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (10) with all_7_0, all_24_2, all_7_1, all_7_1, % 9.66/2.08 | simplifying with (15), (37) gives: % 9.66/2.08 | (40) all_24_2 = all_7_0 % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (10) with all_19_0, all_24_2, all_7_1, all_7_1, % 9.66/2.08 | simplifying with (30), (37) gives: % 9.66/2.08 | (41) all_24_2 = all_19_0 % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (9) with all_17_0, all_21_0, all_7_1, simplifying % 9.66/2.08 | with (26), (32) gives: % 9.66/2.08 | (42) all_21_0 = all_17_0 % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (9) with all_21_0, all_24_0, all_7_1, simplifying % 9.66/2.08 | with (32), (38) gives: % 9.66/2.08 | (43) all_24_0 = all_21_0 % 9.66/2.08 | % 9.66/2.08 | GROUND_INST: instantiating (9) with all_15_0, all_24_0, all_7_1, simplifying % 9.66/2.08 | with (22), (38) gives: % 9.66/2.08 | (44) all_24_0 = all_15_0 % 9.66/2.08 | % 9.66/2.08 | COMBINE_EQS: (43), (44) imply: % 9.66/2.08 | (45) all_21_0 = all_15_0 % 9.66/2.08 | % 9.66/2.08 | SIMP: (45) implies: % 9.66/2.08 | (46) all_21_0 = all_15_0 % 9.66/2.08 | % 9.66/2.08 | COMBINE_EQS: (40), (41) imply: % 9.66/2.08 | (47) all_19_0 = all_7_0 % 9.66/2.08 | % 9.66/2.08 | SIMP: (47) implies: % 9.66/2.08 | (48) all_19_0 = all_7_0 % 9.66/2.08 | % 9.66/2.08 | COMBINE_EQS: (42), (46) imply: % 9.66/2.08 | (49) all_17_0 = all_15_0 % 9.66/2.08 | % 9.66/2.08 | SIMP: (49) implies: % 9.66/2.08 | (50) all_17_0 = all_15_0 % 9.66/2.08 | % 9.66/2.08 | REDUCE: (39), (40) imply: % 9.66/2.08 | (51) j(all_7_0) = all_24_1 % 9.66/2.08 | % 9.66/2.08 | REDUCE: (25), (50) imply: % 9.66/2.08 | (52) h(all_15_0) = all_7_1 % 9.66/2.08 | % 9.66/2.08 | REDUCE: (36), (44), (46) imply: % 9.66/2.08 | (53) op1(all_15_0, all_15_0) = all_24_1 % 9.66/2.08 | % 9.66/2.08 | REDUCE: (29), (48) imply: % 9.66/2.09 | (54) $i(all_7_0) % 9.66/2.09 | % 9.66/2.09 | REDUCE: (24), (50) imply: % 9.66/2.09 | (55) $i(all_15_0) % 9.66/2.09 | % 9.66/2.09 | REDUCE: (28), (48) imply: % 9.66/2.09 | (56) sorti2(all_7_0) % 9.66/2.09 | % 9.66/2.09 | GROUND_INST: instantiating (3) with all_15_0, simplifying with (21), (55) % 9.66/2.09 | gives: % 9.66/2.09 | (57) ? [v0: $i] : (h(all_15_0) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) | % 9.66/2.09 | ~ sorti1(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (h(v2) = % 9.66/2.09 | v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_15_0, v1) = v2 & % 9.66/2.09 | $i(v4) & $i(v3) & $i(v2)))) % 9.66/2.09 | % 9.66/2.09 | GROUND_INST: instantiating (2) with all_15_0, all_24_1, simplifying with (21), % 9.66/2.09 | (53), (55) gives: % 9.66/2.09 | (58) all_24_1 = all_15_0 % 9.66/2.09 | % 9.66/2.09 | GROUND_INST: instantiating (7) with all_7_0, all_24_1, simplifying with (51), % 9.79/2.09 | (54), (56) gives: % 9.79/2.09 | (59) h(all_24_1) = all_7_0 % 9.79/2.09 | % 9.79/2.09 | DELTA: instantiating (57) with fresh symbol all_52_0 gives: % 9.79/2.09 | (60) h(all_15_0) = all_52_0 & $i(all_52_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 9.79/2.09 | sorti1(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 & % 9.79/2.09 | h(v0) = v3 & op2(all_52_0, v3) = v2 & op1(all_15_0, v0) = v1 & % 9.79/2.09 | $i(v3) & $i(v2) & $i(v1))) % 9.79/2.09 | % 9.79/2.09 | ALPHA: (60) implies: % 9.79/2.09 | (61) h(all_15_0) = all_52_0 % 9.79/2.09 | (62) ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : ? [v2: $i] : % 9.79/2.09 | ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_52_0, v3) = v2 & % 9.79/2.09 | op1(all_15_0, v0) = v1 & $i(v3) & $i(v2) & $i(v1))) % 9.79/2.09 | % 9.79/2.09 | GROUND_INST: instantiating (62) with all_15_0, simplifying with (21), (55) % 9.79/2.09 | gives: % 9.79/2.09 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & h(all_15_0) = % 9.79/2.09 | v2 & op2(all_52_0, v2) = v1 & op1(all_15_0, all_15_0) = v0 & $i(v2) % 9.79/2.09 | & $i(v1) & $i(v0)) % 9.79/2.09 | % 9.79/2.09 | DELTA: instantiating (63) with fresh symbols all_58_0, all_58_1, all_58_2 % 9.79/2.09 | gives: % 9.79/2.09 | (64) h(all_58_2) = all_58_1 & h(all_15_0) = all_58_0 & op2(all_52_0, % 9.79/2.09 | all_58_0) = all_58_1 & op1(all_15_0, all_15_0) = all_58_2 & % 9.79/2.09 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) % 9.79/2.09 | % 9.79/2.09 | ALPHA: (64) implies: % 9.79/2.09 | (65) h(all_15_0) = all_58_0 % 9.79/2.09 | % 9.79/2.09 | REDUCE: (58), (59) imply: % 9.79/2.09 | (66) h(all_15_0) = all_7_0 % 9.79/2.09 | % 9.79/2.09 | GROUND_INST: instantiating (8) with all_7_1, all_58_0, all_15_0, simplifying % 9.79/2.09 | with (52), (65) gives: % 9.79/2.09 | (67) all_58_0 = all_7_1 % 9.79/2.09 | % 9.79/2.09 | GROUND_INST: instantiating (8) with all_52_0, all_58_0, all_15_0, simplifying % 9.79/2.09 | with (61), (65) gives: % 9.79/2.09 | (68) all_58_0 = all_52_0 % 9.79/2.09 | % 9.79/2.09 | GROUND_INST: instantiating (8) with all_7_0, all_58_0, all_15_0, simplifying % 9.79/2.09 | with (65), (66) gives: % 9.79/2.09 | (69) all_58_0 = all_7_0 % 9.79/2.09 | % 9.79/2.09 | COMBINE_EQS: (68), (69) imply: % 9.79/2.09 | (70) all_52_0 = all_7_0 % 9.79/2.09 | % 9.79/2.09 | COMBINE_EQS: (67), (68) imply: % 9.79/2.09 | (71) all_52_0 = all_7_1 % 9.79/2.09 | % 9.79/2.09 | COMBINE_EQS: (70), (71) imply: % 9.79/2.09 | (72) all_7_0 = all_7_1 % 9.79/2.09 | % 9.79/2.09 | REDUCE: (12), (72) imply: % 9.79/2.09 | (73) $false % 9.79/2.10 | % 9.79/2.10 | CLOSE: (73) is inconsistent. % 9.79/2.10 | % 9.79/2.10 End of proof % 9.79/2.10 % SZS output end Proof for theBenchmark % 9.79/2.10 % 9.79/2.10 1489ms %------------------------------------------------------------------------------