%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM847+2 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.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 : Thu Aug 31 11:50:22 EDT 2023 % Result : Theorem 6.41s 1.55s % Output : Proof 9.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM847+2 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.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 : Fri Aug 25 17:52:55 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.34/1.00 Prover 1: Preprocessing ... % 2.34/1.01 Prover 4: Preprocessing ... % 2.34/1.05 Prover 3: Preprocessing ... % 2.34/1.05 Prover 6: Preprocessing ... % 2.34/1.05 Prover 2: Preprocessing ... % 2.34/1.05 Prover 5: Preprocessing ... % 2.34/1.05 Prover 0: Preprocessing ... % 4.44/1.32 Prover 1: Warning: ignoring some quantifiers % 4.44/1.33 Prover 3: Warning: ignoring some quantifiers % 4.44/1.35 Prover 3: Constructing countermodel ... % 4.44/1.35 Prover 6: Proving ... % 4.44/1.36 Prover 1: Constructing countermodel ... % 5.11/1.37 Prover 4: Constructing countermodel ... % 5.11/1.40 Prover 5: Proving ... % 5.11/1.41 Prover 0: Proving ... % 5.11/1.45 Prover 2: Proving ... % 6.32/1.54 Prover 3: proved (929ms) % 6.41/1.55 % 6.41/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.41/1.55 % 6.41/1.55 Prover 5: stopped % 6.41/1.55 Prover 0: stopped % 6.41/1.55 Prover 6: stopped % 6.41/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.41/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.41/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.41/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.41/1.56 Prover 2: stopped % 6.41/1.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.41/1.58 Prover 8: Preprocessing ... % 6.41/1.58 Prover 10: Preprocessing ... % 6.41/1.60 Prover 11: Preprocessing ... % 6.41/1.60 Prover 13: Preprocessing ... % 6.41/1.60 Prover 7: Preprocessing ... % 7.24/1.68 Prover 10: Constructing countermodel ... % 7.24/1.71 Prover 13: Warning: ignoring some quantifiers % 7.24/1.71 Prover 13: Constructing countermodel ... % 7.24/1.72 Prover 8: Warning: ignoring some quantifiers % 7.24/1.73 Prover 8: Constructing countermodel ... % 7.24/1.73 Prover 7: Constructing countermodel ... % 7.24/1.74 Prover 11: Constructing countermodel ... % 8.51/1.83 Prover 1: Found proof (size 77) % 8.51/1.83 Prover 1: proved (1226ms) % 8.51/1.83 Prover 10: stopped % 8.51/1.83 Prover 8: stopped % 8.51/1.83 Prover 7: stopped % 8.51/1.84 Prover 11: stopped % 8.51/1.84 Prover 13: stopped % 8.58/1.85 Prover 4: stopped % 8.58/1.85 % 8.58/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.58/1.85 % 8.58/1.87 % SZS output start Proof for theBenchmark % 8.58/1.87 Assumptions after simplification: % 8.58/1.87 --------------------------------- % 8.58/1.87 % 8.58/1.87 (ass(cond(33, 0), 0)) % 8.58/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.58/1.90 (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.58/1.90 $i(v0) | ? [v5: $i] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4 & $i(v5) & % 8.58/1.90 $i(v4))) % 8.58/1.90 % 8.58/1.90 (holds(284, 438, 1)) % 8.58/1.90 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.58/1.90 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & % 8.58/1.90 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 8.58/1.90 % 8.58/1.90 (holds(284, 438, 2)) % 8.58/1.90 $i(v1) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.58/1.90 (vmul(vd436, v1) = v2 & vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & % 8.58/1.90 vplus(v0, vd436) = v1 & $i(v2) & $i(v1) & $i(v0)) % 8.58/1.90 % 8.58/1.90 (holds(285, 440, 0)) % 8.58/1.90 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.58/1.90 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, % 8.58/1.90 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & % 8.58/1.90 $i(v2) & $i(v1) & $i(v0)) % 8.58/1.90 % 8.58/1.90 (holds(286, 441, 0)) % 8.58/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.58/1.91 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, % 8.58/1.91 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, % 8.58/1.91 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.58/1.91 % 8.58/1.91 (holds(286, 441, 1)) % 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.87/1.91 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & % 8.87/1.91 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) % 8.87/1.91 & $i(v0)) % 8.87/1.91 % 8.87/1.91 (holds(286, 441, 2)) % 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.87/1.91 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, % 8.87/1.91 vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, % 8.87/1.91 v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & % 8.87/1.91 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.91 % 8.87/1.91 (holds(286, 441, 3)) % 8.87/1.91 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 8.87/1.91 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) = % 8.87/1.91 v1 & vmul(vd436, vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 % 8.87/1.91 & vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 8.87/1.91 $i(v2) & $i(v1) & $i(v0)) % 8.87/1.91 % 8.87/1.91 (function-axioms) % 8.87/1.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.87/1.92 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0: % 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.87/1.92 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0: % 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.87/1.92 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 8.87/1.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.87/1.92 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : ! % 8.87/1.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ % 8.87/1.92 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 8.87/1.92 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] % 8.87/1.92 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ % 8.87/1.92 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 8.87/1.92 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) % 8.87/1.92 % 8.87/1.92 Further assumptions not needed in the proof: % 8.87/1.92 -------------------------------------------- % 8.87/1.92 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(241, % 8.87/1.92 0), 0), ass(cond(253, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), % 8.87/1.92 ass(cond(61, 0), 0), holds(284, 438, 0), qu(cond(conseq(axiom(3)), 3), % 8.87/1.92 and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), % 8.87/1.92 qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), % 8.87/1.92 holds(definiens(249), 398, 0))) % 8.87/1.92 % 8.87/1.92 Those formulas are unsatisfiable: % 8.87/1.92 --------------------------------- % 8.87/1.92 % 8.87/1.92 Begin of proof % 8.87/1.92 | % 8.87/1.92 | ALPHA: (holds(286, 441, 2)) implies: % 8.87/1.92 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.87/1.92 | ? [v5: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 & % 8.87/1.92 | vmul(vd436, vd437) = v3 & vplus(v5, vd436) = v2 & vplus(v3, v4) = v5 % 8.87/1.92 | & vplus(v1, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v5) & $i(v4) % 8.87/1.92 | & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.92 | % 8.87/1.92 | ALPHA: (holds(286, 441, 1)) implies: % 8.87/1.93 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1 % 8.87/1.93 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2 % 8.87/1.93 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (holds(286, 441, 0)) implies: % 8.87/1.93 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.87/1.93 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 & % 8.87/1.93 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) = % 8.87/1.93 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (holds(285, 440, 0)) implies: % 8.87/1.93 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436, % 8.87/1.93 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 & % 8.87/1.93 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & % 8.87/1.93 | $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (holds(284, 438, 2)) implies: % 8.87/1.93 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vmul(vd436, v1) = v2 & % 8.87/1.93 | vmul(vd436, vd437) = v0 & vplus(v0, v2) = v1 & vplus(v0, vd436) = v1 % 8.87/1.93 | & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (holds(284, 438, 1)) implies: % 8.87/1.93 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 & % 8.87/1.93 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) = % 8.87/1.93 | v1 & $i(v2) & $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (holds(286, 441, 3)) implies: % 8.87/1.93 | (7) $i(vd436) % 8.87/1.93 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 8.87/1.93 | ? [v5: $i] : ( ~ (v5 = v3) & vmul(vd436, vd439) = v1 & vmul(vd436, % 8.87/1.93 | vd437) = v0 & vplus(v2, vd436) = v3 & vplus(v1, vd436) = v4 & % 8.87/1.93 | vplus(v0, v4) = v5 & vplus(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 8.87/1.93 | $i(v2) & $i(v1) & $i(v0)) % 8.87/1.93 | % 8.87/1.93 | ALPHA: (function-axioms) implies: % 8.87/1.93 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.87/1.93 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) % 8.87/1.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.87/1.93 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) % 8.87/1.93 | % 8.87/1.94 | DELTA: instantiating (6) with fresh symbols all_19_0, all_19_1, all_19_2 % 8.87/1.94 | gives: % 8.87/1.94 | (11) vsucc(vd437) = all_19_2 & vmul(vd436, all_19_2) = all_19_1 & % 8.87/1.94 | vmul(vd436, vd437) = all_19_0 & vplus(all_19_0, vd436) = all_19_1 & % 8.87/1.94 | $i(all_19_0) & $i(all_19_1) & $i(all_19_2) % 8.87/1.94 | % 8.87/1.94 | ALPHA: (11) implies: % 8.87/1.94 | (12) vmul(vd436, vd437) = all_19_0 % 8.87/1.94 | % 8.87/1.94 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1, all_23_2 % 8.87/1.94 | gives: % 8.87/1.94 | (13) vmul(vd436, v1) = all_23_0 & vmul(vd436, vd437) = all_23_2 & % 8.87/1.94 | vplus(all_23_2, all_23_0) = all_23_1 & vplus(all_23_2, vd436) = % 8.87/1.94 | all_23_1 & $i(all_23_0) & $i(all_23_1) & $i(all_23_2) % 8.87/1.94 | % 8.87/1.94 | ALPHA: (13) implies: % 8.87/1.94 | (14) $i(all_23_2) % 8.87/1.94 | (15) vmul(vd436, vd437) = all_23_2 % 8.87/1.94 | % 8.87/1.94 | DELTA: instantiating (2) with fresh symbols all_25_0, all_25_1, all_25_2, % 8.87/1.94 | all_25_3 gives: % 8.87/1.94 | (16) vsucc(all_25_3) = all_25_2 & vmul(vd436, all_25_2) = all_25_1 & % 8.87/1.94 | vmul(vd436, all_25_3) = all_25_0 & vplus(all_25_0, vd436) = all_25_1 & % 8.87/1.94 | vplus(vd437, vd439) = all_25_3 & $i(all_25_0) & $i(all_25_1) & % 8.87/1.94 | $i(all_25_2) & $i(all_25_3) % 8.87/1.94 | % 8.87/1.94 | ALPHA: (16) implies: % 8.87/1.94 | (17) vplus(vd437, vd439) = all_25_3 % 8.87/1.94 | (18) vplus(all_25_0, vd436) = all_25_1 % 8.87/1.94 | (19) vmul(vd436, all_25_3) = all_25_0 % 8.87/1.94 | % 8.87/1.94 | DELTA: instantiating (4) with fresh symbols all_27_0, all_27_1, all_27_2, % 8.87/1.94 | all_27_3 gives: % 8.87/1.94 | (20) vmul(vd436, all_27_3) = all_27_2 & vmul(vd436, vd439) = all_27_0 & % 8.87/1.94 | vmul(vd436, vd437) = all_27_1 & vplus(all_27_1, all_27_0) = all_27_2 & % 8.87/1.94 | vplus(vd437, vd439) = all_27_3 & $i(all_27_0) & $i(all_27_1) & % 8.87/1.94 | $i(all_27_2) & $i(all_27_3) % 8.87/1.94 | % 8.87/1.94 | ALPHA: (20) implies: % 8.87/1.94 | (21) vplus(vd437, vd439) = all_27_3 % 8.87/1.94 | (22) vplus(all_27_1, all_27_0) = all_27_2 % 8.87/1.94 | (23) vmul(vd436, vd437) = all_27_1 % 8.87/1.94 | (24) vmul(vd436, vd439) = all_27_0 % 8.87/1.94 | (25) vmul(vd436, all_27_3) = all_27_2 % 8.87/1.94 | % 8.87/1.94 | DELTA: instantiating (3) with fresh symbols all_29_0, all_29_1, all_29_2, % 8.87/1.94 | all_29_3, all_29_4 gives: % 8.87/1.94 | (26) vsucc(all_29_1) = all_29_0 & vsucc(vd439) = all_29_4 & vmul(vd436, % 8.87/1.94 | all_29_0) = all_29_2 & vmul(vd436, all_29_3) = all_29_2 & % 8.87/1.94 | vplus(vd437, all_29_4) = all_29_3 & vplus(vd437, vd439) = all_29_1 & % 8.87/1.94 | $i(all_29_0) & $i(all_29_1) & $i(all_29_2) & $i(all_29_3) & % 8.87/1.94 | $i(all_29_4) % 8.87/1.94 | % 8.87/1.94 | ALPHA: (26) implies: % 8.87/1.94 | (27) vplus(vd437, vd439) = all_29_1 % 8.87/1.94 | % 8.87/1.94 | DELTA: instantiating (8) with fresh symbols all_31_0, all_31_1, all_31_2, % 8.87/1.94 | all_31_3, all_31_4, all_31_5 gives: % 8.87/1.95 | (28) ~ (all_31_0 = all_31_2) & vmul(vd436, vd439) = all_31_4 & vmul(vd436, % 8.87/1.95 | vd437) = all_31_5 & vplus(all_31_3, vd436) = all_31_2 & % 8.87/1.95 | vplus(all_31_4, vd436) = all_31_1 & vplus(all_31_5, all_31_1) = % 8.87/1.95 | all_31_0 & vplus(all_31_5, all_31_4) = all_31_3 & $i(all_31_0) & % 8.87/1.95 | $i(all_31_1) & $i(all_31_2) & $i(all_31_3) & $i(all_31_4) & % 8.87/1.95 | $i(all_31_5) % 8.87/1.95 | % 8.87/1.95 | ALPHA: (28) implies: % 8.87/1.95 | (29) ~ (all_31_0 = all_31_2) % 8.87/1.95 | (30) $i(all_31_4) % 8.87/1.95 | (31) vplus(all_31_5, all_31_4) = all_31_3 % 8.87/1.95 | (32) vplus(all_31_5, all_31_1) = all_31_0 % 8.87/1.95 | (33) vplus(all_31_4, vd436) = all_31_1 % 8.87/1.95 | (34) vplus(all_31_3, vd436) = all_31_2 % 8.87/1.95 | (35) vmul(vd436, vd437) = all_31_5 % 8.87/1.95 | (36) vmul(vd436, vd439) = all_31_4 % 8.87/1.95 | % 8.87/1.95 | DELTA: instantiating (1) with fresh symbols all_33_0, all_33_1, all_33_2, % 8.87/1.95 | all_33_3, all_33_4, all_33_5 gives: % 8.87/1.95 | (37) vmul(vd436, all_33_5) = all_33_4 & vmul(vd436, vd439) = all_33_1 & % 8.87/1.95 | vmul(vd436, vd437) = all_33_2 & vplus(all_33_0, vd436) = all_33_3 & % 8.87/1.95 | vplus(all_33_2, all_33_1) = all_33_0 & vplus(all_33_4, vd436) = % 8.87/1.95 | all_33_3 & vplus(vd437, vd439) = all_33_5 & $i(all_33_0) & % 8.87/1.95 | $i(all_33_1) & $i(all_33_2) & $i(all_33_3) & $i(all_33_4) & % 8.87/1.95 | $i(all_33_5) % 8.87/1.95 | % 8.87/1.95 | ALPHA: (37) implies: % 8.87/1.95 | (38) vplus(vd437, vd439) = all_33_5 % 8.87/1.95 | (39) vplus(all_33_4, vd436) = all_33_3 % 8.87/1.95 | (40) vplus(all_33_2, all_33_1) = all_33_0 % 8.87/1.95 | (41) vmul(vd436, vd437) = all_33_2 % 8.87/1.95 | (42) vmul(vd436, vd439) = all_33_1 % 8.87/1.95 | (43) vmul(vd436, all_33_5) = all_33_4 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (9) with all_27_3, all_29_1, vd439, vd437, % 8.87/1.95 | simplifying with (21), (27) gives: % 8.87/1.95 | (44) all_29_1 = all_27_3 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (9) with all_29_1, all_33_5, vd439, vd437, % 8.87/1.95 | simplifying with (27), (38) gives: % 8.87/1.95 | (45) all_33_5 = all_29_1 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (9) with all_25_3, all_33_5, vd439, vd437, % 8.87/1.95 | simplifying with (17), (38) gives: % 8.87/1.95 | (46) all_33_5 = all_25_3 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (10) with all_23_2, all_27_1, vd437, vd436, % 8.87/1.95 | simplifying with (15), (23) gives: % 8.87/1.95 | (47) all_27_1 = all_23_2 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (10) with all_27_1, all_31_5, vd437, vd436, % 8.87/1.95 | simplifying with (23), (35) gives: % 8.87/1.95 | (48) all_31_5 = all_27_1 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (10) with all_31_5, all_33_2, vd437, vd436, % 8.87/1.95 | simplifying with (35), (41) gives: % 8.87/1.95 | (49) all_33_2 = all_31_5 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (10) with all_19_0, all_33_2, vd437, vd436, % 8.87/1.95 | simplifying with (12), (41) gives: % 8.87/1.95 | (50) all_33_2 = all_19_0 % 8.87/1.95 | % 8.87/1.95 | GROUND_INST: instantiating (10) with all_31_4, all_33_1, vd439, vd436, % 8.87/1.95 | simplifying with (36), (42) gives: % 8.87/1.96 | (51) all_33_1 = all_31_4 % 8.87/1.96 | % 8.87/1.96 | GROUND_INST: instantiating (10) with all_27_0, all_33_1, vd439, vd436, % 8.87/1.96 | simplifying with (24), (42) gives: % 8.87/1.96 | (52) all_33_1 = all_27_0 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (51), (52) imply: % 8.87/1.96 | (53) all_31_4 = all_27_0 % 8.87/1.96 | % 8.87/1.96 | SIMP: (53) implies: % 8.87/1.96 | (54) all_31_4 = all_27_0 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (49), (50) imply: % 8.87/1.96 | (55) all_31_5 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | SIMP: (55) implies: % 8.87/1.96 | (56) all_31_5 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (45), (46) imply: % 8.87/1.96 | (57) all_29_1 = all_25_3 % 8.87/1.96 | % 8.87/1.96 | SIMP: (57) implies: % 8.87/1.96 | (58) all_29_1 = all_25_3 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (48), (56) imply: % 8.87/1.96 | (59) all_27_1 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | SIMP: (59) implies: % 8.87/1.96 | (60) all_27_1 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (44), (58) imply: % 8.87/1.96 | (61) all_27_3 = all_25_3 % 8.87/1.96 | % 8.87/1.96 | SIMP: (61) implies: % 8.87/1.96 | (62) all_27_3 = all_25_3 % 8.87/1.96 | % 8.87/1.96 | COMBINE_EQS: (47), (60) imply: % 8.87/1.96 | (63) all_23_2 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | SIMP: (63) implies: % 8.87/1.96 | (64) all_23_2 = all_19_0 % 8.87/1.96 | % 8.87/1.96 | REDUCE: (43), (46) imply: % 8.87/1.96 | (65) vmul(vd436, all_25_3) = all_33_4 % 8.87/1.96 | % 8.87/1.96 | REDUCE: (25), (62) imply: % 8.87/1.96 | (66) vmul(vd436, all_25_3) = all_27_2 % 8.87/1.96 | % 8.87/1.96 | REDUCE: (40), (50), (52) imply: % 8.87/1.96 | (67) vplus(all_19_0, all_27_0) = all_33_0 % 8.87/1.96 | % 8.87/1.96 | REDUCE: (33), (54) imply: % 8.87/1.96 | (68) vplus(all_27_0, vd436) = all_31_1 % 8.87/1.96 | % 8.87/1.96 | REDUCE: (32), (56) imply: % 9.14/1.96 | (69) vplus(all_19_0, all_31_1) = all_31_0 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (31), (54), (56) imply: % 9.14/1.96 | (70) vplus(all_19_0, all_27_0) = all_31_3 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (22), (60) imply: % 9.14/1.96 | (71) vplus(all_19_0, all_27_0) = all_27_2 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (30), (54) imply: % 9.14/1.96 | (72) $i(all_27_0) % 9.14/1.96 | % 9.14/1.96 | REDUCE: (14), (64) imply: % 9.14/1.96 | (73) $i(all_19_0) % 9.14/1.96 | % 9.14/1.96 | GROUND_INST: instantiating (9) with all_31_3, all_33_0, all_27_0, all_19_0, % 9.14/1.96 | simplifying with (67), (70) gives: % 9.14/1.96 | (74) all_33_0 = all_31_3 % 9.14/1.96 | % 9.14/1.96 | GROUND_INST: instantiating (9) with all_27_2, all_33_0, all_27_0, all_19_0, % 9.14/1.96 | simplifying with (67), (71) gives: % 9.14/1.96 | (75) all_33_0 = all_27_2 % 9.14/1.96 | % 9.14/1.96 | GROUND_INST: instantiating (10) with all_25_0, all_33_4, all_25_3, vd436, % 9.14/1.96 | simplifying with (19), (65) gives: % 9.14/1.96 | (76) all_33_4 = all_25_0 % 9.14/1.96 | % 9.14/1.96 | GROUND_INST: instantiating (10) with all_27_2, all_33_4, all_25_3, vd436, % 9.14/1.96 | simplifying with (65), (66) gives: % 9.14/1.96 | (77) all_33_4 = all_27_2 % 9.14/1.96 | % 9.14/1.96 | COMBINE_EQS: (74), (75) imply: % 9.14/1.96 | (78) all_31_3 = all_27_2 % 9.14/1.96 | % 9.14/1.96 | SIMP: (78) implies: % 9.14/1.96 | (79) all_31_3 = all_27_2 % 9.14/1.96 | % 9.14/1.96 | COMBINE_EQS: (76), (77) imply: % 9.14/1.96 | (80) all_27_2 = all_25_0 % 9.14/1.96 | % 9.14/1.96 | SIMP: (80) implies: % 9.14/1.96 | (81) all_27_2 = all_25_0 % 9.14/1.96 | % 9.14/1.96 | COMBINE_EQS: (79), (81) imply: % 9.14/1.96 | (82) all_31_3 = all_25_0 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (39), (76) imply: % 9.14/1.96 | (83) vplus(all_25_0, vd436) = all_33_3 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (34), (82) imply: % 9.14/1.96 | (84) vplus(all_25_0, vd436) = all_31_2 % 9.14/1.96 | % 9.14/1.96 | REDUCE: (71), (81) imply: % 9.14/1.97 | (85) vplus(all_19_0, all_27_0) = all_25_0 % 9.14/1.97 | % 9.14/1.97 | GROUND_INST: instantiating (9) with all_25_1, all_33_3, vd436, all_25_0, % 9.14/1.97 | simplifying with (18), (83) gives: % 9.14/1.97 | (86) all_33_3 = all_25_1 % 9.14/1.97 | % 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_2, all_33_3, vd436, all_25_0, % 9.14/1.97 | simplifying with (83), (84) gives: % 9.14/1.97 | (87) all_33_3 = all_31_2 % 9.14/1.97 | % 9.14/1.97 | COMBINE_EQS: (86), (87) imply: % 9.14/1.97 | (88) all_31_2 = all_25_1 % 9.14/1.97 | % 9.14/1.97 | REDUCE: (29), (88) imply: % 9.14/1.97 | (89) ~ (all_31_0 = all_25_1) % 9.14/1.97 | % 9.14/1.97 | GROUND_INST: instantiating (ass(cond(33, 0), 0)) with all_19_0, all_27_0, % 9.14/1.97 | vd436, all_25_0, all_25_1, simplifying with (7), (18), (72), % 9.14/1.97 | (73), (85) gives: % 9.14/1.97 | (90) ? [v0: $i] : (vplus(all_27_0, vd436) = v0 & vplus(all_19_0, v0) = % 9.14/1.97 | all_25_1 & $i(v0) & $i(all_25_1)) % 9.14/1.97 | % 9.14/1.97 | DELTA: instantiating (90) with fresh symbol all_53_0 gives: % 9.14/1.97 | (91) vplus(all_27_0, vd436) = all_53_0 & vplus(all_19_0, all_53_0) = % 9.14/1.97 | all_25_1 & $i(all_53_0) & $i(all_25_1) % 9.14/1.97 | % 9.14/1.97 | ALPHA: (91) implies: % 9.14/1.97 | (92) vplus(all_19_0, all_53_0) = all_25_1 % 9.14/1.97 | (93) vplus(all_27_0, vd436) = all_53_0 % 9.14/1.97 | % 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_1, all_53_0, vd436, all_27_0, % 9.14/1.97 | simplifying with (68), (93) gives: % 9.14/1.97 | (94) all_53_0 = all_31_1 % 9.14/1.97 | % 9.14/1.97 | REDUCE: (92), (94) imply: % 9.14/1.97 | (95) vplus(all_19_0, all_31_1) = all_25_1 % 9.14/1.97 | % 9.14/1.97 | GROUND_INST: instantiating (9) with all_31_0, all_25_1, all_31_1, all_19_0, % 9.14/1.97 | simplifying with (69), (95) gives: % 9.14/1.97 | (96) all_31_0 = all_25_1 % 9.14/1.97 | % 9.14/1.97 | REDUCE: (89), (96) imply: % 9.14/1.97 | (97) $false % 9.14/1.97 | % 9.14/1.97 | CLOSE: (97) is inconsistent. % 9.14/1.97 | % 9.14/1.97 End of proof % 9.14/1.97 % SZS output end Proof for theBenchmark % 9.14/1.97 % 9.14/1.97 1383ms %------------------------------------------------------------------------------