%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO277+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 23:22:54 EDT 2023 % Result : Theorem 38.43s 5.72s % Output : Proof 55.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO277+1 : TPTP v8.1.2. Released v4.1.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n029.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 : Wed Aug 30 00:02:57 EDT 2023 % 0.13/0.34 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.64/0.61 Running up to 7 provers in parallel. % 0.64/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.64/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.64/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.64/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.64/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.64/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.64/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 6.78/1.67 Prover 1: Preprocessing ... % 8.10/1.80 Prover 4: Preprocessing ... % 8.21/1.82 Prover 2: Preprocessing ... % 8.21/1.82 Prover 5: Preprocessing ... % 8.21/1.82 Prover 0: Preprocessing ... % 8.21/1.82 Prover 3: Preprocessing ... % 8.21/1.83 Prover 6: Preprocessing ... % 22.72/3.73 Prover 3: Constructing countermodel ... % 22.72/3.76 Prover 1: Constructing countermodel ... % 24.33/3.90 Prover 6: Proving ... % 24.91/4.01 Prover 2: Proving ... % 26.19/4.18 Prover 5: Proving ... % 38.43/5.71 Prover 3: proved (5086ms) % 38.43/5.71 % 38.43/5.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 38.43/5.72 % 38.43/5.72 Prover 6: stopped % 38.43/5.74 Prover 2: stopped % 38.43/5.74 Prover 5: stopped % 38.43/5.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 38.43/5.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 38.43/5.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 38.43/5.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.01/5.84 Prover 4: Constructing countermodel ... % 41.33/6.09 Prover 10: Preprocessing ... % 41.33/6.17 Prover 7: Preprocessing ... % 42.37/6.23 Prover 11: Preprocessing ... % 42.37/6.25 Prover 8: Preprocessing ... % 42.37/6.26 Prover 0: Proving ... % 42.37/6.28 Prover 0: stopped % 42.37/6.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 43.05/6.39 Prover 10: Warning: ignoring some quantifiers % 43.72/6.42 Prover 10: Constructing countermodel ... % 44.40/6.55 Prover 13: Preprocessing ... % 46.10/6.74 Prover 8: Warning: ignoring some quantifiers % 46.10/6.76 Prover 8: Constructing countermodel ... % 47.89/6.96 Prover 13: Warning: ignoring some quantifiers % 48.45/7.03 Prover 13: Constructing countermodel ... % 48.45/7.04 Prover 7: Warning: ignoring some quantifiers % 49.00/7.09 Prover 7: Constructing countermodel ... % 49.74/7.18 Prover 1: Found proof (size 51) % 49.74/7.18 Prover 1: proved (6562ms) % 49.74/7.18 Prover 7: stopped % 49.74/7.18 Prover 10: stopped % 49.74/7.18 Prover 8: stopped % 49.94/7.22 Prover 13: stopped % 51.65/7.59 Prover 4: stopped % 54.18/8.19 Prover 11: Constructing countermodel ... % 54.46/8.22 Prover 11: stopped % 54.46/8.22 % 54.46/8.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 54.46/8.22 % 54.46/8.24 % SZS output start Proof for theBenchmark % 54.46/8.25 Assumptions after simplification: % 54.46/8.25 --------------------------------- % 54.46/8.25 % 54.46/8.25 (and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))) % 54.73/8.29 ron(vd1089, vd1099) = 0 & ron(vd1085, vd1099) = 0 & rline(vd1099) = 0 & % 54.73/8.29 $i(vd1099) & $i(vd1089) & $i(vd1085) % 54.73/8.29 % 54.73/8.29 (holds(226, 1090, 0)) % 54.73/8.29 $i(vd1080) & $i(vd1089) & $i(vd1085) & ? [v0: $i] : (vf(vd1089, vd1080) = v0 % 54.73/8.29 & vf(vd1089, vd1085) = v0 & $i(v0)) % 54.73/8.29 % 54.73/8.29 (holds(226, 1090, 1)) % 54.73/8.30 $i(vd1080) & $i(vd1089) & $i(vd1085) & ? [v0: $i] : (vf(vd1089, vd1080) = v0 % 54.73/8.30 & vf(vd1085, vd1080) = v0 & $i(v0)) % 54.73/8.30 % 54.73/8.30 (holds(conjunct1(225), 1087, 0)) % 54.73/8.30 ~ (vd1080 = vd1085) & $i(vd1080) & $i(vd1085) % 54.73/8.30 % 54.73/8.30 (pred(225, 1)) % 54.73/8.30 rpoint(vd1086) = 0 & $i(vd1086) % 54.73/8.30 % 54.73/8.30 (pred(225, 4)) % 54.73/8.30 vd1086 = vd1085 & $i(vd1085) % 54.73/8.30 % 54.73/8.30 (pred(226, 0)) % 54.73/8.30 rpoint(vd1089) = 0 & $i(vd1089) % 54.73/8.30 % 54.73/8.30 (qe(s1(plural(224)))) % 54.73/8.30 rpoint(vd1080) = 0 & $i(vd1080) % 54.73/8.30 % 54.73/8.30 (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))) % 54.73/8.30 $i(v0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vf(v0, v1) = v2) | ~ % 54.73/8.30 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = % 54.73/8.30 v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0))) % 54.73/8.30 % 54.73/8.30 (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))) % 54.73/8.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = v0 | % 54.73/8.31 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v3) = 0) | ~ % 54.73/8.31 (ron(v0, v2) = 0) | ~ (rline(v3) = 0) | ~ (rline(v2) = 0) | ~ $i(v3) | ~ % 54.73/8.31 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (ron(v1, v2) % 54.73/8.31 = v4 & ron(v0, v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 54.73/8.31 % 54.73/8.31 (qu(theu(the(230), 1), imp(the(230)))) % 54.73/8.31 $i(vd1099) & $i(vd1089) & $i(vd1085) & ? [v0: $i] : ( ~ (v0 = vd1099) & % 54.73/8.31 ron(vd1089, v0) = 0 & ron(vd1085, v0) = 0 & rline(v0) = 0 & $i(v0)) % 54.73/8.31 % 54.73/8.31 (function-axioms) % 54.73/8.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 54.73/8.33 $i] : (v1 = v0 | ~ (vskolem1052(v5, v4, v3, v2) = v1) | ~ (vskolem1052(v5, % 54.73/8.33 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 54.73/8.33 $i] : ! [v4: $i] : (v1 = v0 | ~ (vtriangle(v4, v3, v2) = v1) | ~ % 54.73/8.33 (vtriangle(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 54.73/8.33 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, % 54.73/8.33 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 54.73/8.33 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | % 54.73/8.33 ~ (rS(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 54.73/8.33 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ % 54.73/8.33 (vangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 54.73/8.33 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 54.73/8.33 (rR(v4, v3, v2) = v1) | ~ (rR(v4, v3, v2) = v0)) & ! [v0: % 54.73/8.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 54.73/8.33 : (v1 = v0 | ~ (rgeq(v3, v2) = v1) | ~ (rgeq(v3, v2) = v0)) & ! [v0: % 54.73/8.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 54.73/8.33 : (v1 = v0 | ~ (rless(v3, v2) = v1) | ~ (rless(v3, v2) = v0)) & ! [v0: % 54.73/8.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 54.73/8.33 : (v1 = v0 | ~ (rintersect(v3, v2) = v1) | ~ (rintersect(v3, v2) = v0)) & ! % 54.73/8.33 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 54.73/8.33 $i] : (v1 = v0 | ~ (rleq(v3, v2) = v1) | ~ (rleq(v3, v2) = v0)) & ! [v0: % 54.73/8.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) % 54.73/8.33 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 54.73/8.33 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rinside(v3, % 54.73/8.33 v2) = v1) | ~ (rinside(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 54.73/8.33 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 54.73/8.33 (rcenter(v3, v2) = v1) | ~ (rcenter(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 54.73/8.33 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ % 54.73/8.33 (vf(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 54.73/8.33 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, % 54.73/8.33 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 54.73/8.33 ! [v2: $i] : (v1 = v0 | ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & % 54.73/8.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 54.73/8.33 v0 | ~ (rreal(v2) = v1) | ~ (rreal(v2) = v0)) & ! [v0: MultipleValueBool] % 54.73/8.33 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rcircle(v2) = v1) % 54.73/8.33 | ~ (rcircle(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 54.73/8.33 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | ~ % 54.73/8.33 (rpoint(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 54.73/8.33 : ! [v2: $i] : (v1 = v0 | ~ (rline(v2) = v1) | ~ (rline(v2) = v0)) % 54.73/8.33 % 54.73/8.33 Further assumptions not needed in the proof: % 54.73/8.33 -------------------------------------------- % 54.73/8.33 ass(cond(156, 0), 0), ass(cond(goal(206), 0), 0), ass(cond(goal(206), 0), 1), % 54.73/8.33 ass(cond(goal(206), 0), 2), holds(conjunct2(225), 1088, 0), % 54.73/8.33 holds(conjunct2(comma_conjunct2(229)), 1097, 0), pred(224, 5), pred(229, 0), % 54.73/8.33 pred(axiom(137), 1), pred(axiom(137), 2), pred(axiom(5), 0), % 54.73/8.33 pred(comma_conjunct1(229), 0), pred(conjunct1(comma_conjunct2(229)), 0), % 54.73/8.33 qe(s2(plural(224))), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), % 54.73/8.33 qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), qu(cond(axiom(103), 0), % 54.73/8.33 imp(cond(axiom(103), 0))), qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), % 54.73/8.33 qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), qu(cond(axiom(109), 0), % 54.73/8.33 imp(cond(axiom(109), 0))), qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), % 54.73/8.33 qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), qu(cond(axiom(113), 0), % 54.73/8.33 imp(cond(axiom(113), 0))), qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), % 54.73/8.33 qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), qu(cond(axiom(119), 0), % 54.73/8.33 imp(cond(axiom(119), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), % 54.73/8.33 qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(125), 0), % 54.73/8.33 imp(cond(axiom(125), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), % 54.73/8.33 qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(13), 0), % 54.73/8.33 imp(cond(axiom(13), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), % 54.73/8.33 qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(135), 0), % 54.73/8.33 imp(cond(axiom(135), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), % 54.73/8.33 qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(143), 0), % 54.73/8.33 imp(cond(axiom(143), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), % 54.73/8.33 qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(149), 0), % 54.73/8.33 imp(cond(axiom(149), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), % 54.73/8.33 qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), qu(cond(axiom(153), 0), % 54.73/8.33 imp(cond(axiom(153), 0))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), % 54.73/8.33 qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), qu(cond(axiom(166), 0), % 54.73/8.33 imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), % 54.73/8.33 qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), qu(cond(axiom(170), 0), % 54.73/8.33 imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), % 54.73/8.33 qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), qu(cond(axiom(176), 0), % 54.73/8.33 imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), % 54.73/8.33 qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), qu(cond(axiom(182), 0), % 54.73/8.33 imp(cond(axiom(182), 0))), qu(cond(axiom(184), 0), imp(cond(axiom(184), 0))), % 54.73/8.33 qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(188), 0), % 54.73/8.33 imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), % 54.73/8.33 qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(192), 0), % 54.73/8.33 imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), % 54.73/8.33 qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(198), 0), % 54.73/8.33 imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), % 54.73/8.33 qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(204), 0), % 54.73/8.33 imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), % 54.73/8.33 qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(25), 0), % 54.73/8.33 imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), % 54.73/8.33 qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(3), 0), % 54.73/8.33 imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), % 54.73/8.33 qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(35), 0), % 54.73/8.33 imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), % 54.73/8.33 qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(41), 0), % 54.73/8.33 imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), % 54.73/8.33 qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(47), 0), % 54.73/8.33 imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), % 54.73/8.33 qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(53), 0), % 54.73/8.33 imp(cond(axiom(53), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), % 54.73/8.33 qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(59), 0), % 54.73/8.33 imp(cond(axiom(59), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), % 54.73/8.33 qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(65), 0), % 54.73/8.33 imp(cond(axiom(65), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), % 54.73/8.33 qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(7), 0), % 54.73/8.33 imp(cond(axiom(7), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), % 54.73/8.33 qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), % 54.73/8.33 imp(cond(axiom(77), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), % 54.73/8.33 qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), % 54.73/8.33 imp(cond(axiom(83), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), % 54.73/8.33 qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), % 54.73/8.33 imp(cond(axiom(89), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), % 54.73/8.33 qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), % 54.73/8.33 imp(cond(axiom(93), 0))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), % 54.73/8.33 qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), % 54.73/8.33 imp(cond(axiom(99), 0))), replace(pred(227, 2)), replace(pred(228, 2)), % 54.73/8.33 replace(qu(theu(the(227), 1), imp(the(227)))), replace(qu(theu(the(228), 1), % 54.73/8.33 imp(the(228)))), replace(replace(and(pred(comma_conjunct2(the(228)), 0), % 54.73/8.33 and(pred(comma_conjunct1(the(228)), 0), pred(the(228), 0))))), % 54.73/8.33 replace(replace(and(pred(s2(plural(the(227))), 0), % 54.73/8.33 and(pred(s1(plural(the(227))), 0), pred(the(227), 0))))) % 54.73/8.33 % 54.73/8.33 Those formulas are unsatisfiable: % 54.73/8.33 --------------------------------- % 54.73/8.33 % 54.73/8.33 Begin of proof % 54.73/8.33 | % 54.73/8.33 | ALPHA: (and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), % 54.73/8.33 | pred(the(230), 0)))) implies: % 54.73/8.34 | (1) rline(vd1099) = 0 % 54.73/8.34 | (2) ron(vd1085, vd1099) = 0 % 54.73/8.34 | (3) ron(vd1089, vd1099) = 0 % 54.73/8.34 | % 54.73/8.34 | ALPHA: (pred(226, 0)) implies: % 54.73/8.34 | (4) rpoint(vd1089) = 0 % 54.73/8.34 | % 54.73/8.34 | ALPHA: (pred(225, 4)) implies: % 54.73/8.34 | (5) vd1086 = vd1085 % 54.73/8.34 | % 54.73/8.34 | ALPHA: (pred(225, 1)) implies: % 54.73/8.34 | (6) $i(vd1086) % 54.73/8.34 | (7) rpoint(vd1086) = 0 % 54.73/8.34 | % 54.73/8.34 | ALPHA: (holds(226, 1090, 1)) implies: % 54.73/8.34 | (8) ? [v0: $i] : (vf(vd1089, vd1080) = v0 & vf(vd1085, vd1080) = v0 & % 54.73/8.34 | $i(v0)) % 54.73/8.34 | % 54.73/8.34 | ALPHA: (holds(226, 1090, 0)) implies: % 54.73/8.34 | (9) ? [v0: $i] : (vf(vd1089, vd1080) = v0 & vf(vd1089, vd1085) = v0 & % 54.73/8.34 | $i(v0)) % 54.73/8.34 | % 54.73/8.34 | ALPHA: (holds(conjunct1(225), 1087, 0)) implies: % 54.73/8.34 | (10) ~ (vd1080 = vd1085) % 54.73/8.34 | % 54.73/8.34 | ALPHA: (qe(s1(plural(224)))) implies: % 54.73/8.34 | (11) $i(vd1080) % 54.73/8.34 | (12) rpoint(vd1080) = 0 % 54.73/8.34 | % 54.73/8.34 | ALPHA: (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))) implies: % 54.73/8.34 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vf(v0, v1) = v2) | ~ % 54.73/8.34 | (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ $i(v1) | ~ $i(v0) | (( % 54.73/8.34 | ~ (v2 = v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0))) % 54.73/8.34 | % 54.73/8.34 | ALPHA: (qu(theu(the(230), 1), imp(the(230)))) implies: % 54.73/8.34 | (14) $i(vd1089) % 54.73/8.34 | (15) $i(vd1099) % 54.73/8.34 | (16) ? [v0: $i] : ( ~ (v0 = vd1099) & ron(vd1089, v0) = 0 & ron(vd1085, % 54.73/8.34 | v0) = 0 & rline(v0) = 0 & $i(v0)) % 54.73/8.34 | % 54.73/8.34 | ALPHA: (function-axioms) implies: % 54.73/8.34 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 54.73/8.34 | : ! [v3: $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = % 54.73/8.34 | v0)) % 54.73/8.34 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 54.73/8.34 | (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) % 54.73/8.34 | % 54.73/8.34 | DELTA: instantiating (8) with fresh symbol all_106_0 gives: % 54.73/8.34 | (19) vf(vd1089, vd1080) = all_106_0 & vf(vd1085, vd1080) = all_106_0 & % 54.73/8.34 | $i(all_106_0) % 54.73/8.35 | % 54.73/8.35 | ALPHA: (19) implies: % 54.73/8.35 | (20) vf(vd1085, vd1080) = all_106_0 % 54.73/8.35 | (21) vf(vd1089, vd1080) = all_106_0 % 54.73/8.35 | % 54.73/8.35 | DELTA: instantiating (9) with fresh symbol all_108_0 gives: % 54.73/8.35 | (22) vf(vd1089, vd1080) = all_108_0 & vf(vd1089, vd1085) = all_108_0 & % 54.73/8.35 | $i(all_108_0) % 54.73/8.35 | % 54.73/8.35 | ALPHA: (22) implies: % 54.73/8.35 | (23) vf(vd1089, vd1085) = all_108_0 % 54.73/8.35 | (24) vf(vd1089, vd1080) = all_108_0 % 54.73/8.35 | % 54.73/8.35 | DELTA: instantiating (16) with fresh symbol all_110_0 gives: % 54.73/8.35 | (25) ~ (all_110_0 = vd1099) & ron(vd1089, all_110_0) = 0 & ron(vd1085, % 54.73/8.35 | all_110_0) = 0 & rline(all_110_0) = 0 & $i(all_110_0) % 54.73/8.35 | % 54.73/8.35 | ALPHA: (25) implies: % 54.73/8.35 | (26) ~ (all_110_0 = vd1099) % 54.73/8.35 | (27) $i(all_110_0) % 54.73/8.35 | (28) rline(all_110_0) = 0 % 54.73/8.35 | (29) ron(vd1085, all_110_0) = 0 % 54.73/8.35 | (30) ron(vd1089, all_110_0) = 0 % 54.73/8.35 | % 54.73/8.35 | REDUCE: (5), (7) imply: % 54.73/8.35 | (31) rpoint(vd1085) = 0 % 54.73/8.35 | % 54.73/8.35 | REDUCE: (5), (6) imply: % 54.73/8.35 | (32) $i(vd1085) % 54.73/8.35 | % 54.73/8.35 | GROUND_INST: instantiating (18) with all_106_0, all_108_0, vd1080, vd1089, % 54.73/8.35 | simplifying with (21), (24) gives: % 54.73/8.35 | (33) all_108_0 = all_106_0 % 54.73/8.35 | % 54.73/8.35 | REDUCE: (23), (33) imply: % 54.73/8.35 | (34) vf(vd1089, vd1085) = all_106_0 % 54.73/8.35 | % 54.73/8.35 | GROUND_INST: instantiating (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))) % 54.73/8.35 | with vd1089, vd1085, all_110_0, vd1099, simplifying with (1), % 54.73/8.35 | (2), (4), (14), (15), (27), (28), (30), (31), (32) gives: % 54.73/8.35 | (35) all_110_0 = vd1099 | vd1089 = vd1085 | ? [v0: any] : ? [v1: any] : % 54.73/8.35 | (ron(vd1089, vd1099) = v1 & ron(vd1085, all_110_0) = v0 & ( ~ (v1 = 0) % 54.73/8.35 | | ~ (v0 = 0))) % 54.73/8.35 | % 54.73/8.35 | GROUND_INST: instantiating (13) with vd1085, vd1080, all_106_0, simplifying % 54.73/8.35 | with (11), (12), (20), (31), (32) gives: % 54.73/8.35 | (36) ( ~ (all_106_0 = v0) | vd1080 = vd1085) & ( ~ (vd1080 = vd1085) | % 54.73/8.35 | all_106_0 = v0) % 54.73/8.35 | % 54.73/8.35 | ALPHA: (36) implies: % 54.73/8.35 | (37) ~ (all_106_0 = v0) | vd1080 = vd1085 % 54.73/8.35 | % 54.73/8.35 | GROUND_INST: instantiating (13) with vd1089, vd1085, all_106_0, simplifying % 54.73/8.35 | with (4), (14), (31), (32), (34) gives: % 54.73/8.35 | (38) ( ~ (all_106_0 = v0) | vd1089 = vd1085) & ( ~ (vd1089 = vd1085) | % 54.73/8.35 | all_106_0 = v0) % 54.73/8.35 | % 54.73/8.35 | ALPHA: (38) implies: % 54.73/8.35 | (39) ~ (vd1089 = vd1085) | all_106_0 = v0 % 54.73/8.35 | % 54.73/8.35 | BETA: splitting (35) gives: % 54.73/8.35 | % 54.73/8.35 | Case 1: % 54.73/8.35 | | % 54.73/8.35 | | (40) vd1089 = vd1085 % 54.73/8.35 | | % 54.73/8.35 | | BETA: splitting (39) gives: % 54.73/8.35 | | % 54.73/8.35 | | Case 1: % 54.73/8.35 | | | % 54.73/8.35 | | | (41) ~ (vd1089 = vd1085) % 54.73/8.35 | | | % 54.73/8.35 | | | REDUCE: (40), (41) imply: % 54.73/8.35 | | | (42) $false % 54.73/8.36 | | | % 54.73/8.36 | | | CLOSE: (42) is inconsistent. % 54.73/8.36 | | | % 54.73/8.36 | | Case 2: % 54.73/8.36 | | | % 54.73/8.36 | | | (43) all_106_0 = v0 % 54.73/8.36 | | | % 54.73/8.36 | | | BETA: splitting (37) gives: % 54.73/8.36 | | | % 54.73/8.36 | | | Case 1: % 54.73/8.36 | | | | % 54.73/8.36 | | | | (44) ~ (all_106_0 = v0) % 54.73/8.36 | | | | % 54.73/8.36 | | | | REDUCE: (43), (44) imply: % 54.73/8.36 | | | | (45) $false % 54.73/8.36 | | | | % 54.73/8.36 | | | | CLOSE: (45) is inconsistent. % 54.73/8.36 | | | | % 54.73/8.36 | | | Case 2: % 54.73/8.36 | | | | % 54.73/8.36 | | | | (46) vd1080 = vd1085 % 54.73/8.36 | | | | % 54.73/8.36 | | | | REDUCE: (10), (46) imply: % 54.73/8.36 | | | | (47) $false % 54.73/8.36 | | | | % 54.73/8.36 | | | | CLOSE: (47) is inconsistent. % 54.73/8.36 | | | | % 54.73/8.36 | | | End of split % 54.73/8.36 | | | % 54.73/8.36 | | End of split % 54.73/8.36 | | % 54.73/8.36 | Case 2: % 54.73/8.36 | | % 54.73/8.36 | | (48) all_110_0 = vd1099 | ? [v0: any] : ? [v1: any] : (ron(vd1089, % 54.73/8.36 | | vd1099) = v1 & ron(vd1085, all_110_0) = v0 & ( ~ (v1 = 0) | ~ % 54.73/8.36 | | (v0 = 0))) % 54.73/8.36 | | % 54.73/8.36 | | BETA: splitting (48) gives: % 54.73/8.36 | | % 54.73/8.36 | | Case 1: % 54.73/8.36 | | | % 54.73/8.36 | | | (49) all_110_0 = vd1099 % 54.73/8.36 | | | % 54.73/8.36 | | | REDUCE: (26), (49) imply: % 54.73/8.36 | | | (50) $false % 54.73/8.36 | | | % 54.73/8.36 | | | CLOSE: (50) is inconsistent. % 54.73/8.36 | | | % 54.73/8.36 | | Case 2: % 54.73/8.36 | | | % 54.73/8.36 | | | (51) ? [v0: any] : ? [v1: any] : (ron(vd1089, vd1099) = v1 & % 54.73/8.36 | | | ron(vd1085, all_110_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 54.73/8.36 | | | % 54.73/8.36 | | | DELTA: instantiating (51) with fresh symbols all_341_0, all_341_1 gives: % 54.73/8.36 | | | (52) ron(vd1089, vd1099) = all_341_0 & ron(vd1085, all_110_0) = % 54.73/8.36 | | | all_341_1 & ( ~ (all_341_0 = 0) | ~ (all_341_1 = 0)) % 54.73/8.36 | | | % 54.73/8.36 | | | ALPHA: (52) implies: % 54.73/8.36 | | | (53) ron(vd1085, all_110_0) = all_341_1 % 55.17/8.36 | | | (54) ron(vd1089, vd1099) = all_341_0 % 55.17/8.36 | | | (55) ~ (all_341_0 = 0) | ~ (all_341_1 = 0) % 55.17/8.36 | | | % 55.17/8.36 | | | GROUND_INST: instantiating (17) with 0, all_341_1, all_110_0, vd1085, % 55.17/8.36 | | | simplifying with (29), (53) gives: % 55.17/8.36 | | | (56) all_341_1 = 0 % 55.17/8.36 | | | % 55.17/8.36 | | | GROUND_INST: instantiating (17) with 0, all_341_0, vd1099, vd1089, % 55.17/8.36 | | | simplifying with (3), (54) gives: % 55.17/8.36 | | | (57) all_341_0 = 0 % 55.17/8.36 | | | % 55.17/8.36 | | | BETA: splitting (55) gives: % 55.17/8.36 | | | % 55.17/8.36 | | | Case 1: % 55.17/8.36 | | | | % 55.17/8.36 | | | | (58) ~ (all_341_0 = 0) % 55.17/8.36 | | | | % 55.17/8.36 | | | | REDUCE: (57), (58) imply: % 55.17/8.36 | | | | (59) $false % 55.17/8.36 | | | | % 55.17/8.36 | | | | CLOSE: (59) is inconsistent. % 55.17/8.36 | | | | % 55.17/8.36 | | | Case 2: % 55.17/8.36 | | | | % 55.17/8.36 | | | | (60) ~ (all_341_1 = 0) % 55.17/8.36 | | | | % 55.17/8.36 | | | | REDUCE: (56), (60) imply: % 55.17/8.36 | | | | (61) $false % 55.17/8.36 | | | | % 55.17/8.36 | | | | CLOSE: (61) is inconsistent. % 55.17/8.36 | | | | % 55.17/8.36 | | | End of split % 55.17/8.36 | | | % 55.17/8.36 | | End of split % 55.17/8.36 | | % 55.17/8.36 | End of split % 55.17/8.36 | % 55.17/8.36 End of proof % 55.17/8.36 % SZS output end Proof for theBenchmark % 55.17/8.36 % 55.17/8.36 7758ms %------------------------------------------------------------------------------