%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO274+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 : n002.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 31.80s 5.01s % Output : Proof 40.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO274+1 : TPTP v8.1.2. Released v4.1.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.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 : Tue Aug 29 23:21:50 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 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 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 8.45/1.91 Prover 4: Preprocessing ... % 8.45/2.01 Prover 1: Preprocessing ... % 8.45/2.01 Prover 5: Preprocessing ... % 8.45/2.01 Prover 6: Preprocessing ... % 8.45/2.01 Prover 3: Preprocessing ... % 8.45/2.01 Prover 0: Preprocessing ... % 8.45/2.02 Prover 2: Preprocessing ... % 21.26/3.58 Prover 3: Constructing countermodel ... % 21.26/3.60 Prover 1: Constructing countermodel ... % 21.92/3.64 Prover 6: Proving ... % 22.76/3.89 Prover 2: Proving ... % 24.88/4.05 Prover 5: Proving ... % 31.80/5.01 Prover 3: proved (4361ms) % 31.80/5.01 % 31.80/5.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.80/5.01 % 31.80/5.01 Prover 6: stopped % 31.80/5.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 31.80/5.01 Prover 2: stopped % 31.80/5.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 32.54/5.03 Prover 5: stopped % 32.54/5.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 32.54/5.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 35.80/5.47 Prover 10: Preprocessing ... % 35.80/5.47 Prover 8: Preprocessing ... % 36.09/5.49 Prover 11: Preprocessing ... % 36.09/5.49 Prover 7: Preprocessing ... % 36.09/5.52 Prover 4: Constructing countermodel ... % 36.44/5.57 Prover 1: Found proof (size 57) % 36.44/5.57 Prover 1: proved (4943ms) % 36.44/5.59 Prover 4: stopped % 36.44/5.59 Prover 10: stopped % 36.44/5.60 Prover 7: stopped % 37.30/5.79 Prover 11: stopped % 38.31/5.87 Prover 8: Warning: ignoring some quantifiers % 38.56/5.89 Prover 8: Constructing countermodel ... % 38.56/5.90 Prover 8: stopped % 39.29/6.08 Prover 0: Proving ... % 39.29/6.09 Prover 0: stopped % 39.29/6.09 % 39.29/6.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 39.29/6.09 % 39.29/6.10 % SZS output start Proof for theBenchmark % 39.29/6.13 Assumptions after simplification: % 39.29/6.13 --------------------------------- % 39.29/6.13 % 39.29/6.13 (and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0), pred(the(227), 0)))) % 39.66/6.16 ron(vd1080, vd1092) = 0 & ron(vd1089, vd1092) = 0 & rline(vd1092) = 0 & % 39.66/6.16 $i(vd1092) & $i(vd1080) & $i(vd1089) % 39.66/6.16 % 39.66/6.16 (holds(226, 1090, 0)) % 39.66/6.17 $i(vd1085) & $i(vd1080) & $i(vd1089) & ? [v0: $i] : (vf(vd1089, vd1085) = v0 % 39.66/6.17 & vf(vd1089, vd1080) = v0 & $i(v0)) % 39.66/6.17 % 39.66/6.17 (holds(226, 1090, 1)) % 39.66/6.17 $i(vd1085) & $i(vd1080) & $i(vd1089) & ? [v0: $i] : (vf(vd1085, vd1080) = v0 % 39.66/6.17 & vf(vd1089, vd1080) = v0 & $i(v0)) % 39.66/6.17 % 39.66/6.17 (holds(conjunct1(225), 1087, 0)) % 39.66/6.17 ~ (vd1085 = vd1080) & $i(vd1085) & $i(vd1080) % 39.66/6.17 % 39.66/6.17 (pred(224, 5)) % 39.66/6.17 ~ (vd1081 = vd1080) & $i(vd1081) & $i(vd1080) % 39.66/6.17 % 39.66/6.17 (pred(225, 1)) % 39.66/6.17 rpoint(vd1086) = 0 & $i(vd1086) % 39.66/6.17 % 39.66/6.17 (pred(225, 4)) % 39.66/6.17 vd1086 = vd1085 & $i(vd1085) % 39.66/6.17 % 39.66/6.17 (pred(226, 0)) % 39.66/6.17 rpoint(vd1089) = 0 & $i(vd1089) % 39.66/6.17 % 39.66/6.17 (qe(s1(plural(224)))) % 39.66/6.17 rpoint(vd1080) = 0 & $i(vd1080) % 39.66/6.17 % 39.66/6.17 (qe(s2(plural(224)))) % 39.66/6.17 rpoint(vd1081) = 0 & $i(vd1081) % 39.66/6.17 % 39.66/6.17 (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))) % 39.66/6.17 $i(v0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (rpoint(v1) = 0) | ~ % 39.66/6.18 (rpoint(v0) = 0) | ~ (vf(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (( ~ (v2 = % 39.66/6.18 v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0))) % 39.66/6.18 % 39.66/6.18 (qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))) % 39.66/6.18 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = % 39.66/6.18 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (rcenter(v0, v2) = 0 & % 39.66/6.18 rcircle(v2) = 0 & ron(v1, v2) = 0 & $i(v2))) % 39.66/6.18 % 39.66/6.18 (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))) % 39.66/6.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 = v0 | % 39.66/6.18 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v3) = 0) | ~ % 39.66/6.18 (ron(v0, v2) = 0) | ~ (rline(v3) = 0) | ~ (rline(v2) = 0) | ~ $i(v3) | ~ % 39.66/6.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (ron(v1, v2) % 39.66/6.18 = v4 & ron(v0, v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 39.66/6.18 % 39.66/6.18 (qu(theu(the(227), 1), imp(the(227)))) % 39.66/6.18 $i(vd1092) & $i(vd1080) & $i(vd1089) & ? [v0: $i] : ( ~ (v0 = vd1092) & % 39.66/6.18 ron(vd1080, v0) = 0 & ron(vd1089, v0) = 0 & rline(v0) = 0 & $i(v0)) % 39.66/6.18 % 39.66/6.18 (function-axioms) % 39.82/6.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 39.82/6.19 $i] : (v1 = v0 | ~ (vskolem1052(v5, v4, v3, v2) = v1) | ~ (vskolem1052(v5, % 39.82/6.19 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 39.82/6.19 $i] : ! [v4: $i] : (v1 = v0 | ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, v2) % 39.82/6.19 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 39.82/6.19 $i] : (v1 = v0 | ~ (vtriangle(v4, v3, v2) = v1) | ~ (vtriangle(v4, v3, v2) % 39.82/6.19 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 39.82/6.20 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | ~ % 39.82/6.20 (rS(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 39.82/6.20 $i] : ! [v4: $i] : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ (vangle(v4, % 39.82/6.20 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 39.82/6.20 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rR(v4, v3, v2) = % 39.82/6.20 v1) | ~ (rR(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.82/6.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rgeq(v3, v2) % 39.82/6.20 = v1) | ~ (rgeq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.82/6.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3, % 39.82/6.20 v2) = v1) | ~ (rcenter(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 39.82/6.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.82/6.20 (rintersect(v3, v2) = v1) | ~ (rintersect(v3, v2) = v0)) & ! [v0: % 39.82/6.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 39.82/6.20 : (v1 = v0 | ~ (rless(v3, v2) = v1) | ~ (rless(v3, v2) = v0)) & ! [v0: % 39.82/6.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 39.82/6.20 : (v1 = v0 | ~ (rinside(v3, v2) = v1) | ~ (rinside(v3, v2) = v0)) & ! [v0: % 39.82/6.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) % 39.82/6.20 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 39.82/6.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rleq(v3, v2) % 39.82/6.20 = v1) | ~ (rleq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 39.82/6.20 : ! [v3: $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) & ! % 39.82/6.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 39.82/6.20 $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = v0)) & ! [v0: % 39.82/6.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 39.82/6.20 ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & ! [v0: % 39.82/6.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 39.82/6.20 ~ (rcircle(v2) = v1) | ~ (rcircle(v2) = v0)) & ! [v0: MultipleValueBool] : % 39.82/6.20 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rreal(v2) = v1) | ~ % 39.82/6.20 (rreal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 39.82/6.20 : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | ~ (rpoint(v2) = v0)) & ! % 39.82/6.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 39.82/6.20 | ~ (rline(v2) = v1) | ~ (rline(v2) = v0)) % 39.82/6.20 % 39.82/6.20 Further assumptions not needed in the proof: % 39.82/6.20 -------------------------------------------- % 39.82/6.20 ass(cond(156, 0), 0), ass(cond(goal(206), 0), 0), ass(cond(goal(206), 0), 1), % 39.82/6.20 ass(cond(goal(206), 0), 2), holds(conjunct2(225), 1088, 0), pred(axiom(137), 1), % 39.82/6.20 pred(axiom(137), 2), pred(axiom(5), 0), qu(cond(axiom(1), 0), imp(cond(axiom(1), % 39.82/6.20 0))), qu(cond(axiom(101), 0), imp(cond(axiom(101), 0))), % 39.82/6.20 qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), qu(cond(axiom(105), 0), % 39.82/6.20 imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), imp(cond(axiom(107), 0))), % 39.82/6.20 qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), qu(cond(axiom(11), 0), % 39.82/6.20 imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), imp(cond(axiom(111), 0))), % 39.82/6.20 qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), qu(cond(axiom(115), 0), % 39.82/6.20 imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0), imp(cond(axiom(117), 0))), % 39.82/6.20 qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), qu(cond(axiom(121), 0), % 39.82/6.20 imp(cond(axiom(121), 0))), qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), % 39.82/6.20 qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), qu(cond(axiom(127), 0), % 39.82/6.20 imp(cond(axiom(127), 0))), qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), % 39.82/6.20 qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), qu(cond(axiom(131), 0), % 39.82/6.20 imp(cond(axiom(131), 0))), qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), % 39.82/6.20 qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), qu(cond(axiom(139), 0), % 39.82/6.20 imp(cond(axiom(139), 0))), qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), % 39.82/6.20 qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), qu(cond(axiom(145), 0), % 39.82/6.20 imp(cond(axiom(145), 0))), qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), % 39.82/6.20 qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), qu(cond(axiom(15), 0), % 39.82/6.20 imp(cond(axiom(15), 0))), qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), % 39.82/6.20 qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), qu(cond(axiom(160), 0), % 39.82/6.20 imp(cond(axiom(160), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), % 39.82/6.20 qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0), % 39.82/6.20 imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), % 39.82/6.20 qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0), % 39.82/6.20 imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), % 39.82/6.20 qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0), % 39.82/6.20 imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), % 39.82/6.20 qu(cond(axiom(182), 0), imp(cond(axiom(182), 0))), qu(cond(axiom(184), 0), % 39.82/6.20 imp(cond(axiom(184), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), % 39.82/6.20 qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0), % 39.82/6.20 imp(cond(axiom(19), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), % 39.82/6.20 qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0), % 39.82/6.20 imp(cond(axiom(194), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), % 39.82/6.20 qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0), % 39.82/6.20 imp(cond(axiom(200), 0))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), % 39.82/6.20 qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0), % 39.82/6.20 imp(cond(axiom(21), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), % 39.82/6.20 qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0), % 39.82/6.20 imp(cond(axiom(27), 0))), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), % 39.82/6.20 qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0), % 39.82/6.20 imp(cond(axiom(31), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), % 39.82/6.20 qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0), % 39.82/6.20 imp(cond(axiom(37), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), % 39.82/6.20 qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0), % 39.82/6.20 imp(cond(axiom(43), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), % 39.82/6.20 qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0), % 39.82/6.20 imp(cond(axiom(49), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), % 39.82/6.20 qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), qu(cond(axiom(57), 0), % 39.82/6.20 imp(cond(axiom(57), 0))), qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), % 39.82/6.20 qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), qu(cond(axiom(63), 0), % 39.82/6.20 imp(cond(axiom(63), 0))), qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), % 39.82/6.20 qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), qu(cond(axiom(69), 0), % 39.82/6.20 imp(cond(axiom(69), 0))), qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), % 39.82/6.20 qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), qu(cond(axiom(75), 0), % 39.82/6.20 imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), % 39.82/6.20 qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(81), 0), % 39.82/6.20 imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), % 39.82/6.20 qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), qu(cond(axiom(87), 0), % 39.82/6.20 imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), % 39.82/6.20 qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(91), 0), % 39.82/6.20 imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), % 39.82/6.20 qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(97), 0), % 39.82/6.20 imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))) % 39.82/6.20 % 39.82/6.20 Those formulas are unsatisfiable: % 39.82/6.20 --------------------------------- % 39.82/6.20 % 39.82/6.20 Begin of proof % 39.82/6.20 | % 39.82/6.20 | ALPHA: (and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0), % 39.82/6.20 | pred(the(227), 0)))) implies: % 39.82/6.20 | (1) rline(vd1092) = 0 % 39.82/6.20 | (2) ron(vd1089, vd1092) = 0 % 39.82/6.20 | (3) ron(vd1080, vd1092) = 0 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (holds(226, 1090, 1)) implies: % 39.82/6.21 | (4) ? [v0: $i] : (vf(vd1085, vd1080) = v0 & vf(vd1089, vd1080) = v0 & % 39.82/6.21 | $i(v0)) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (holds(226, 1090, 0)) implies: % 39.82/6.21 | (5) ? [v0: $i] : (vf(vd1089, vd1085) = v0 & vf(vd1089, vd1080) = v0 & % 39.82/6.21 | $i(v0)) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (pred(226, 0)) implies: % 39.82/6.21 | (6) rpoint(vd1089) = 0 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (pred(225, 4)) implies: % 39.82/6.21 | (7) vd1086 = vd1085 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (holds(conjunct1(225), 1087, 0)) implies: % 39.82/6.21 | (8) ~ (vd1085 = vd1080) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (pred(225, 1)) implies: % 39.82/6.21 | (9) $i(vd1086) % 39.82/6.21 | (10) rpoint(vd1086) = 0 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (qe(s1(plural(224)))) implies: % 39.82/6.21 | (11) rpoint(vd1080) = 0 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))) implies: % 39.82/6.21 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (rpoint(v1) = 0) | ~ % 39.82/6.21 | (rpoint(v0) = 0) | ~ (vf(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | (( % 39.82/6.21 | ~ (v2 = v0) | v1 = v0) & ( ~ (v1 = v0) | v2 = v0))) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (pred(224, 5)) implies: % 39.82/6.21 | (13) ~ (vd1081 = vd1080) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (qe(s2(plural(224)))) implies: % 39.82/6.21 | (14) $i(vd1081) % 39.82/6.21 | (15) rpoint(vd1081) = 0 % 39.82/6.21 | % 39.82/6.21 | ALPHA: (qu(theu(the(227), 1), imp(the(227)))) implies: % 39.82/6.21 | (16) $i(vd1089) % 39.82/6.21 | (17) $i(vd1080) % 39.82/6.21 | (18) $i(vd1092) % 39.82/6.21 | (19) ? [v0: $i] : ( ~ (v0 = vd1092) & ron(vd1080, v0) = 0 & ron(vd1089, % 39.82/6.21 | v0) = 0 & rline(v0) = 0 & $i(v0)) % 39.82/6.21 | % 39.82/6.21 | ALPHA: (function-axioms) implies: % 39.82/6.21 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 39.82/6.21 | : ! [v3: $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = % 39.82/6.21 | v0)) % 39.82/6.21 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 39.82/6.21 | (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) % 39.82/6.21 | % 39.82/6.22 | DELTA: instantiating (4) with fresh symbol all_104_0 gives: % 39.82/6.22 | (22) vf(vd1085, vd1080) = all_104_0 & vf(vd1089, vd1080) = all_104_0 & % 39.82/6.22 | $i(all_104_0) % 39.82/6.22 | % 39.82/6.22 | ALPHA: (22) implies: % 39.82/6.22 | (23) vf(vd1089, vd1080) = all_104_0 % 39.82/6.22 | (24) vf(vd1085, vd1080) = all_104_0 % 39.82/6.22 | % 39.82/6.22 | DELTA: instantiating (5) with fresh symbol all_106_0 gives: % 39.82/6.22 | (25) vf(vd1089, vd1085) = all_106_0 & vf(vd1089, vd1080) = all_106_0 & % 39.82/6.22 | $i(all_106_0) % 39.82/6.22 | % 39.82/6.22 | ALPHA: (25) implies: % 39.82/6.22 | (26) vf(vd1089, vd1080) = all_106_0 % 39.82/6.22 | % 39.82/6.22 | DELTA: instantiating (19) with fresh symbol all_108_0 gives: % 39.82/6.22 | (27) ~ (all_108_0 = vd1092) & ron(vd1080, all_108_0) = 0 & ron(vd1089, % 39.82/6.22 | all_108_0) = 0 & rline(all_108_0) = 0 & $i(all_108_0) % 39.82/6.22 | % 39.82/6.22 | ALPHA: (27) implies: % 39.82/6.22 | (28) ~ (all_108_0 = vd1092) % 39.82/6.22 | (29) $i(all_108_0) % 39.82/6.22 | (30) rline(all_108_0) = 0 % 39.82/6.22 | (31) ron(vd1089, all_108_0) = 0 % 39.82/6.22 | (32) ron(vd1080, all_108_0) = 0 % 39.82/6.22 | % 39.82/6.22 | REDUCE: (7), (10) imply: % 39.82/6.22 | (33) rpoint(vd1085) = 0 % 39.82/6.22 | % 39.82/6.22 | REDUCE: (7), (9) imply: % 39.82/6.22 | (34) $i(vd1085) % 39.82/6.22 | % 39.82/6.22 | GROUND_INST: instantiating (21) with all_104_0, all_106_0, vd1080, vd1089, % 39.82/6.22 | simplifying with (23), (26) gives: % 39.82/6.22 | (35) all_106_0 = all_104_0 % 39.82/6.22 | % 39.82/6.22 | GROUND_INST: instantiating (qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))) % 39.82/6.22 | with vd1080, vd1089, vd1092, all_108_0, simplifying with (1), % 39.82/6.22 | (3), (6), (11), (16), (17), (18), (29), (30), (31) gives: % 39.82/6.22 | (36) all_108_0 = vd1092 | vd1080 = vd1089 | ? [v0: any] : ? [v1: any] : % 39.82/6.22 | (ron(vd1080, all_108_0) = v1 & ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0) % 39.82/6.22 | | ~ (v0 = 0))) % 39.82/6.22 | % 39.82/6.22 | GROUND_INST: instantiating (12) with vd1089, vd1080, all_104_0, simplifying % 39.82/6.22 | with (6), (11), (16), (17), (23) gives: % 39.82/6.23 | (37) ( ~ (all_104_0 = v0) | vd1080 = vd1089) & ( ~ (vd1080 = vd1089) | % 39.82/6.23 | all_104_0 = v0) % 39.82/6.23 | % 39.82/6.23 | ALPHA: (37) implies: % 39.82/6.23 | (38) ~ (vd1080 = vd1089) | all_104_0 = v0 % 39.82/6.23 | % 39.82/6.23 | GROUND_INST: instantiating (12) with vd1085, vd1080, all_104_0, simplifying % 39.82/6.23 | with (11), (17), (24), (33), (34) gives: % 39.82/6.23 | (39) ( ~ (all_104_0 = v0) | vd1085 = vd1080) & ( ~ (vd1085 = vd1080) | % 39.82/6.23 | all_104_0 = v0) % 39.82/6.23 | % 39.82/6.23 | ALPHA: (39) implies: % 39.82/6.23 | (40) ~ (all_104_0 = v0) | vd1085 = vd1080 % 39.82/6.23 | % 39.82/6.23 | GROUND_INST: instantiating (qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))) % 39.82/6.23 | with vd1081, vd1080, simplifying with (11), (14), (15), (17) % 39.82/6.23 | gives: % 39.82/6.23 | (41) vd1081 = vd1080 | ? [v0: $i] : (rcenter(vd1081, v0) = 0 & rcircle(v0) % 39.82/6.23 | = 0 & ron(vd1080, v0) = 0 & $i(v0)) % 39.82/6.23 | % 39.82/6.23 | BETA: splitting (40) gives: % 39.82/6.23 | % 39.82/6.23 | Case 1: % 39.82/6.23 | | % 39.82/6.23 | | (42) ~ (all_104_0 = v0) % 39.82/6.23 | | % 39.82/6.23 | | BETA: splitting (38) gives: % 39.82/6.23 | | % 39.82/6.23 | | Case 1: % 39.82/6.23 | | | % 39.82/6.23 | | | (43) ~ (vd1080 = vd1089) % 39.82/6.23 | | | % 39.82/6.23 | | | BETA: splitting (36) gives: % 39.82/6.23 | | | % 39.82/6.23 | | | Case 1: % 39.82/6.23 | | | | % 39.82/6.23 | | | | (44) vd1080 = vd1089 % 39.82/6.23 | | | | % 39.82/6.23 | | | | REDUCE: (43), (44) imply: % 39.82/6.23 | | | | (45) $false % 40.03/6.23 | | | | % 40.03/6.23 | | | | CLOSE: (45) is inconsistent. % 40.03/6.23 | | | | % 40.03/6.23 | | | Case 2: % 40.03/6.23 | | | | % 40.03/6.23 | | | | (46) all_108_0 = vd1092 | ? [v0: any] : ? [v1: any] : (ron(vd1080, % 40.03/6.23 | | | | all_108_0) = v1 & ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0) | % 40.03/6.23 | | | | ~ (v0 = 0))) % 40.03/6.23 | | | | % 40.03/6.23 | | | | BETA: splitting (46) gives: % 40.03/6.23 | | | | % 40.03/6.23 | | | | Case 1: % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | (47) all_108_0 = vd1092 % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | REDUCE: (28), (47) imply: % 40.03/6.23 | | | | | (48) $false % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | CLOSE: (48) is inconsistent. % 40.03/6.23 | | | | | % 40.03/6.23 | | | | Case 2: % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | (49) ? [v0: any] : ? [v1: any] : (ron(vd1080, all_108_0) = v1 & % 40.03/6.23 | | | | | ron(vd1089, vd1092) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | DELTA: instantiating (49) with fresh symbols all_251_0, all_251_1 % 40.03/6.23 | | | | | gives: % 40.03/6.23 | | | | | (50) ron(vd1080, all_108_0) = all_251_0 & ron(vd1089, vd1092) = % 40.03/6.23 | | | | | all_251_1 & ( ~ (all_251_0 = 0) | ~ (all_251_1 = 0)) % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | ALPHA: (50) implies: % 40.03/6.23 | | | | | (51) ron(vd1089, vd1092) = all_251_1 % 40.03/6.23 | | | | | (52) ron(vd1080, all_108_0) = all_251_0 % 40.03/6.23 | | | | | (53) ~ (all_251_0 = 0) | ~ (all_251_1 = 0) % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | BETA: splitting (41) gives: % 40.03/6.23 | | | | | % 40.03/6.23 | | | | | Case 1: % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | (54) vd1081 = vd1080 % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | REDUCE: (13), (54) imply: % 40.03/6.23 | | | | | | (55) $false % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | CLOSE: (55) is inconsistent. % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | Case 2: % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | GROUND_INST: instantiating (20) with 0, all_251_1, vd1092, vd1089, % 40.03/6.23 | | | | | | simplifying with (2), (51) gives: % 40.03/6.23 | | | | | | (56) all_251_1 = 0 % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | GROUND_INST: instantiating (20) with 0, all_251_0, all_108_0, % 40.03/6.23 | | | | | | vd1080, simplifying with (32), (52) gives: % 40.03/6.23 | | | | | | (57) all_251_0 = 0 % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | BETA: splitting (53) gives: % 40.03/6.23 | | | | | | % 40.03/6.23 | | | | | | Case 1: % 40.03/6.23 | | | | | | | % 40.03/6.23 | | | | | | | (58) ~ (all_251_0 = 0) % 40.03/6.23 | | | | | | | % 40.03/6.23 | | | | | | | REDUCE: (57), (58) imply: % 40.03/6.23 | | | | | | | (59) $false % 40.03/6.23 | | | | | | | % 40.03/6.23 | | | | | | | CLOSE: (59) is inconsistent. % 40.03/6.23 | | | | | | | % 40.03/6.23 | | | | | | Case 2: % 40.03/6.23 | | | | | | | % 40.03/6.23 | | | | | | | (60) ~ (all_251_1 = 0) % 40.03/6.23 | | | | | | | % 40.03/6.24 | | | | | | | REDUCE: (56), (60) imply: % 40.03/6.24 | | | | | | | (61) $false % 40.03/6.24 | | | | | | | % 40.03/6.24 | | | | | | | CLOSE: (61) is inconsistent. % 40.03/6.24 | | | | | | | % 40.03/6.24 | | | | | | End of split % 40.03/6.24 | | | | | | % 40.03/6.24 | | | | | End of split % 40.03/6.24 | | | | | % 40.03/6.24 | | | | End of split % 40.03/6.24 | | | | % 40.03/6.24 | | | End of split % 40.03/6.24 | | | % 40.03/6.24 | | Case 2: % 40.03/6.24 | | | % 40.03/6.24 | | | (62) all_104_0 = v0 % 40.03/6.24 | | | % 40.03/6.24 | | | REDUCE: (42), (62) imply: % 40.03/6.24 | | | (63) $false % 40.03/6.24 | | | % 40.03/6.24 | | | CLOSE: (63) is inconsistent. % 40.03/6.24 | | | % 40.03/6.24 | | End of split % 40.03/6.24 | | % 40.03/6.24 | Case 2: % 40.03/6.24 | | % 40.03/6.24 | | (64) vd1085 = vd1080 % 40.03/6.24 | | % 40.03/6.24 | | REDUCE: (8), (64) imply: % 40.03/6.24 | | (65) $false % 40.03/6.24 | | % 40.03/6.24 | | CLOSE: (65) is inconsistent. % 40.03/6.24 | | % 40.03/6.24 | End of split % 40.03/6.24 | % 40.03/6.24 End of proof % 40.03/6.24 % SZS output end Proof for theBenchmark % 40.03/6.24 % 40.03/6.24 5626ms %------------------------------------------------------------------------------