%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : KRS113+1 : TPTP v8.1.2. Released v3.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 05:51:18 EDT 2023 % Result : Unsatisfiable 7.77s 1.95s % Output : Proof 11.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : KRS113+1 : TPTP v8.1.2. Released v3.1.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 01:35:58 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.66 ________ _____ % 0.18/0.66 ___ __ \_________(_)________________________________ % 0.18/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.66 % 0.18/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.66 (2023-06-19) % 0.18/0.66 % 0.18/0.66 (c) Philipp Rümmer, 2009-2023 % 0.18/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.66 Amanda Stjerna. % 0.18/0.66 Free software under BSD-3-Clause. % 0.18/0.66 % 0.18/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.66 % 0.18/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.68 Running up to 7 provers in parallel. % 0.18/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.67/1.18 Prover 4: Preprocessing ... % 2.67/1.18 Prover 1: Preprocessing ... % 2.97/1.24 Prover 3: Preprocessing ... % 2.97/1.24 Prover 0: Preprocessing ... % 2.97/1.24 Prover 5: Preprocessing ... % 2.97/1.24 Prover 6: Preprocessing ... % 2.97/1.24 Prover 2: Preprocessing ... % 5.76/1.65 Prover 2: Proving ... % 5.76/1.65 Prover 5: Proving ... % 6.16/1.73 Prover 6: Proving ... % 6.66/1.78 Prover 3: Constructing countermodel ... % 6.92/1.83 Prover 1: Constructing countermodel ... % 7.15/1.90 Prover 4: Constructing countermodel ... % 7.77/1.94 Prover 5: proved (1238ms) % 7.77/1.94 % 7.77/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.77/1.95 % 7.77/1.95 Prover 2: proved (1249ms) % 7.77/1.95 % 7.77/1.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.77/1.95 % 7.77/1.95 Prover 3: stopped % 7.77/1.96 Prover 6: stopped % 7.77/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.77/1.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.77/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.77/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.13/2.02 Prover 0: Proving ... % 8.13/2.02 Prover 0: stopped % 8.13/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.60/2.05 Prover 7: Preprocessing ... % 8.60/2.07 Prover 10: Preprocessing ... % 8.60/2.09 Prover 11: Preprocessing ... % 8.60/2.09 Prover 8: Preprocessing ... % 8.60/2.14 Prover 7: Warning: ignoring some quantifiers % 8.60/2.15 Prover 1: gave up % 8.60/2.16 Prover 13: Preprocessing ... % 8.60/2.17 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.60/2.19 Prover 10: Warning: ignoring some quantifiers % 8.60/2.19 Prover 7: Constructing countermodel ... % 8.60/2.20 Prover 10: Constructing countermodel ... % 9.05/2.22 Prover 16: Preprocessing ... % 10.00/2.28 Prover 13: Warning: ignoring some quantifiers % 10.00/2.29 Prover 8: Warning: ignoring some quantifiers % 10.00/2.29 Prover 10: Found proof (size 24) % 10.32/2.29 Prover 10: proved (335ms) % 10.32/2.31 Prover 13: Constructing countermodel ... % 10.32/2.31 Prover 16: Warning: ignoring some quantifiers % 10.32/2.31 Prover 8: Constructing countermodel ... % 10.32/2.31 Prover 7: Found proof (size 27) % 10.32/2.31 Prover 7: proved (346ms) % 10.32/2.31 Prover 16: Constructing countermodel ... % 10.32/2.31 Prover 4: stopped % 10.32/2.31 Prover 13: stopped % 10.32/2.31 Prover 8: stopped % 10.32/2.33 Prover 16: stopped % 10.87/2.46 Prover 11: Constructing countermodel ... % 11.15/2.47 Prover 11: stopped % 11.15/2.47 % 11.15/2.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.15/2.47 % 11.15/2.48 % SZS output start Proof for theBenchmark % 11.15/2.48 Assumptions after simplification: % 11.15/2.48 --------------------------------- % 11.15/2.48 % 11.15/2.48 (axiom_2) % 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ $i(v1) | % 11.15/2.50 ~ $i(v0) | ~ rr(v0, v2) | ~ rr(v0, v1) | ~ cUnsatisfiable(v0)) & ! [v0: % 11.15/2.50 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 11.15/2.50 rs(v0, v1) | ~ rr(v0, v2) | ~ cpxcomp(v0) | ~ cp(v1) | ~ ca_Vx2(v2) | % 11.15/2.50 cUnsatisfiable(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & $i(v4) & % 11.15/2.50 $i(v3) & rr(v0, v4) & rr(v0, v3))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 11.15/2.50 cUnsatisfiable(v0) | cpxcomp(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 11.15/2.50 cUnsatisfiable(v0) | ? [v1: $i] : ($i(v1) & rs(v0, v1) & cp(v1))) & ! [v0: % 11.15/2.50 $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] : ($i(v1) & rr(v0, % 11.15/2.50 v1) & ca_Vx2(v1))) % 11.15/2.50 % 11.15/2.50 (axiom_3) % 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1) | ~ % 11.15/2.50 cp(v0)) & ? [v0: $i] : ( ~ $i(v0) | cp(v0) | ? [v1: $i] : ($i(v1) & % 11.15/2.50 ra_Px1(v0, v1))) % 11.15/2.50 % 11.15/2.50 (axiom_4) % 11.15/2.50 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1) | % 11.15/2.50 cpxcomp(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ cpxcomp(v0) | ? [v1: $i] : % 11.15/2.50 ($i(v1) & ra_Px1(v0, v1))) % 11.15/2.50 % 11.15/2.50 (axiom_5) % 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0, v1) | ~ % 11.15/2.51 ca_Vx2(v0) | cp(v1)) & ? [v0: $i] : ( ~ $i(v0) | ca_Vx2(v0) | ? [v1: $i] : % 11.15/2.51 ($i(v1) & rinvS(v0, v1) & ~ cp(v1))) % 11.15/2.51 % 11.15/2.51 (axiom_6) % 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v1, v0) | rinvS(v0, % 11.15/2.51 v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0, % 11.15/2.51 v1) | rs(v1, v0)) % 11.15/2.51 % 11.15/2.51 (axiom_7) % 11.15/2.51 $i(i2003_11_14_17_21_22376) & cUnsatisfiable(i2003_11_14_17_21_22376) % 11.15/2.51 % 11.15/2.51 (axiom_8) % 11.15/2.51 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v0, v1) | rr(v0, % 11.15/2.51 v1)) % 11.15/2.51 % 11.15/2.51 Further assumptions not needed in the proof: % 11.15/2.51 -------------------------------------------- % 11.15/2.51 axiom_0, axiom_1, cUnsatisfiable_substitution_1, ca_Vx2_substitution_1, % 11.15/2.51 cowlNothing_substitution_1, cowlThing_substitution_1, cp_substitution_1, % 11.15/2.51 cpxcomp_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2, % 11.15/2.51 rinvS_substitution_1, rinvS_substitution_2, rr_substitution_1, % 11.15/2.51 rr_substitution_2, rs_substitution_1, rs_substitution_2, % 11.15/2.51 xsd_integer_substitution_1, xsd_string_substitution_1 % 11.15/2.51 % 11.15/2.51 Those formulas are unsatisfiable: % 11.15/2.51 --------------------------------- % 11.15/2.51 % 11.15/2.51 Begin of proof % 11.15/2.51 | % 11.15/2.51 | ALPHA: (axiom_7) implies: % 11.15/2.52 | (1) cUnsatisfiable(i2003_11_14_17_21_22376) % 11.15/2.52 | (2) $i(i2003_11_14_17_21_22376) % 11.15/2.52 | % 11.15/2.52 | ALPHA: (axiom_6) implies: % 11.15/2.52 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rs(v1, v0) | % 11.15/2.52 | rinvS(v0, v1)) % 11.15/2.52 | % 11.15/2.52 | ALPHA: (axiom_5) implies: % 11.15/2.52 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ rinvS(v0, v1) | % 11.15/2.52 | ~ ca_Vx2(v0) | cp(v1)) % 11.15/2.52 | % 11.15/2.52 | ALPHA: (axiom_4) implies: % 11.15/2.52 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ cpxcomp(v0) | ? [v1: $i] : ($i(v1) & % 11.15/2.52 | ra_Px1(v0, v1))) % 11.15/2.52 | % 11.15/2.52 | ALPHA: (axiom_3) implies: % 11.15/2.52 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ra_Px1(v0, v1) % 11.15/2.52 | | ~ cp(v0)) % 11.15/2.52 | % 11.15/2.52 | ALPHA: (axiom_2) implies: % 11.15/2.52 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] : % 11.15/2.52 | ($i(v1) & rr(v0, v1) & ca_Vx2(v1))) % 11.15/2.52 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | ? [v1: $i] : % 11.15/2.52 | ($i(v1) & rs(v0, v1) & cp(v1))) % 11.15/2.52 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ cUnsatisfiable(v0) | cpxcomp(v0)) % 11.15/2.52 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 11.15/2.52 | $i(v1) | ~ $i(v0) | ~ rr(v0, v2) | ~ rr(v0, v1) | ~ % 11.15/2.52 | cUnsatisfiable(v0)) % 11.15/2.52 | % 11.15/2.53 | GROUND_INST: instantiating (9) with i2003_11_14_17_21_22376, simplifying with % 11.15/2.53 | (1), (2) gives: % 11.15/2.53 | (11) cpxcomp(i2003_11_14_17_21_22376) % 11.15/2.53 | % 11.15/2.53 | GROUND_INST: instantiating (8) with i2003_11_14_17_21_22376, simplifying with % 11.15/2.53 | (1), (2) gives: % 11.15/2.53 | (12) ? [v0: $i] : ($i(v0) & rs(i2003_11_14_17_21_22376, v0) & cp(v0)) % 11.15/2.53 | % 11.15/2.53 | GROUND_INST: instantiating (7) with i2003_11_14_17_21_22376, simplifying with % 11.15/2.53 | (1), (2) gives: % 11.15/2.53 | (13) ? [v0: $i] : ($i(v0) & rr(i2003_11_14_17_21_22376, v0) & ca_Vx2(v0)) % 11.15/2.53 | % 11.15/2.53 | DELTA: instantiating (12) with fresh symbol all_21_0 gives: % 11.15/2.53 | (14) $i(all_21_0) & rs(i2003_11_14_17_21_22376, all_21_0) & cp(all_21_0) % 11.15/2.53 | % 11.15/2.53 | ALPHA: (14) implies: % 11.15/2.53 | (15) rs(i2003_11_14_17_21_22376, all_21_0) % 11.15/2.53 | (16) $i(all_21_0) % 11.15/2.53 | % 11.15/2.53 | DELTA: instantiating (13) with fresh symbol all_23_0 gives: % 11.15/2.53 | (17) $i(all_23_0) & rr(i2003_11_14_17_21_22376, all_23_0) & % 11.15/2.53 | ca_Vx2(all_23_0) % 11.15/2.53 | % 11.15/2.53 | ALPHA: (17) implies: % 11.15/2.53 | (18) ca_Vx2(all_23_0) % 11.15/2.53 | (19) rr(i2003_11_14_17_21_22376, all_23_0) % 11.15/2.53 | (20) $i(all_23_0) % 11.15/2.53 | % 11.15/2.53 | GROUND_INST: instantiating (5) with i2003_11_14_17_21_22376, simplifying with % 11.15/2.54 | (2), (11) gives: % 11.15/2.54 | (21) ? [v0: $i] : ($i(v0) & ra_Px1(i2003_11_14_17_21_22376, v0)) % 11.15/2.54 | % 11.15/2.54 | GROUND_INST: instantiating (3) with all_21_0, i2003_11_14_17_21_22376, % 11.15/2.54 | simplifying with (2), (15), (16) gives: % 11.15/2.54 | (22) rinvS(all_21_0, i2003_11_14_17_21_22376) % 11.15/2.54 | % 11.15/2.54 | GROUND_INST: instantiating (axiom_8) with i2003_11_14_17_21_22376, all_21_0, % 11.15/2.54 | simplifying with (2), (15), (16) gives: % 11.15/2.54 | (23) rr(i2003_11_14_17_21_22376, all_21_0) % 11.15/2.54 | % 11.15/2.54 | DELTA: instantiating (21) with fresh symbol all_31_0 gives: % 11.15/2.54 | (24) $i(all_31_0) & ra_Px1(i2003_11_14_17_21_22376, all_31_0) % 11.15/2.54 | % 11.15/2.54 | ALPHA: (24) implies: % 11.15/2.54 | (25) ra_Px1(i2003_11_14_17_21_22376, all_31_0) % 11.15/2.54 | (26) $i(all_31_0) % 11.15/2.54 | % 11.15/2.54 | GROUND_INST: instantiating (10) with i2003_11_14_17_21_22376, all_23_0, % 11.15/2.54 | all_21_0, simplifying with (1), (2), (16), (19), (20), (23) % 11.15/2.54 | gives: % 11.15/2.54 | (27) all_23_0 = all_21_0 % 11.15/2.54 | % 11.15/2.54 | REDUCE: (18), (27) imply: % 11.15/2.54 | (28) ca_Vx2(all_21_0) % 11.15/2.54 | % 11.15/2.54 | GROUND_INST: instantiating (4) with all_21_0, i2003_11_14_17_21_22376, % 11.15/2.54 | simplifying with (2), (16), (22), (28) gives: % 11.15/2.54 | (29) cp(i2003_11_14_17_21_22376) % 11.15/2.54 | % 11.15/2.54 | GROUND_INST: instantiating (6) with i2003_11_14_17_21_22376, all_31_0, % 11.15/2.54 | simplifying with (2), (25), (26), (29) gives: % 11.15/2.54 | (30) $false % 11.15/2.55 | % 11.15/2.55 | CLOSE: (30) is inconsistent. % 11.15/2.55 | % 11.15/2.55 End of proof % 11.15/2.55 % SZS output end Proof for theBenchmark % 11.15/2.55 % 11.15/2.55 1889ms %------------------------------------------------------------------------------