%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0. % 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 : Fri Sep 1 03:26:22 EDT 2023 % Result : Theorem 3.87s 1.22s % Output : Proof 4.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYN056+1 : TPTP v8.1.2. Released v2.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n019.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sat Aug 26 19:18:58 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.94/0.95 Prover 4: Preprocessing ... % 1.94/0.95 Prover 1: Preprocessing ... % 1.94/0.99 Prover 0: Preprocessing ... % 1.94/0.99 Prover 2: Preprocessing ... % 1.94/0.99 Prover 6: Preprocessing ... % 1.94/0.99 Prover 3: Preprocessing ... % 1.94/0.99 Prover 5: Preprocessing ... % 2.85/1.09 Prover 5: Constructing countermodel ... % 2.85/1.09 Prover 2: Constructing countermodel ... % 2.85/1.11 Prover 3: Constructing countermodel ... % 2.85/1.11 Prover 6: Proving ... % 2.85/1.11 Prover 1: Constructing countermodel ... % 2.85/1.16 Prover 4: Constructing countermodel ... % 3.51/1.18 Prover 0: Proving ... % 3.68/1.22 Prover 2: proved (594ms) % 3.87/1.22 % 3.87/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.87/1.22 % 3.87/1.22 Prover 3: gave up % 3.87/1.22 Prover 5: stopped % 3.87/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.87/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.87/1.22 Prover 6: stopped % 3.87/1.23 Prover 0: stopped % 3.92/1.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.92/1.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.92/1.23 Prover 1: gave up % 3.92/1.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.92/1.25 Prover 7: Preprocessing ... % 3.92/1.25 Prover 8: Preprocessing ... % 3.92/1.25 Prover 10: Preprocessing ... % 3.92/1.25 Prover 11: Preprocessing ... % 3.92/1.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 3.92/1.25 Prover 13: Preprocessing ... % 3.92/1.26 Prover 10: Constructing countermodel ... % 3.92/1.26 Prover 7: Constructing countermodel ... % 3.92/1.27 Prover 16: Preprocessing ... % 3.92/1.28 Prover 13: Constructing countermodel ... % 3.92/1.29 Prover 8: Warning: ignoring some quantifiers % 3.92/1.29 Prover 8: Constructing countermodel ... % 3.92/1.30 Prover 16: Constructing countermodel ... % 3.92/1.34 Prover 10: Found proof (size 24) % 3.92/1.34 Prover 10: proved (117ms) % 3.92/1.34 Prover 4: stopped % 3.92/1.34 Prover 13: stopped % 3.92/1.34 Prover 16: stopped % 3.92/1.34 Prover 8: stopped % 3.92/1.34 Prover 7: stopped % 3.92/1.38 Prover 11: Constructing countermodel ... % 3.92/1.38 Prover 11: stopped % 3.92/1.38 % 3.92/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.92/1.38 % 3.92/1.39 % SZS output start Proof for theBenchmark % 3.92/1.39 Assumptions after simplification: % 3.92/1.39 --------------------------------- % 3.92/1.39 % 3.92/1.39 (pel26) % 3.92/1.40 ? [v0: $i] : ($i(v0) & ((big_q(v0) & ~ big_s(v0) & ! [v1: $i] : ( ~ $i(v1) % 3.92/1.40 | ~ big_p(v1) | big_r(v1))) | (big_p(v0) & ~ big_r(v0) & ! [v1: $i] % 3.92/1.40 : ( ~ $i(v1) | ~ big_q(v1) | big_s(v1))))) % 3.92/1.40 % 3.92/1.40 (pel26_1) % 3.92/1.40 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & ((big_q(v0) & big_p(v1)) | ( ! % 3.92/1.40 [v2: $i] : ( ~ $i(v2) | ~ big_q(v2)) & ! [v2: $i] : ( ~ $i(v2) | ~ % 3.92/1.40 big_p(v2))))) % 3.92/1.40 % 3.92/1.40 (pel26_2) % 3.92/1.40 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_s(v1) | ~ % 3.92/1.40 big_q(v1) | ~ big_p(v0) | big_r(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 3.92/1.40 $i(v1) | ~ $i(v0) | ~ big_r(v0) | ~ big_q(v1) | ~ big_p(v0) | big_s(v1)) % 3.92/1.40 % 3.92/1.40 Those formulas are unsatisfiable: % 3.92/1.40 --------------------------------- % 3.92/1.40 % 3.92/1.40 Begin of proof % 3.92/1.40 | % 3.92/1.40 | ALPHA: (pel26_2) implies: % 3.92/1.41 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_r(v0) | ~ % 3.92/1.41 | big_q(v1) | ~ big_p(v0) | big_s(v1)) % 3.92/1.41 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ big_s(v1) | ~ % 3.92/1.41 | big_q(v1) | ~ big_p(v0) | big_r(v0)) % 3.92/1.41 | % 3.92/1.41 | DELTA: instantiating (pel26_1) with fresh symbols all_3_0, all_3_1 gives: % 3.92/1.41 | (3) $i(all_3_0) & $i(all_3_1) & ((big_q(all_3_1) & big_p(all_3_0)) | ( ! % 3.92/1.41 | [v0: $i] : ( ~ $i(v0) | ~ big_q(v0)) & ! [v0: $i] : ( ~ $i(v0) | % 3.92/1.41 | ~ big_p(v0)))) % 3.92/1.41 | % 3.92/1.41 | ALPHA: (3) implies: % 4.88/1.41 | (4) $i(all_3_1) % 4.88/1.41 | (5) $i(all_3_0) % 4.88/1.41 | (6) (big_q(all_3_1) & big_p(all_3_0)) | ( ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.41 | big_q(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0))) % 4.88/1.41 | % 4.88/1.41 | DELTA: instantiating (pel26) with fresh symbol all_5_0 gives: % 4.88/1.41 | (7) $i(all_5_0) & ((big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ % 4.88/1.41 | $i(v0) | ~ big_p(v0) | big_r(v0))) | (big_p(all_5_0) & ~ % 4.88/1.41 | big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) | % 4.88/1.41 | big_s(v0)))) % 4.88/1.41 | % 4.88/1.41 | ALPHA: (7) implies: % 4.88/1.41 | (8) $i(all_5_0) % 4.88/1.41 | (9) (big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.42 | big_p(v0) | big_r(v0))) | (big_p(all_5_0) & ~ big_r(all_5_0) & ! % 4.88/1.42 | [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) | big_s(v0))) % 4.88/1.42 | % 4.88/1.42 | BETA: splitting (6) gives: % 4.88/1.42 | % 4.88/1.42 | Case 1: % 4.88/1.42 | | % 4.88/1.42 | | (10) big_q(all_3_1) & big_p(all_3_0) % 4.88/1.42 | | % 4.88/1.42 | | ALPHA: (10) implies: % 4.88/1.42 | | (11) big_p(all_3_0) % 4.88/1.42 | | (12) big_q(all_3_1) % 4.88/1.42 | | % 4.88/1.42 | | BETA: splitting (9) gives: % 4.88/1.42 | | % 4.88/1.42 | | Case 1: % 4.88/1.42 | | | % 4.88/1.42 | | | (13) big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.42 | | | big_p(v0) | big_r(v0)) % 4.88/1.42 | | | % 4.88/1.42 | | | ALPHA: (13) implies: % 4.88/1.42 | | | (14) ~ big_s(all_5_0) % 4.88/1.42 | | | (15) big_q(all_5_0) % 4.88/1.42 | | | (16) ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0) | big_r(v0)) % 4.88/1.42 | | | % 4.88/1.42 | | | GROUND_INST: instantiating (16) with all_3_0, simplifying with (5), (11) % 4.88/1.42 | | | gives: % 4.88/1.42 | | | (17) big_r(all_3_0) % 4.88/1.42 | | | % 4.88/1.42 | | | GROUND_INST: instantiating (1) with all_3_0, all_5_0, simplifying with % 4.88/1.42 | | | (5), (8), (11), (14), (15), (17) gives: % 4.88/1.42 | | | (18) $false % 4.88/1.42 | | | % 4.88/1.42 | | | CLOSE: (18) is inconsistent. % 4.88/1.42 | | | % 4.88/1.42 | | Case 2: % 4.88/1.42 | | | % 4.88/1.42 | | | (19) big_p(all_5_0) & ~ big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.42 | | | big_q(v0) | big_s(v0)) % 4.88/1.42 | | | % 4.88/1.42 | | | ALPHA: (19) implies: % 4.88/1.42 | | | (20) ~ big_r(all_5_0) % 4.88/1.42 | | | (21) big_p(all_5_0) % 4.88/1.42 | | | (22) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0) | big_s(v0)) % 4.88/1.42 | | | % 4.88/1.42 | | | GROUND_INST: instantiating (22) with all_3_1, simplifying with (4), (12) % 4.88/1.42 | | | gives: % 4.88/1.42 | | | (23) big_s(all_3_1) % 4.88/1.42 | | | % 4.88/1.43 | | | GROUND_INST: instantiating (2) with all_5_0, all_3_1, simplifying with % 4.88/1.43 | | | (4), (8), (12), (20), (21), (23) gives: % 4.88/1.43 | | | (24) $false % 4.88/1.43 | | | % 4.88/1.43 | | | CLOSE: (24) is inconsistent. % 4.88/1.43 | | | % 4.88/1.43 | | End of split % 4.88/1.43 | | % 4.88/1.43 | Case 2: % 4.88/1.43 | | % 4.88/1.43 | | (25) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0)) & ! [v0: $i] : ( ~ $i(v0) % 4.88/1.43 | | | ~ big_p(v0)) % 4.88/1.43 | | % 4.88/1.43 | | ALPHA: (25) implies: % 4.88/1.43 | | (26) ! [v0: $i] : ( ~ $i(v0) | ~ big_p(v0)) % 4.88/1.43 | | (27) ! [v0: $i] : ( ~ $i(v0) | ~ big_q(v0)) % 4.88/1.43 | | % 4.88/1.43 | | BETA: splitting (9) gives: % 4.88/1.43 | | % 4.88/1.43 | | Case 1: % 4.88/1.43 | | | % 4.88/1.43 | | | (28) big_q(all_5_0) & ~ big_s(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.43 | | | big_p(v0) | big_r(v0)) % 4.88/1.43 | | | % 4.88/1.43 | | | ALPHA: (28) implies: % 4.88/1.43 | | | (29) big_q(all_5_0) % 4.88/1.43 | | | % 4.88/1.43 | | | GROUND_INST: instantiating (27) with all_5_0, simplifying with (8), (29) % 4.88/1.43 | | | gives: % 4.88/1.43 | | | (30) $false % 4.88/1.43 | | | % 4.88/1.43 | | | CLOSE: (30) is inconsistent. % 4.88/1.43 | | | % 4.88/1.43 | | Case 2: % 4.88/1.43 | | | % 4.88/1.43 | | | (31) big_p(all_5_0) & ~ big_r(all_5_0) & ! [v0: $i] : ( ~ $i(v0) | ~ % 4.88/1.43 | | | big_q(v0) | big_s(v0)) % 4.88/1.43 | | | % 4.88/1.43 | | | ALPHA: (31) implies: % 4.88/1.43 | | | (32) big_p(all_5_0) % 4.88/1.43 | | | % 4.88/1.43 | | | GROUND_INST: instantiating (26) with all_5_0, simplifying with (8), (32) % 4.88/1.43 | | | gives: % 4.88/1.43 | | | (33) $false % 4.88/1.43 | | | % 4.88/1.43 | | | CLOSE: (33) is inconsistent. % 4.88/1.43 | | | % 4.88/1.43 | | End of split % 4.88/1.43 | | % 4.88/1.43 | End of split % 4.88/1.43 | % 4.88/1.43 End of proof % 4.88/1.43 % SZS output end Proof for theBenchmark % 4.88/1.43 % 4.88/1.43 825ms %------------------------------------------------------------------------------