%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0. % 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 : Thu Aug 31 15:26:53 EDT 2023 % Result : Theorem 4.59s 1.40s % Output : Proof 5.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % 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 : Sat Aug 26 10:50:48 EDT 2023 % 0.13/0.34 % 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 % 0.19/0.60 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.13/1.00 Prover 1: Preprocessing ... % 2.13/1.00 Prover 4: Preprocessing ... % 2.13/1.05 Prover 6: Preprocessing ... % 2.13/1.05 Prover 5: Preprocessing ... % 2.13/1.05 Prover 0: Preprocessing ... % 2.13/1.05 Prover 2: Preprocessing ... % 2.13/1.05 Prover 3: Preprocessing ... % 3.45/1.21 Prover 1: Warning: ignoring some quantifiers % 3.45/1.21 Prover 4: Warning: ignoring some quantifiers % 3.45/1.23 Prover 3: Warning: ignoring some quantifiers % 3.45/1.23 Prover 6: Proving ... % 3.45/1.23 Prover 3: Constructing countermodel ... % 3.45/1.23 Prover 2: Proving ... % 3.45/1.23 Prover 1: Constructing countermodel ... % 3.74/1.24 Prover 4: Constructing countermodel ... % 3.74/1.24 Prover 5: Proving ... % 3.74/1.24 Prover 0: Proving ... % 4.59/1.40 Prover 2: proved (773ms) % 4.59/1.40 % 4.59/1.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.59/1.40 % 4.59/1.40 Prover 1: Found proof (size 11) % 4.59/1.40 Prover 1: proved (777ms) % 4.59/1.40 Prover 0: proved (773ms) % 4.59/1.40 Prover 3: proved (774ms) % 4.59/1.40 Prover 4: Found proof (size 9) % 4.59/1.40 Prover 4: proved (772ms) % 4.59/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.59/1.40 Prover 6: stopped % 4.59/1.40 Prover 5: stopped % 4.59/1.41 Prover 7: Preprocessing ... % 4.95/1.44 Prover 7: Warning: ignoring some quantifiers % 4.95/1.45 Prover 7: Constructing countermodel ... % 4.95/1.45 Prover 7: stopped % 4.95/1.45 % 4.95/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.95/1.45 % 5.10/1.46 % SZS output start Proof for theBenchmark % 5.10/1.46 Assumptions after simplification: % 5.10/1.46 --------------------------------- % 5.10/1.46 % 5.10/1.46 (d1_tarski) % 5.10/1.49 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | % 5.10/1.49 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & % 5.10/1.49 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i] % 5.10/1.49 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: % 5.10/1.49 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = % 5.10/1.49 0 | ~ (in(v0, v1) = v2)))) % 5.10/1.49 % 5.10/1.49 (l36_zfmisc_1) % 5.10/1.50 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 5.10/1.50 empty_set | ~ (set_difference(v2, v1) = v3) | ~ (singleton(v0) = v2) | ~ % 5.10/1.50 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! % 5.10/1.50 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) = % 5.10/1.50 empty_set) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) % 5.10/1.50 = 0) % 5.10/1.50 % 5.10/1.50 (t21_zfmisc_1) % 5.10/1.50 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 5.10/1.50 (v1 = v0) & set_difference(v2, v3) = empty_set & singleton(v1) = v3 & % 5.10/1.50 singleton(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.10/1.50 % 5.10/1.50 Further assumptions not needed in the proof: % 5.10/1.50 -------------------------------------------- % 5.10/1.50 antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0 % 5.10/1.50 % 5.10/1.50 Those formulas are unsatisfiable: % 5.10/1.50 --------------------------------- % 5.10/1.50 % 5.10/1.50 Begin of proof % 5.10/1.50 | % 5.10/1.50 | ALPHA: (d1_tarski) implies: % 5.10/1.50 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 5.10/1.50 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & % 5.10/1.50 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2)))) % 5.10/1.50 | % 5.10/1.50 | ALPHA: (l36_zfmisc_1) implies: % 5.10/1.51 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v2, v1) = % 5.10/1.51 | empty_set) | ~ (singleton(v0) = v2) | ~ $i(v1) | ~ $i(v0) | % 5.10/1.51 | in(v0, v1) = 0) % 5.10/1.51 | % 5.10/1.51 | ALPHA: (t21_zfmisc_1) implies: % 5.10/1.51 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) & % 5.10/1.51 | set_difference(v2, v3) = empty_set & singleton(v1) = v3 & % 5.10/1.51 | singleton(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.10/1.51 | % 5.10/1.51 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2, % 5.10/1.51 | all_11_3 gives: % 5.10/1.51 | (4) ~ (all_11_2 = all_11_3) & set_difference(all_11_1, all_11_0) = % 5.10/1.51 | empty_set & singleton(all_11_2) = all_11_0 & singleton(all_11_3) = % 5.10/1.51 | all_11_1 & $i(all_11_0) & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) % 5.10/1.51 | % 5.10/1.51 | ALPHA: (4) implies: % 5.10/1.51 | (5) ~ (all_11_2 = all_11_3) % 5.10/1.52 | (6) $i(all_11_3) % 5.10/1.52 | (7) $i(all_11_2) % 5.10/1.52 | (8) $i(all_11_0) % 5.10/1.52 | (9) singleton(all_11_3) = all_11_1 % 5.10/1.52 | (10) singleton(all_11_2) = all_11_0 % 5.10/1.52 | (11) set_difference(all_11_1, all_11_0) = empty_set % 5.10/1.52 | % 5.10/1.52 | GROUND_INST: instantiating (1) with all_11_2, all_11_0, simplifying with (7), % 5.10/1.52 | (8), (10) gives: % 5.10/1.52 | (12) ! [v0: any] : (v0 = all_11_2 | ~ (in(v0, all_11_0) = 0) | ~ $i(v0)) % 5.10/1.52 | & ! [v0: int] : (v0 = 0 | ~ (in(all_11_2, all_11_0) = v0)) % 5.10/1.52 | % 5.10/1.52 | ALPHA: (12) implies: % 5.10/1.52 | (13) ! [v0: any] : (v0 = all_11_2 | ~ (in(v0, all_11_0) = 0) | ~ $i(v0)) % 5.10/1.52 | % 5.10/1.52 | GROUND_INST: instantiating (2) with all_11_3, all_11_0, all_11_1, simplifying % 5.10/1.52 | with (6), (8), (9), (11) gives: % 5.10/1.52 | (14) in(all_11_3, all_11_0) = 0 % 5.10/1.52 | % 5.10/1.52 | GROUND_INST: instantiating (13) with all_11_3, simplifying with (6), (14) % 5.10/1.52 | gives: % 5.10/1.52 | (15) all_11_2 = all_11_3 % 5.10/1.52 | % 5.10/1.52 | REDUCE: (5), (15) imply: % 5.10/1.52 | (16) $false % 5.10/1.52 | % 5.10/1.52 | CLOSE: (16) is inconsistent. % 5.10/1.52 | % 5.10/1.52 End of proof % 5.10/1.52 % SZS output end Proof for theBenchmark % 5.10/1.52 % 5.10/1.52 920ms %------------------------------------------------------------------------------