%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET988+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 : n028.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 15:27:18 EDT 2023 % Result : Theorem 9.08s 1.96s % Output : Proof 9.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET988+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 : n028.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 13:01:22 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 ... % 0.19/0.61 Running up to 7 provers in parallel. % 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 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 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 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 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 % 2.23/1.05 Prover 1: Preprocessing ... % 2.23/1.05 Prover 4: Preprocessing ... % 2.83/1.09 Prover 5: Preprocessing ... % 2.83/1.09 Prover 6: Preprocessing ... % 2.83/1.09 Prover 3: Preprocessing ... % 2.83/1.09 Prover 2: Preprocessing ... % 2.83/1.09 Prover 0: Preprocessing ... % 4.98/1.49 Prover 1: Warning: ignoring some quantifiers % 4.98/1.50 Prover 5: Proving ... % 4.98/1.52 Prover 1: Constructing countermodel ... % 5.91/1.56 Prover 2: Proving ... % 6.32/1.57 Prover 6: Proving ... % 6.36/1.58 Prover 3: Warning: ignoring some quantifiers % 6.36/1.58 Prover 0: Proving ... % 6.36/1.58 Prover 4: Warning: ignoring some quantifiers % 6.36/1.59 Prover 3: Constructing countermodel ... % 6.36/1.60 Prover 4: Constructing countermodel ... % 9.08/1.95 Prover 1: Found proof (size 28) % 9.08/1.95 Prover 1: proved (1330ms) % 9.08/1.95 Prover 3: stopped % 9.08/1.95 Prover 4: stopped % 9.08/1.95 Prover 6: stopped % 9.08/1.95 Prover 5: stopped % 9.08/1.95 Prover 2: stopped % 9.08/1.95 Prover 0: stopped % 9.08/1.96 % 9.08/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.08/1.96 % 9.08/1.96 % SZS output start Proof for theBenchmark % 9.08/1.96 Assumptions after simplification: % 9.08/1.96 --------------------------------- % 9.08/1.97 % 9.08/1.97 (d1_funct_1) % 9.08/2.00 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ $i(v0) | ? % 9.08/2.00 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v4 = % 9.08/2.00 v3) & ordered_pair(v2, v4) = v6 & ordered_pair(v2, v3) = v5 & in(v6, v0) % 9.08/2.00 = 0 & in(v5, v0) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! % 9.08/2.00 [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! % 9.08/2.00 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v3 = v2 | ~ (ordered_pair(v1, v3) = % 9.08/2.00 v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (in(v5, v0) = 0) | ~ (in(v4, % 9.08/2.00 v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1))) % 9.08/2.00 % 9.08/2.00 (d1_relat_1) % 9.08/2.00 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (relation(v0) = v1) | ~ $i(v0) | ? % 9.08/2.00 [v2: $i] : (in(v2, v0) = 0 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ % 9.08/2.00 (ordered_pair(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3)))) & ! [v0: $i] : ( % 9.08/2.00 ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ % 9.08/2.00 $i(v1) | ? [v2: $i] : ? [v3: $i] : (ordered_pair(v2, v3) = v1 & $i(v3) & % 9.08/2.00 $i(v2)))) % 9.08/2.00 % 9.08/2.00 (t2_funct_1) % 9.08/2.01 ? [v0: $i] : ? [v1: any] : ? [v2: any] : (function(v0) = v2 & relation(v0) % 9.08/2.01 = v1 & $i(v0) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 9.08/2.01 [v7: $i] : (v5 = v4 | ~ (ordered_pair(v3, v5) = v7) | ~ (ordered_pair(v3, % 9.08/2.01 v4) = v6) | ~ (in(v7, v0) = 0) | ~ (in(v6, v0) = 0) | ~ $i(v5) | ~ % 9.08/2.01 $i(v4) | ~ $i(v3)) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) | ~ $i(v3) | ? % 9.08/2.01 [v4: $i] : ? [v5: $i] : (ordered_pair(v4, v5) = v3 & $i(v5) & $i(v4))) & % 9.08/2.01 ( ~ (v2 = 0) | ~ (v1 = 0))) % 9.08/2.01 % 9.08/2.01 Further assumptions not needed in the proof: % 9.08/2.01 -------------------------------------------- % 9.08/2.01 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k2_tarski, % 9.08/2.01 d5_tarski, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, % 9.08/2.01 fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1, rc1_funct_1, rc1_relat_1, % 9.08/2.01 rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, % 9.08/2.01 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 9.08/2.01 t5_subset, t6_boole, t7_boole, t8_boole % 9.08/2.01 % 9.08/2.01 Those formulas are unsatisfiable: % 9.08/2.01 --------------------------------- % 9.08/2.01 % 9.08/2.01 Begin of proof % 9.08/2.01 | % 9.08/2.01 | ALPHA: (d1_funct_1) implies: % 9.08/2.01 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (function(v0) = v1) | ~ % 9.08/2.01 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 9.08/2.01 | [v6: $i] : ( ~ (v4 = v3) & ordered_pair(v2, v4) = v6 & % 9.08/2.01 | ordered_pair(v2, v3) = v5 & in(v6, v0) = 0 & in(v5, v0) = 0 & % 9.08/2.01 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 9.08/2.01 | % 9.08/2.01 | ALPHA: (d1_relat_1) implies: % 9.08/2.01 | (2) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (relation(v0) = v1) | ~ % 9.08/2.01 | $i(v0) | ? [v2: $i] : (in(v2, v0) = 0 & $i(v2) & ! [v3: $i] : ! % 9.08/2.02 | [v4: $i] : ( ~ (ordered_pair(v3, v4) = v2) | ~ $i(v4) | ~ % 9.08/2.02 | $i(v3)))) % 9.08/2.02 | % 9.08/2.02 | DELTA: instantiating (t2_funct_1) with fresh symbols all_40_0, all_40_1, % 9.08/2.02 | all_40_2 gives: % 9.08/2.02 | (3) function(all_40_2) = all_40_0 & relation(all_40_2) = all_40_1 & % 9.08/2.02 | $i(all_40_2) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 9.08/2.02 | ! [v4: $i] : (v2 = v1 | ~ (ordered_pair(v0, v2) = v4) | ~ % 9.08/2.02 | (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_40_2) = 0) | ~ (in(v3, % 9.08/2.02 | all_40_2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] % 9.08/2.02 | : ( ~ (in(v0, all_40_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 9.08/2.02 | (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1))) & ( ~ (all_40_0 = 0) | % 9.08/2.02 | ~ (all_40_1 = 0)) % 9.08/2.02 | % 9.08/2.02 | ALPHA: (3) implies: % 9.08/2.02 | (4) $i(all_40_2) % 9.08/2.02 | (5) relation(all_40_2) = all_40_1 % 9.08/2.02 | (6) function(all_40_2) = all_40_0 % 9.08/2.02 | (7) ~ (all_40_0 = 0) | ~ (all_40_1 = 0) % 9.08/2.02 | (8) ! [v0: $i] : ( ~ (in(v0, all_40_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 9.08/2.02 | [v2: $i] : (ordered_pair(v1, v2) = v0 & $i(v2) & $i(v1))) % 9.08/2.02 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 9.08/2.02 | (v2 = v1 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = % 9.08/2.02 | v3) | ~ (in(v4, all_40_2) = 0) | ~ (in(v3, all_40_2) = 0) | ~ % 9.08/2.02 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 9.08/2.02 | % 9.08/2.02 | GROUND_INST: instantiating (2) with all_40_2, all_40_1, simplifying with (4), % 9.08/2.02 | (5) gives: % 9.08/2.03 | (10) all_40_1 = 0 | ? [v0: $i] : (in(v0, all_40_2) = 0 & $i(v0) & ! [v1: % 9.08/2.03 | $i] : ! [v2: $i] : ( ~ (ordered_pair(v1, v2) = v0) | ~ $i(v2) | % 9.08/2.03 | ~ $i(v1))) % 9.08/2.03 | % 9.08/2.03 | GROUND_INST: instantiating (1) with all_40_2, all_40_0, simplifying with (4), % 9.08/2.03 | (6) gives: % 9.08/2.03 | (11) all_40_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 9.08/2.03 | ? [v4: $i] : ( ~ (v2 = v1) & ordered_pair(v0, v2) = v4 & % 9.08/2.03 | ordered_pair(v0, v1) = v3 & in(v4, all_40_2) = 0 & in(v3, all_40_2) % 9.08/2.03 | = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.08/2.03 | % 9.08/2.03 | BETA: splitting (7) gives: % 9.08/2.03 | % 9.08/2.03 | Case 1: % 9.08/2.03 | | % 9.08/2.03 | | (12) ~ (all_40_0 = 0) % 9.08/2.03 | | % 9.08/2.03 | | BETA: splitting (11) gives: % 9.08/2.03 | | % 9.08/2.03 | | Case 1: % 9.08/2.03 | | | % 9.08/2.03 | | | (13) all_40_0 = 0 % 9.08/2.03 | | | % 9.08/2.03 | | | REDUCE: (12), (13) imply: % 9.08/2.03 | | | (14) $false % 9.08/2.03 | | | % 9.08/2.03 | | | CLOSE: (14) is inconsistent. % 9.08/2.03 | | | % 9.08/2.03 | | Case 2: % 9.08/2.03 | | | % 9.08/2.03 | | | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 9.08/2.03 | | | $i] : ( ~ (v2 = v1) & ordered_pair(v0, v2) = v4 & % 9.08/2.03 | | | ordered_pair(v0, v1) = v3 & in(v4, all_40_2) = 0 & in(v3, % 9.08/2.03 | | | all_40_2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.08/2.03 | | | % 9.08/2.03 | | | DELTA: instantiating (15) with fresh symbols all_87_0, all_87_1, all_87_2, % 9.08/2.03 | | | all_87_3, all_87_4 gives: % 9.08/2.03 | | | (16) ~ (all_87_2 = all_87_3) & ordered_pair(all_87_4, all_87_2) = % 9.08/2.03 | | | all_87_0 & ordered_pair(all_87_4, all_87_3) = all_87_1 & % 9.08/2.03 | | | in(all_87_0, all_40_2) = 0 & in(all_87_1, all_40_2) = 0 & % 9.08/2.03 | | | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & % 9.08/2.03 | | | $i(all_87_4) % 9.08/2.03 | | | % 9.08/2.03 | | | ALPHA: (16) implies: % 9.08/2.03 | | | (17) ~ (all_87_2 = all_87_3) % 9.08/2.03 | | | (18) $i(all_87_4) % 9.08/2.03 | | | (19) $i(all_87_3) % 9.08/2.03 | | | (20) $i(all_87_2) % 9.08/2.03 | | | (21) in(all_87_1, all_40_2) = 0 % 9.08/2.03 | | | (22) in(all_87_0, all_40_2) = 0 % 9.08/2.03 | | | (23) ordered_pair(all_87_4, all_87_3) = all_87_1 % 9.08/2.03 | | | (24) ordered_pair(all_87_4, all_87_2) = all_87_0 % 9.08/2.03 | | | % 9.08/2.03 | | | GROUND_INST: instantiating (9) with all_87_4, all_87_3, all_87_2, % 9.08/2.03 | | | all_87_1, all_87_0, simplifying with (18), (19), (20), (21), % 9.08/2.03 | | | (22), (23), (24) gives: % 9.08/2.03 | | | (25) all_87_2 = all_87_3 % 9.08/2.03 | | | % 9.08/2.04 | | | REDUCE: (17), (25) imply: % 9.08/2.04 | | | (26) $false % 9.08/2.04 | | | % 9.08/2.04 | | | CLOSE: (26) is inconsistent. % 9.08/2.04 | | | % 9.08/2.04 | | End of split % 9.08/2.04 | | % 9.08/2.04 | Case 2: % 9.08/2.04 | | % 9.08/2.04 | | (27) ~ (all_40_1 = 0) % 9.08/2.04 | | % 9.08/2.04 | | BETA: splitting (10) gives: % 9.08/2.04 | | % 9.08/2.04 | | Case 1: % 9.08/2.04 | | | % 9.08/2.04 | | | (28) all_40_1 = 0 % 9.08/2.04 | | | % 9.08/2.04 | | | REDUCE: (27), (28) imply: % 9.08/2.04 | | | (29) $false % 9.08/2.04 | | | % 9.08/2.04 | | | CLOSE: (29) is inconsistent. % 9.08/2.04 | | | % 9.08/2.04 | | Case 2: % 9.08/2.04 | | | % 9.08/2.04 | | | (30) ? [v0: $i] : (in(v0, all_40_2) = 0 & $i(v0) & ! [v1: $i] : ! % 9.08/2.04 | | | [v2: $i] : ( ~ (ordered_pair(v1, v2) = v0) | ~ $i(v2) | ~ % 9.08/2.04 | | | $i(v1))) % 9.08/2.04 | | | % 9.08/2.04 | | | DELTA: instantiating (30) with fresh symbol all_82_0 gives: % 9.08/2.04 | | | (31) in(all_82_0, all_40_2) = 0 & $i(all_82_0) & ! [v0: $i] : ! [v1: % 9.08/2.04 | | | $i] : ( ~ (ordered_pair(v0, v1) = all_82_0) | ~ $i(v1) | ~ % 9.08/2.04 | | | $i(v0)) % 9.08/2.04 | | | % 9.08/2.04 | | | ALPHA: (31) implies: % 9.08/2.04 | | | (32) $i(all_82_0) % 9.08/2.04 | | | (33) in(all_82_0, all_40_2) = 0 % 9.08/2.04 | | | (34) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = all_82_0) % 9.08/2.04 | | | | ~ $i(v1) | ~ $i(v0)) % 9.08/2.04 | | | % 9.08/2.04 | | | GROUND_INST: instantiating (8) with all_82_0, simplifying with (32), (33) % 9.08/2.04 | | | gives: % 9.08/2.04 | | | (35) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_82_0 & % 9.08/2.04 | | | $i(v1) & $i(v0)) % 9.08/2.04 | | | % 9.08/2.04 | | | DELTA: instantiating (35) with fresh symbols all_98_0, all_98_1 gives: % 9.08/2.04 | | | (36) ordered_pair(all_98_1, all_98_0) = all_82_0 & $i(all_98_0) & % 9.08/2.04 | | | $i(all_98_1) % 9.08/2.04 | | | % 9.08/2.04 | | | ALPHA: (36) implies: % 9.08/2.04 | | | (37) $i(all_98_1) % 9.08/2.04 | | | (38) $i(all_98_0) % 9.08/2.04 | | | (39) ordered_pair(all_98_1, all_98_0) = all_82_0 % 9.08/2.04 | | | % 9.08/2.04 | | | GROUND_INST: instantiating (34) with all_98_1, all_98_0, simplifying with % 9.08/2.04 | | | (37), (38), (39) gives: % 9.08/2.04 | | | (40) $false % 9.08/2.04 | | | % 9.08/2.04 | | | CLOSE: (40) is inconsistent. % 9.08/2.04 | | | % 9.08/2.04 | | End of split % 9.08/2.04 | | % 9.08/2.04 | End of split % 9.08/2.04 | % 9.08/2.04 End of proof % 9.08/2.04 % SZS output end Proof for theBenchmark % 9.08/2.04 % 9.08/2.04 1441ms %------------------------------------------------------------------------------