%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN084+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 : n015.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 03:26:32 EDT 2023 % Result : Theorem 4.17s 1.27s % Output : Proof 5.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN084+1 : TPTP v8.1.2. Released v2.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n015.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 17:25:23 EDT 2023 % 0.14/0.34 % 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 ... % 0.20/0.63 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.15/0.97 Prover 4: Preprocessing ... % 2.15/0.97 Prover 1: Preprocessing ... % 2.15/1.01 Prover 3: Preprocessing ... % 2.15/1.01 Prover 0: Preprocessing ... % 2.15/1.01 Prover 5: Preprocessing ... % 2.15/1.01 Prover 6: Preprocessing ... % 2.15/1.01 Prover 2: Preprocessing ... % 2.94/1.12 Prover 5: Constructing countermodel ... % 2.94/1.12 Prover 1: Constructing countermodel ... % 2.94/1.12 Prover 3: Constructing countermodel ... % 3.20/1.15 Prover 6: Proving ... % 3.20/1.15 Prover 2: Proving ... % 3.20/1.17 Prover 4: Constructing countermodel ... % 3.20/1.17 Prover 0: Proving ... % 4.17/1.27 Prover 5: proved (627ms) % 4.17/1.27 % 4.17/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.17/1.27 % 4.17/1.27 Prover 3: stopped % 4.17/1.27 Prover 6: stopped % 4.17/1.27 Prover 0: stopped % 4.17/1.27 Prover 2: stopped % 4.17/1.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.17/1.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.17/1.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.17/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.17/1.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.17/1.29 Prover 13: Preprocessing ... % 4.17/1.30 Prover 11: Preprocessing ... % 4.17/1.30 Prover 8: Preprocessing ... % 4.17/1.30 Prover 7: Preprocessing ... % 4.17/1.30 Prover 10: Preprocessing ... % 4.17/1.34 Prover 7: Constructing countermodel ... % 4.17/1.35 Prover 8: Warning: ignoring some quantifiers % 4.17/1.36 Prover 8: Constructing countermodel ... % 4.17/1.36 Prover 10: Constructing countermodel ... % 4.17/1.36 Prover 13: Constructing countermodel ... % 4.88/1.38 Prover 11: Constructing countermodel ... % 4.88/1.45 Prover 10: Found proof (size 44) % 4.88/1.45 Prover 10: proved (174ms) % 4.88/1.45 Prover 11: stopped % 4.88/1.45 Prover 7: stopped % 4.88/1.45 Prover 8: stopped % 4.88/1.45 Prover 1: stopped % 4.88/1.45 Prover 13: stopped % 4.88/1.47 Prover 4: stopped % 4.88/1.47 % 4.88/1.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.88/1.47 % 4.88/1.47 % SZS output start Proof for theBenchmark % 4.88/1.48 Assumptions after simplification: % 4.88/1.48 --------------------------------- % 4.88/1.48 % 4.88/1.48 (pel62) % 4.88/1.51 $i(a) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 4.88/1.51 ? [v5: $i] : ($i(v3) & $i(v0) & ((f(v4) = v5 & f(v3) = v4 & $i(v5) & $i(v4) & % 4.88/1.51 big_p(a) & ~ big_p(v5) & ! [v6: $i] : ! [v7: $i] : ( ~ (f(v6) = v7) | % 4.88/1.51 ~ $i(v6) | ~ big_p(v7) | ? [v8: $i] : (f(v7) = v8 & $i(v8) & % 4.88/1.51 big_p(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~ (f(v6) = v7) | ~ % 4.88/1.51 $i(v6) | big_p(v6) | ? [v8: $i] : (f(v7) = v8 & $i(v8) & big_p(v8))) % 4.88/1.51 & ( ~ big_p(v3) | big_p(v4))) | (f(v1) = v2 & f(v0) = v1 & $i(v2) & % 4.88/1.51 $i(v1) & big_p(a) & ~ big_p(v2) & ! [v6: $i] : ! [v7: $i] : ( ~ % 4.88/1.51 (f(v6) = v7) | ~ $i(v6) | ~ big_p(v7) | ? [v8: $i] : (f(v7) = v8 & % 4.88/1.51 $i(v8) & big_p(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~ (f(v6) = v7) % 4.88/1.51 | ~ $i(v6) | big_p(v6) | ? [v8: $i] : (f(v7) = v8 & $i(v8) & % 4.88/1.51 big_p(v8))) & ( ~ big_p(v0) | big_p(v1))))) % 4.88/1.52 % 4.88/1.52 (function-axioms) % 4.88/1.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | ~ % 4.88/1.52 (f(v2) = v0)) % 4.88/1.52 % 4.88/1.52 Those formulas are unsatisfiable: % 5.66/1.52 --------------------------------- % 5.66/1.52 % 5.66/1.52 Begin of proof % 5.66/1.52 | % 5.66/1.52 | ALPHA: (pel62) implies: % 5.66/1.53 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 5.66/1.53 | ? [v5: $i] : ($i(v3) & $i(v0) & ((f(v4) = v5 & f(v3) = v4 & $i(v5) & % 5.66/1.53 | $i(v4) & big_p(a) & ~ big_p(v5) & ! [v6: $i] : ! [v7: $i] : ( % 5.66/1.53 | ~ (f(v6) = v7) | ~ $i(v6) | ~ big_p(v7) | ? [v8: $i] : % 5.66/1.53 | (f(v7) = v8 & $i(v8) & big_p(v8))) & ! [v6: $i] : ! [v7: $i] % 5.66/1.53 | : ( ~ (f(v6) = v7) | ~ $i(v6) | big_p(v6) | ? [v8: $i] : (f(v7) % 5.66/1.53 | = v8 & $i(v8) & big_p(v8))) & ( ~ big_p(v3) | big_p(v4))) | % 5.66/1.53 | (f(v1) = v2 & f(v0) = v1 & $i(v2) & $i(v1) & big_p(a) & ~ % 5.66/1.53 | big_p(v2) & ! [v6: $i] : ! [v7: $i] : ( ~ (f(v6) = v7) | ~ % 5.66/1.53 | $i(v6) | ~ big_p(v7) | ? [v8: $i] : (f(v7) = v8 & $i(v8) & % 5.66/1.53 | big_p(v8))) & ! [v6: $i] : ! [v7: $i] : ( ~ (f(v6) = v7) | % 5.66/1.53 | ~ $i(v6) | big_p(v6) | ? [v8: $i] : (f(v7) = v8 & $i(v8) & % 5.66/1.53 | big_p(v8))) & ( ~ big_p(v0) | big_p(v1))))) % 5.66/1.53 | % 5.66/1.53 | DELTA: instantiating (1) with fresh symbols all_4_0, all_4_1, all_4_2, % 5.66/1.53 | all_4_3, all_4_4, all_4_5 gives: % 5.66/1.54 | (2) $i(all_4_2) & $i(all_4_5) & ((f(all_4_1) = all_4_0 & f(all_4_2) = % 5.66/1.54 | all_4_1 & $i(all_4_0) & $i(all_4_1) & big_p(a) & ~ big_p(all_4_0) % 5.66/1.54 | & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ % 5.66/1.54 | big_p(v1) | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) & ! % 5.66/1.54 | [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) | % 5.66/1.54 | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) & ( ~ % 5.66/1.54 | big_p(all_4_2) | big_p(all_4_1))) | (f(all_4_4) = all_4_3 & % 5.66/1.54 | f(all_4_5) = all_4_4 & $i(all_4_3) & $i(all_4_4) & big_p(a) & ~ % 5.66/1.54 | big_p(all_4_3) & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ % 5.66/1.54 | $i(v0) | ~ big_p(v1) | ? [v2: $i] : (f(v1) = v2 & $i(v2) & % 5.66/1.54 | big_p(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ % 5.66/1.54 | $i(v0) | big_p(v0) | ? [v2: $i] : (f(v1) = v2 & $i(v2) & % 5.66/1.54 | big_p(v2))) & ( ~ big_p(all_4_5) | big_p(all_4_4)))) % 5.66/1.54 | % 5.66/1.54 | ALPHA: (2) implies: % 5.66/1.54 | (3) $i(all_4_5) % 5.66/1.54 | (4) $i(all_4_2) % 5.66/1.54 | (5) (f(all_4_1) = all_4_0 & f(all_4_2) = all_4_1 & $i(all_4_0) & % 5.66/1.54 | $i(all_4_1) & big_p(a) & ~ big_p(all_4_0) & ! [v0: $i] : ! [v1: % 5.66/1.54 | $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ big_p(v1) | ? [v2: $i] : % 5.66/1.54 | (f(v1) = v2 & $i(v2) & big_p(v2))) & ! [v0: $i] : ! [v1: $i] : ( % 5.66/1.54 | ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) | ? [v2: $i] : (f(v1) = v2 % 5.66/1.54 | & $i(v2) & big_p(v2))) & ( ~ big_p(all_4_2) | big_p(all_4_1))) | % 5.66/1.54 | (f(all_4_4) = all_4_3 & f(all_4_5) = all_4_4 & $i(all_4_3) & % 5.66/1.54 | $i(all_4_4) & big_p(a) & ~ big_p(all_4_3) & ! [v0: $i] : ! [v1: % 5.66/1.54 | $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ big_p(v1) | ? [v2: $i] : % 5.66/1.54 | (f(v1) = v2 & $i(v2) & big_p(v2))) & ! [v0: $i] : ! [v1: $i] : ( % 5.66/1.54 | ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) | ? [v2: $i] : (f(v1) = v2 % 5.66/1.54 | & $i(v2) & big_p(v2))) & ( ~ big_p(all_4_5) | big_p(all_4_4))) % 5.66/1.54 | % 5.66/1.54 | BETA: splitting (5) gives: % 5.66/1.54 | % 5.66/1.54 | Case 1: % 5.66/1.54 | | % 5.66/1.55 | | (6) f(all_4_1) = all_4_0 & f(all_4_2) = all_4_1 & $i(all_4_0) & % 5.66/1.55 | | $i(all_4_1) & big_p(a) & ~ big_p(all_4_0) & ! [v0: $i] : ! [v1: % 5.66/1.55 | | $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ big_p(v1) | ? [v2: $i] : % 5.66/1.55 | | (f(v1) = v2 & $i(v2) & big_p(v2))) & ! [v0: $i] : ! [v1: $i] : ( % 5.66/1.55 | | ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) | ? [v2: $i] : (f(v1) = v2 % 5.66/1.55 | | & $i(v2) & big_p(v2))) & ( ~ big_p(all_4_2) | big_p(all_4_1)) % 5.66/1.55 | | % 5.66/1.55 | | ALPHA: (6) implies: % 5.66/1.55 | | (7) ~ big_p(all_4_0) % 5.66/1.55 | | (8) f(all_4_2) = all_4_1 % 5.66/1.55 | | (9) f(all_4_1) = all_4_0 % 5.66/1.55 | | (10) ~ big_p(all_4_2) | big_p(all_4_1) % 5.66/1.55 | | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) % 5.66/1.55 | | | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) % 5.66/1.55 | | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ % 5.66/1.55 | | big_p(v1) | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) % 5.66/1.55 | | % 5.87/1.55 | | GROUND_INST: instantiating (11) with all_4_2, all_4_1, simplifying with (4), % 5.87/1.55 | | (8) gives: % 5.87/1.55 | | (13) big_p(all_4_2) | ? [v0: $i] : (f(all_4_1) = v0 & $i(v0) & % 5.87/1.55 | | big_p(v0)) % 5.87/1.55 | | % 5.87/1.55 | | BETA: splitting (10) gives: % 5.87/1.55 | | % 5.87/1.55 | | Case 1: % 5.87/1.55 | | | % 5.87/1.55 | | | (14) ~ big_p(all_4_2) % 5.87/1.55 | | | % 5.87/1.55 | | | BETA: splitting (13) gives: % 5.87/1.55 | | | % 5.87/1.55 | | | Case 1: % 5.87/1.55 | | | | % 5.87/1.55 | | | | (15) big_p(all_4_2) % 5.87/1.55 | | | | % 5.87/1.55 | | | | PRED_UNIFY: (14), (15) imply: % 5.87/1.55 | | | | (16) $false % 5.87/1.55 | | | | % 5.87/1.55 | | | | CLOSE: (16) is inconsistent. % 5.87/1.55 | | | | % 5.87/1.55 | | | Case 2: % 5.87/1.55 | | | | % 5.89/1.55 | | | | (17) ? [v0: $i] : (f(all_4_1) = v0 & $i(v0) & big_p(v0)) % 5.89/1.55 | | | | % 5.89/1.55 | | | | DELTA: instantiating (17) with fresh symbol all_25_0 gives: % 5.89/1.55 | | | | (18) f(all_4_1) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.55 | | | | % 5.89/1.55 | | | | REF_CLOSE: (7), (9), (18), (function-axioms) are inconsistent by % 5.89/1.55 | | | | sub-proof #2. % 5.89/1.55 | | | | % 5.89/1.55 | | | End of split % 5.89/1.55 | | | % 5.89/1.55 | | Case 2: % 5.89/1.55 | | | % 5.89/1.55 | | | (19) big_p(all_4_1) % 5.89/1.55 | | | % 5.89/1.55 | | | GROUND_INST: instantiating (12) with all_4_2, all_4_1, simplifying with % 5.89/1.55 | | | (4), (8), (19) gives: % 5.89/1.56 | | | (20) ? [v0: $i] : (f(all_4_1) = v0 & $i(v0) & big_p(v0)) % 5.89/1.56 | | | % 5.89/1.56 | | | DELTA: instantiating (20) with fresh symbol all_25_0 gives: % 5.89/1.56 | | | (21) f(all_4_1) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.56 | | | % 5.89/1.56 | | | REF_CLOSE: (7), (9), (21), (function-axioms) are inconsistent by sub-proof % 5.89/1.56 | | | #2. % 5.89/1.56 | | | % 5.89/1.56 | | End of split % 5.89/1.56 | | % 5.89/1.56 | Case 2: % 5.89/1.56 | | % 5.89/1.56 | | (22) f(all_4_4) = all_4_3 & f(all_4_5) = all_4_4 & $i(all_4_3) & % 5.89/1.56 | | $i(all_4_4) & big_p(a) & ~ big_p(all_4_3) & ! [v0: $i] : ! [v1: % 5.89/1.56 | | $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ big_p(v1) | ? [v2: $i] : % 5.89/1.56 | | (f(v1) = v2 & $i(v2) & big_p(v2))) & ! [v0: $i] : ! [v1: $i] : ( % 5.89/1.56 | | ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) | ? [v2: $i] : (f(v1) = v2 % 5.89/1.56 | | & $i(v2) & big_p(v2))) & ( ~ big_p(all_4_5) | big_p(all_4_4)) % 5.89/1.56 | | % 5.89/1.56 | | ALPHA: (22) implies: % 5.89/1.56 | | (23) ~ big_p(all_4_3) % 5.89/1.56 | | (24) f(all_4_5) = all_4_4 % 5.89/1.56 | | (25) f(all_4_4) = all_4_3 % 5.89/1.56 | | (26) ~ big_p(all_4_5) | big_p(all_4_4) % 5.89/1.56 | | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | big_p(v0) % 5.89/1.56 | | | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) % 5.89/1.56 | | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (f(v0) = v1) | ~ $i(v0) | ~ % 5.89/1.56 | | big_p(v1) | ? [v2: $i] : (f(v1) = v2 & $i(v2) & big_p(v2))) % 5.89/1.56 | | % 5.89/1.56 | | GROUND_INST: instantiating (27) with all_4_5, all_4_4, simplifying with (3), % 5.89/1.56 | | (24) gives: % 5.89/1.56 | | (29) big_p(all_4_5) | ? [v0: $i] : (f(all_4_4) = v0 & $i(v0) & % 5.89/1.56 | | big_p(v0)) % 5.89/1.56 | | % 5.89/1.56 | | BETA: splitting (26) gives: % 5.89/1.56 | | % 5.89/1.56 | | Case 1: % 5.89/1.56 | | | % 5.89/1.56 | | | (30) ~ big_p(all_4_5) % 5.89/1.56 | | | % 5.89/1.56 | | | BETA: splitting (29) gives: % 5.89/1.56 | | | % 5.89/1.56 | | | Case 1: % 5.89/1.56 | | | | % 5.89/1.56 | | | | (31) big_p(all_4_5) % 5.89/1.56 | | | | % 5.89/1.56 | | | | PRED_UNIFY: (30), (31) imply: % 5.89/1.56 | | | | (32) $false % 5.89/1.56 | | | | % 5.89/1.56 | | | | CLOSE: (32) is inconsistent. % 5.89/1.56 | | | | % 5.89/1.56 | | | Case 2: % 5.89/1.56 | | | | % 5.89/1.56 | | | | (33) ? [v0: $i] : (f(all_4_4) = v0 & $i(v0) & big_p(v0)) % 5.89/1.56 | | | | % 5.89/1.56 | | | | DELTA: instantiating (33) with fresh symbol all_25_0 gives: % 5.89/1.56 | | | | (34) f(all_4_4) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.56 | | | | % 5.89/1.56 | | | | REF_CLOSE: (23), (25), (34), (function-axioms) are inconsistent by % 5.89/1.56 | | | | sub-proof #1. % 5.89/1.56 | | | | % 5.89/1.56 | | | End of split % 5.89/1.56 | | | % 5.89/1.56 | | Case 2: % 5.89/1.56 | | | % 5.89/1.56 | | | (35) big_p(all_4_4) % 5.89/1.56 | | | % 5.89/1.56 | | | GROUND_INST: instantiating (28) with all_4_5, all_4_4, simplifying with % 5.89/1.56 | | | (3), (24), (35) gives: % 5.89/1.57 | | | (36) ? [v0: $i] : (f(all_4_4) = v0 & $i(v0) & big_p(v0)) % 5.89/1.57 | | | % 5.89/1.57 | | | DELTA: instantiating (36) with fresh symbol all_25_0 gives: % 5.89/1.57 | | | (37) f(all_4_4) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.57 | | | % 5.89/1.57 | | | REF_CLOSE: (23), (25), (37), (function-axioms) are inconsistent by % 5.89/1.57 | | | sub-proof #1. % 5.89/1.57 | | | % 5.89/1.57 | | End of split % 5.89/1.57 | | % 5.89/1.57 | End of split % 5.89/1.57 | % 5.89/1.57 End of proof % 5.89/1.57 % 5.89/1.57 Sub-proof #1 shows that the following formulas are inconsistent: % 5.89/1.57 ---------------------------------------------------------------- % 5.89/1.57 (1) f(all_4_4) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | ~ % 5.89/1.57 (f(v2) = v0)) % 5.89/1.57 (3) f(all_4_4) = all_4_3 % 5.89/1.57 (4) ~ big_p(all_4_3) % 5.89/1.57 % 5.89/1.57 Begin of proof % 5.89/1.57 | % 5.89/1.57 | ALPHA: (1) implies: % 5.89/1.57 | (5) big_p(all_25_0) % 5.89/1.57 | (6) f(all_4_4) = all_25_0 % 5.89/1.57 | % 5.89/1.57 | GROUND_INST: instantiating (2) with all_4_3, all_25_0, all_4_4, simplifying % 5.89/1.57 | with (3), (6) gives: % 5.89/1.57 | (7) all_25_0 = all_4_3 % 5.89/1.57 | % 5.89/1.57 | REDUCE: (5), (7) imply: % 5.89/1.57 | (8) big_p(all_4_3) % 5.89/1.57 | % 5.89/1.57 | PRED_UNIFY: (4), (8) imply: % 5.89/1.57 | (9) $false % 5.89/1.57 | % 5.89/1.57 | CLOSE: (9) is inconsistent. % 5.89/1.57 | % 5.89/1.57 End of proof % 5.89/1.57 % 5.89/1.57 Sub-proof #2 shows that the following formulas are inconsistent: % 5.89/1.57 ---------------------------------------------------------------- % 5.89/1.57 (1) f(all_4_1) = all_25_0 & $i(all_25_0) & big_p(all_25_0) % 5.89/1.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (f(v2) = v1) | ~ % 5.89/1.57 (f(v2) = v0)) % 5.89/1.57 (3) f(all_4_1) = all_4_0 % 5.89/1.57 (4) ~ big_p(all_4_0) % 5.89/1.57 % 5.89/1.57 Begin of proof % 5.89/1.57 | % 5.89/1.57 | ALPHA: (1) implies: % 5.89/1.57 | (5) big_p(all_25_0) % 5.89/1.57 | (6) f(all_4_1) = all_25_0 % 5.89/1.57 | % 5.89/1.57 | GROUND_INST: instantiating (2) with all_4_0, all_25_0, all_4_1, simplifying % 5.89/1.57 | with (3), (6) gives: % 5.89/1.57 | (7) all_25_0 = all_4_0 % 5.89/1.57 | % 5.89/1.57 | REDUCE: (5), (7) imply: % 5.89/1.57 | (8) big_p(all_4_0) % 5.89/1.57 | % 5.89/1.57 | PRED_UNIFY: (4), (8) imply: % 5.89/1.57 | (9) $false % 5.89/1.57 | % 5.89/1.57 | CLOSE: (9) is inconsistent. % 5.89/1.57 | % 5.89/1.57 End of proof % 5.89/1.57 % SZS output end Proof for theBenchmark % 5.89/1.57 % 5.89/1.57 958ms %------------------------------------------------------------------------------