%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN393+1.003 : TPTP v8.1.2. Released v2.0.0. % 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 : Fri Sep 1 03:27:30 EDT 2023 % Result : Theorem 2.89s 1.14s % Output : Proof 4.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN393+1.003 : TPTP v8.1.2. Released v2.0.0. % 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 19:27:37 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 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.42/0.95 Prover 1: Preprocessing ... % 1.42/0.95 Prover 4: Preprocessing ... % 2.02/1.00 Prover 6: Preprocessing ... % 2.02/1.00 Prover 2: Preprocessing ... % 2.02/1.00 Prover 3: Preprocessing ... % 2.02/1.00 Prover 5: Preprocessing ... % 2.02/1.00 Prover 0: Preprocessing ... % 2.29/1.04 Prover 4: Constructing countermodel ... % 2.29/1.04 Prover 1: Constructing countermodel ... % 2.29/1.05 Prover 0: Constructing countermodel ... % 2.29/1.05 Prover 3: Constructing countermodel ... % 2.29/1.05 Prover 5: Constructing countermodel ... % 2.29/1.05 Prover 6: Constructing countermodel ... % 2.29/1.05 Prover 2: Constructing countermodel ... % 2.89/1.14 Prover 3: proved (512ms) % 2.89/1.14 % 2.89/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 2.89/1.14 % 2.89/1.14 Prover 2: stopped % 2.89/1.14 Prover 5: stopped % 2.89/1.14 Prover 0: stopped % 2.89/1.14 Prover 6: stopped % 2.89/1.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 2.89/1.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 2.89/1.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 2.89/1.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 2.89/1.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 2.89/1.15 Prover 11: Preprocessing ... % 2.89/1.15 Prover 10: Preprocessing ... % 2.89/1.15 Prover 13: Preprocessing ... % 2.89/1.16 Prover 8: Preprocessing ... % 2.89/1.16 Prover 7: Preprocessing ... % 2.89/1.17 Prover 10: Constructing countermodel ... % 2.89/1.18 Prover 7: Constructing countermodel ... % 2.89/1.18 Prover 8: Constructing countermodel ... % 2.89/1.18 Prover 11: Constructing countermodel ... % 2.89/1.19 Prover 13: Constructing countermodel ... % 3.42/1.25 Prover 4: Found proof (size 140) % 3.42/1.25 Prover 4: proved (630ms) % 3.42/1.26 Prover 1: Found proof (size 140) % 3.42/1.26 Prover 13: stopped % 3.42/1.26 Prover 1: proved (633ms) % 3.42/1.26 Prover 7: stopped % 3.42/1.26 Prover 10: stopped % 3.42/1.26 Prover 8: stopped % 3.42/1.26 Prover 11: stopped % 3.42/1.26 % 3.42/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.42/1.26 % 3.42/1.27 % SZS output start Proof for theBenchmark % 4.01/1.27 Assumptions after simplification: % 4.01/1.27 --------------------------------- % 4.01/1.27 % 4.01/1.27 (pel12) % 4.01/1.28 (((p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 & ~ % 4.01/1.28 p2)))) & ((p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 & ((p3 & p2) % 4.01/1.28 | ( ~ p3 & ~ p2))))) | (((p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ % 4.01/1.28 p3 & ((p2 & p1) | ( ~ p2 & ~ p1)))) & ((p1 & ((p3 & p2) | ( ~ p3 & ~ % 4.01/1.28 p2))) | ( ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3))))) % 4.01/1.28 % 4.01/1.28 Those formulas are unsatisfiable: % 4.01/1.28 --------------------------------- % 4.01/1.28 % 4.01/1.28 Begin of proof % 4.01/1.28 | % 4.01/1.28 | BETA: splitting (pel12) gives: % 4.01/1.28 | % 4.01/1.28 | Case 1: % 4.01/1.28 | | % 4.05/1.28 | | (1) ((p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 % 4.05/1.28 | | & ~ p2)))) & ((p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 % 4.05/1.28 | | & ((p3 & p2) | ( ~ p3 & ~ p2)))) % 4.05/1.28 | | % 4.05/1.28 | | ALPHA: (1) implies: % 4.05/1.28 | | (2) (p1 & ((p3 & ~ p2) | (p2 & ~ p3))) | ( ~ p1 & ((p3 & p2) | ( ~ p3 & % 4.05/1.28 | | ~ p2))) % 4.05/1.28 | | (3) (p3 & ((p2 & p1) | ( ~ p2 & ~ p1))) | ( ~ p3 & ((p2 & ~ p1) | (p1 & % 4.05/1.28 | | ~ p2))) % 4.05/1.28 | | % 4.05/1.28 | | BETA: splitting (2) gives: % 4.05/1.28 | | % 4.05/1.28 | | Case 1: % 4.05/1.28 | | | % 4.05/1.28 | | | (4) p1 & ((p3 & ~ p2) | (p2 & ~ p3)) % 4.05/1.29 | | | % 4.05/1.29 | | | ALPHA: (4) implies: % 4.05/1.29 | | | (5) p1 % 4.05/1.29 | | | (6) (p3 & ~ p2) | (p2 & ~ p3) % 4.05/1.29 | | | % 4.05/1.29 | | | BETA: splitting (3) gives: % 4.05/1.29 | | | % 4.05/1.29 | | | Case 1: % 4.05/1.29 | | | | % 4.05/1.29 | | | | (7) p3 & ((p2 & p1) | ( ~ p2 & ~ p1)) % 4.05/1.29 | | | | % 4.05/1.29 | | | | ALPHA: (7) implies: % 4.05/1.29 | | | | (8) p3 % 4.05/1.29 | | | | (9) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.29 | | | | % 4.05/1.29 | | | | BETA: splitting (6) gives: % 4.05/1.29 | | | | % 4.05/1.29 | | | | Case 1: % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | (10) p3 & ~ p2 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | ALPHA: (10) implies: % 4.05/1.29 | | | | | (11) ~ p2 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | REF_CLOSE: (5), (9), (11) are inconsistent by sub-proof #7. % 4.05/1.29 | | | | | % 4.05/1.29 | | | | Case 2: % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | (12) p2 & ~ p3 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | REF_CLOSE: (8), (12) are inconsistent by sub-proof #6. % 4.05/1.29 | | | | | % 4.05/1.29 | | | | End of split % 4.05/1.29 | | | | % 4.05/1.29 | | | Case 2: % 4.05/1.29 | | | | % 4.05/1.29 | | | | (13) ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2)) % 4.05/1.29 | | | | % 4.05/1.29 | | | | ALPHA: (13) implies: % 4.05/1.29 | | | | (14) ~ p3 % 4.05/1.29 | | | | (15) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.29 | | | | % 4.05/1.29 | | | | BETA: splitting (6) gives: % 4.05/1.29 | | | | % 4.05/1.29 | | | | Case 1: % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | (16) p3 & ~ p2 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | ALPHA: (16) implies: % 4.05/1.29 | | | | | (17) p3 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | PRED_UNIFY: (14), (17) imply: % 4.05/1.29 | | | | | (18) $false % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | CLOSE: (18) is inconsistent. % 4.05/1.29 | | | | | % 4.05/1.29 | | | | Case 2: % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | (19) p2 & ~ p3 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | ALPHA: (19) implies: % 4.05/1.29 | | | | | (20) p2 % 4.05/1.29 | | | | | % 4.05/1.29 | | | | | REF_CLOSE: (5), (15), (20) are inconsistent by sub-proof #5. % 4.05/1.29 | | | | | % 4.05/1.29 | | | | End of split % 4.05/1.29 | | | | % 4.05/1.29 | | | End of split % 4.05/1.29 | | | % 4.05/1.29 | | Case 2: % 4.05/1.29 | | | % 4.05/1.29 | | | (21) ~ p1 & ((p3 & p2) | ( ~ p3 & ~ p2)) % 4.05/1.29 | | | % 4.05/1.29 | | | ALPHA: (21) implies: % 4.05/1.29 | | | (22) ~ p1 % 4.05/1.29 | | | (23) (p3 & p2) | ( ~ p3 & ~ p2) % 4.05/1.29 | | | % 4.05/1.30 | | | BETA: splitting (3) gives: % 4.05/1.30 | | | % 4.05/1.30 | | | Case 1: % 4.05/1.30 | | | | % 4.05/1.30 | | | | (24) p3 & ((p2 & p1) | ( ~ p2 & ~ p1)) % 4.05/1.30 | | | | % 4.05/1.30 | | | | ALPHA: (24) implies: % 4.05/1.30 | | | | (25) p3 % 4.05/1.30 | | | | (26) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.30 | | | | % 4.05/1.30 | | | | BETA: splitting (23) gives: % 4.05/1.30 | | | | % 4.05/1.30 | | | | Case 1: % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | (27) p3 & p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | ALPHA: (27) implies: % 4.05/1.30 | | | | | (28) p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | REF_CLOSE: (22), (26), (28) are inconsistent by sub-proof #4. % 4.05/1.30 | | | | | % 4.05/1.30 | | | | Case 2: % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | (29) ~ p3 & ~ p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | REF_CLOSE: (25), (29) are inconsistent by sub-proof #3. % 4.05/1.30 | | | | | % 4.05/1.30 | | | | End of split % 4.05/1.30 | | | | % 4.05/1.30 | | | Case 2: % 4.05/1.30 | | | | % 4.05/1.30 | | | | (30) ~ p3 & ((p2 & ~ p1) | (p1 & ~ p2)) % 4.05/1.30 | | | | % 4.05/1.30 | | | | ALPHA: (30) implies: % 4.05/1.30 | | | | (31) ~ p3 % 4.05/1.30 | | | | (32) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.30 | | | | % 4.05/1.30 | | | | BETA: splitting (23) gives: % 4.05/1.30 | | | | % 4.05/1.30 | | | | Case 1: % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | (33) p3 & p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | REF_CLOSE: (31), (33) are inconsistent by sub-proof #2. % 4.05/1.30 | | | | | % 4.05/1.30 | | | | Case 2: % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | (34) ~ p3 & ~ p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | ALPHA: (34) implies: % 4.05/1.30 | | | | | (35) ~ p2 % 4.05/1.30 | | | | | % 4.05/1.30 | | | | | REF_CLOSE: (22), (32), (35) are inconsistent by sub-proof #1. % 4.05/1.30 | | | | | % 4.05/1.30 | | | | End of split % 4.05/1.30 | | | | % 4.05/1.30 | | | End of split % 4.05/1.30 | | | % 4.05/1.30 | | End of split % 4.05/1.30 | | % 4.05/1.30 | Case 2: % 4.05/1.30 | | % 4.05/1.30 | | (36) ((p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ p3 & ((p2 & p1) | ( ~ p2 % 4.05/1.30 | | & ~ p1)))) & ((p1 & ((p3 & p2) | ( ~ p3 & ~ p2))) | ( ~ p1 % 4.05/1.30 | | & ((p3 & ~ p2) | (p2 & ~ p3)))) % 4.05/1.30 | | % 4.05/1.30 | | ALPHA: (36) implies: % 4.05/1.30 | | (37) (p1 & ((p3 & p2) | ( ~ p3 & ~ p2))) | ( ~ p1 & ((p3 & ~ p2) | (p2 % 4.05/1.30 | | & ~ p3))) % 4.05/1.30 | | (38) (p3 & ((p2 & ~ p1) | (p1 & ~ p2))) | ( ~ p3 & ((p2 & p1) | ( ~ p2 % 4.05/1.30 | | & ~ p1))) % 4.05/1.30 | | % 4.05/1.30 | | BETA: splitting (37) gives: % 4.05/1.30 | | % 4.05/1.30 | | Case 1: % 4.05/1.30 | | | % 4.05/1.30 | | | (39) p1 & ((p3 & p2) | ( ~ p3 & ~ p2)) % 4.05/1.30 | | | % 4.05/1.30 | | | ALPHA: (39) implies: % 4.05/1.30 | | | (40) p1 % 4.05/1.30 | | | (41) (p3 & p2) | ( ~ p3 & ~ p2) % 4.05/1.30 | | | % 4.05/1.30 | | | BETA: splitting (38) gives: % 4.05/1.30 | | | % 4.05/1.30 | | | Case 1: % 4.05/1.30 | | | | % 4.05/1.30 | | | | (42) p3 & ((p2 & ~ p1) | (p1 & ~ p2)) % 4.05/1.30 | | | | % 4.05/1.30 | | | | ALPHA: (42) implies: % 4.05/1.30 | | | | (43) p3 % 4.05/1.31 | | | | (44) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.31 | | | | % 4.05/1.31 | | | | BETA: splitting (41) gives: % 4.05/1.31 | | | | % 4.05/1.31 | | | | Case 1: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (45) p3 & p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | ALPHA: (45) implies: % 4.05/1.31 | | | | | (46) p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (40), (44), (46) are inconsistent by sub-proof #5. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | Case 2: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (47) ~ p3 & ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (43), (47) are inconsistent by sub-proof #3. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | End of split % 4.05/1.31 | | | | % 4.05/1.31 | | | Case 2: % 4.05/1.31 | | | | % 4.05/1.31 | | | | (48) ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1)) % 4.05/1.31 | | | | % 4.05/1.31 | | | | ALPHA: (48) implies: % 4.05/1.31 | | | | (49) ~ p3 % 4.05/1.31 | | | | (50) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.31 | | | | % 4.05/1.31 | | | | BETA: splitting (41) gives: % 4.05/1.31 | | | | % 4.05/1.31 | | | | Case 1: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (51) p3 & p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (49), (51) are inconsistent by sub-proof #2. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | Case 2: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (52) ~ p3 & ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | ALPHA: (52) implies: % 4.05/1.31 | | | | | (53) ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (40), (50), (53) are inconsistent by sub-proof #7. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | End of split % 4.05/1.31 | | | | % 4.05/1.31 | | | End of split % 4.05/1.31 | | | % 4.05/1.31 | | Case 2: % 4.05/1.31 | | | % 4.05/1.31 | | | (54) ~ p1 & ((p3 & ~ p2) | (p2 & ~ p3)) % 4.05/1.31 | | | % 4.05/1.31 | | | ALPHA: (54) implies: % 4.05/1.31 | | | (55) ~ p1 % 4.05/1.31 | | | (56) (p3 & ~ p2) | (p2 & ~ p3) % 4.05/1.31 | | | % 4.05/1.31 | | | BETA: splitting (38) gives: % 4.05/1.31 | | | % 4.05/1.31 | | | Case 1: % 4.05/1.31 | | | | % 4.05/1.31 | | | | (57) p3 & ((p2 & ~ p1) | (p1 & ~ p2)) % 4.05/1.31 | | | | % 4.05/1.31 | | | | ALPHA: (57) implies: % 4.05/1.31 | | | | (58) p3 % 4.05/1.31 | | | | (59) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.31 | | | | % 4.05/1.31 | | | | BETA: splitting (56) gives: % 4.05/1.31 | | | | % 4.05/1.31 | | | | Case 1: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (60) p3 & ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | ALPHA: (60) implies: % 4.05/1.31 | | | | | (61) ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (55), (59), (61) are inconsistent by sub-proof #1. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | Case 2: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (62) p2 & ~ p3 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (58), (62) are inconsistent by sub-proof #6. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | End of split % 4.05/1.31 | | | | % 4.05/1.31 | | | Case 2: % 4.05/1.31 | | | | % 4.05/1.31 | | | | (63) ~ p3 & ((p2 & p1) | ( ~ p2 & ~ p1)) % 4.05/1.31 | | | | % 4.05/1.31 | | | | ALPHA: (63) implies: % 4.05/1.31 | | | | (64) ~ p3 % 4.05/1.31 | | | | (65) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.31 | | | | % 4.05/1.31 | | | | BETA: splitting (56) gives: % 4.05/1.31 | | | | % 4.05/1.31 | | | | Case 1: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (66) p3 & ~ p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | ALPHA: (66) implies: % 4.05/1.31 | | | | | (67) p3 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | PRED_UNIFY: (64), (67) imply: % 4.05/1.31 | | | | | (68) $false % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | CLOSE: (68) is inconsistent. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | Case 2: % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | (69) p2 & ~ p3 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | ALPHA: (69) implies: % 4.05/1.31 | | | | | (70) p2 % 4.05/1.31 | | | | | % 4.05/1.31 | | | | | REF_CLOSE: (55), (65), (70) are inconsistent by sub-proof #4. % 4.05/1.31 | | | | | % 4.05/1.31 | | | | End of split % 4.05/1.31 | | | | % 4.05/1.31 | | | End of split % 4.05/1.31 | | | % 4.05/1.31 | | End of split % 4.05/1.31 | | % 4.05/1.31 | End of split % 4.05/1.31 | % 4.05/1.31 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #1 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.32 (2) ~ p2 % 4.05/1.32 (3) ~ p1 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | BETA: splitting (1) gives: % 4.05/1.32 | % 4.05/1.32 | Case 1: % 4.05/1.32 | | % 4.05/1.32 | | (4) p2 & ~ p1 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (4) implies: % 4.05/1.32 | | (5) p2 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (2), (5) imply: % 4.05/1.32 | | (6) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (6) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | Case 2: % 4.05/1.32 | | % 4.05/1.32 | | (7) p1 & ~ p2 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (7) implies: % 4.05/1.32 | | (8) p1 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (3), (8) imply: % 4.05/1.32 | | (9) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (9) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | End of split % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #2 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) p3 & p2 % 4.05/1.32 (2) ~ p3 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | ALPHA: (1) implies: % 4.05/1.32 | (3) p3 % 4.05/1.32 | % 4.05/1.32 | PRED_UNIFY: (2), (3) imply: % 4.05/1.32 | (4) $false % 4.05/1.32 | % 4.05/1.32 | CLOSE: (4) is inconsistent. % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #3 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) ~ p3 & ~ p2 % 4.05/1.32 (2) p3 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | ALPHA: (1) implies: % 4.05/1.32 | (3) ~ p3 % 4.05/1.32 | % 4.05/1.32 | PRED_UNIFY: (2), (3) imply: % 4.05/1.32 | (4) $false % 4.05/1.32 | % 4.05/1.32 | CLOSE: (4) is inconsistent. % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #4 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.32 (2) ~ p1 % 4.05/1.32 (3) p2 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | BETA: splitting (1) gives: % 4.05/1.32 | % 4.05/1.32 | Case 1: % 4.05/1.32 | | % 4.05/1.32 | | (4) p2 & p1 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (4) implies: % 4.05/1.32 | | (5) p1 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (2), (5) imply: % 4.05/1.32 | | (6) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (6) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | Case 2: % 4.05/1.32 | | % 4.05/1.32 | | (7) ~ p2 & ~ p1 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (7) implies: % 4.05/1.32 | | (8) ~ p2 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (3), (8) imply: % 4.05/1.32 | | (9) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (9) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | End of split % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #5 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) (p2 & ~ p1) | (p1 & ~ p2) % 4.05/1.32 (2) p1 % 4.05/1.32 (3) p2 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | BETA: splitting (1) gives: % 4.05/1.32 | % 4.05/1.32 | Case 1: % 4.05/1.32 | | % 4.05/1.32 | | (4) p2 & ~ p1 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (4) implies: % 4.05/1.32 | | (5) ~ p1 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (2), (5) imply: % 4.05/1.32 | | (6) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (6) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | Case 2: % 4.05/1.32 | | % 4.05/1.32 | | (7) p1 & ~ p2 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (7) implies: % 4.05/1.32 | | (8) ~ p2 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (3), (8) imply: % 4.05/1.32 | | (9) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (9) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | End of split % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #6 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) p2 & ~ p3 % 4.05/1.32 (2) p3 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | ALPHA: (1) implies: % 4.05/1.32 | (3) ~ p3 % 4.05/1.32 | % 4.05/1.32 | PRED_UNIFY: (2), (3) imply: % 4.05/1.32 | (4) $false % 4.05/1.32 | % 4.05/1.32 | CLOSE: (4) is inconsistent. % 4.05/1.32 | % 4.05/1.32 End of proof % 4.05/1.32 % 4.05/1.32 Sub-proof #7 shows that the following formulas are inconsistent: % 4.05/1.32 ---------------------------------------------------------------- % 4.05/1.32 (1) (p2 & p1) | ( ~ p2 & ~ p1) % 4.05/1.32 (2) ~ p2 % 4.05/1.32 (3) p1 % 4.05/1.32 % 4.05/1.32 Begin of proof % 4.05/1.32 | % 4.05/1.32 | BETA: splitting (1) gives: % 4.05/1.32 | % 4.05/1.32 | Case 1: % 4.05/1.32 | | % 4.05/1.32 | | (4) p2 & p1 % 4.05/1.32 | | % 4.05/1.32 | | ALPHA: (4) implies: % 4.05/1.32 | | (5) p2 % 4.05/1.32 | | % 4.05/1.32 | | PRED_UNIFY: (2), (5) imply: % 4.05/1.32 | | (6) $false % 4.05/1.32 | | % 4.05/1.32 | | CLOSE: (6) is inconsistent. % 4.05/1.32 | | % 4.05/1.32 | Case 2: % 4.05/1.32 | | % 4.05/1.33 | | (7) ~ p2 & ~ p1 % 4.05/1.33 | | % 4.05/1.33 | | ALPHA: (7) implies: % 4.05/1.33 | | (8) ~ p1 % 4.05/1.33 | | % 4.05/1.33 | | PRED_UNIFY: (3), (8) imply: % 4.05/1.33 | | (9) $false % 4.05/1.33 | | % 4.05/1.33 | | CLOSE: (9) is inconsistent. % 4.05/1.33 | | % 4.05/1.33 | End of split % 4.05/1.33 | % 4.05/1.33 End of proof % 4.05/1.33 % SZS output end Proof for theBenchmark % 4.05/1.33 % 4.05/1.33 719ms %------------------------------------------------------------------------------