%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWC438_1 : TPTP v8.3.0. Released v8.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 : Tue May 14 09:00:29 EDT 2024 % Result : Theorem 5.88s 1.60s % Output : Proof 6.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC438_1 : TPTP v8.3.0. Released v8.3.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n008.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 : Mon May 13 14:39:38 EDT 2024 % 0.12/0.34 % CPUTime : % 0.61/0.60 ________ _____ % 0.61/0.60 ___ __ \_________(_)________________________________ % 0.61/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.60 % 0.61/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.60 (2023-06-19) % 0.61/0.60 % 0.61/0.60 (c) Philipp Rümmer, 2009-2023 % 0.61/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.60 Amanda Stjerna. % 0.61/0.60 Free software under BSD-3-Clause. % 0.61/0.60 % 0.61/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.60 % 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.61 Running up to 7 provers in parallel. % 0.66/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.39/1.06 Prover 5: Preprocessing ... % 2.39/1.06 Prover 6: Preprocessing ... % 2.39/1.06 Prover 3: Preprocessing ... % 2.39/1.06 Prover 4: Preprocessing ... % 2.39/1.06 Prover 2: Preprocessing ... % 2.39/1.06 Prover 1: Preprocessing ... % 2.39/1.06 Prover 0: Preprocessing ... % 3.73/1.25 Prover 6: Constructing countermodel ... % 3.73/1.25 Prover 1: Constructing countermodel ... % 3.73/1.26 Prover 0: Proving ... % 3.73/1.26 Prover 5: Proving ... % 3.73/1.26 Prover 4: Constructing countermodel ... % 3.73/1.26 Prover 3: Constructing countermodel ... % 3.73/1.29 Prover 2: Proving ... % 4.66/1.42 Prover 6: gave up % 4.66/1.42 Prover 1: gave up % 4.66/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.66/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.66/1.42 Prover 3: gave up % 4.66/1.43 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 4.66/1.45 Prover 8: Preprocessing ... % 4.66/1.45 Prover 9: Preprocessing ... % 5.31/1.47 Prover 7: Preprocessing ... % 5.48/1.51 Prover 8: Warning: ignoring some quantifiers % 5.48/1.51 Prover 8: Constructing countermodel ... % 5.75/1.52 Prover 7: Constructing countermodel ... % 5.75/1.52 Prover 9: Constructing countermodel ... % 5.88/1.59 Prover 0: proved (976ms) % 5.88/1.60 % 5.88/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.88/1.60 % 5.88/1.60 Prover 2: proved (983ms) % 5.88/1.60 % 5.88/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.88/1.60 % 5.88/1.60 Prover 9: stopped % 5.88/1.60 Prover 5: stopped % 5.88/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.88/1.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.88/1.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.88/1.61 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.44/1.62 Prover 4: Found proof (size 44) % 6.44/1.62 Prover 4: proved (996ms) % 6.44/1.62 Prover 7: stopped % 6.44/1.62 Prover 8: stopped % 6.44/1.63 Prover 13: Preprocessing ... % 6.44/1.63 Prover 11: Preprocessing ... % 6.44/1.63 Prover 16: Preprocessing ... % 6.44/1.64 Prover 10: Preprocessing ... % 6.44/1.64 Prover 11: stopped % 6.44/1.65 Prover 13: stopped % 6.44/1.65 Prover 10: stopped % 6.44/1.65 Prover 16: stopped % 6.44/1.65 % 6.44/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.44/1.65 % 6.44/1.66 % SZS output start Proof for theBenchmark % 6.44/1.66 Assumptions after simplification: % 6.44/1.66 --------------------------------- % 6.44/1.66 % 6.44/1.66 (conjecture_1) % 6.44/1.68 ? [v0: int] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & $lesseq(0, v0) & % 6.44/1.68 fast(v0) = v2 & small(v0) = v1) % 6.44/1.68 % 6.44/1.68 (formula_1) % 6.44/1.68 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(2, v0)) = 1 | ~ % 6.44/1.68 (f0(v0) = v1)) % 6.44/1.68 % 6.44/1.68 (formula_2) % 6.44/1.68 g0 = 2 % 6.44/1.68 % 6.44/1.68 (formula_3) % 6.44/1.68 ! [v0: int] : ! [v1: int] : (v1 = v0 | ~ (h0(v0) = v1)) % 6.44/1.68 % 6.44/1.68 (formula_4) % 6.88/1.69 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, 0) | % 6.88/1.69 ~ (u0(v0, v1) = v2)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ % 6.88/1.69 ($lesseq(1, v0)) | ~ (u0($sum(v0, -1), v1) = v2) | ? [v3: int] : (u0(v0, % 6.88/1.69 v1) = v3 & f0(v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] % 6.88/1.69 : ( ~ ($lesseq(1, v0)) | ~ (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, % 6.88/1.69 -1), v1) = v3 & f0(v3) = v2)) % 6.88/1.69 % 6.88/1.69 (formula_5) % 6.88/1.69 ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : (u0(g0, v2) = % 6.88/1.69 v1 & h0(v0) = v2)) & ! [v0: int] : ! [v1: int] : ( ~ (h0(v0) = v1) | ? % 6.88/1.69 [v2: int] : (v0(v0) = v2 & u0(g0, v1) = v2)) % 6.88/1.69 % 6.88/1.69 (formula_6) % 6.88/1.69 ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : % 6.88/1.69 ($sum($difference($product(2, v2), v1), $product(2, v0)) = 0 & v0(v0) = v2)) % 6.88/1.69 & ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | small(v0) = % 6.88/1.69 $sum($product(2, v1), $product(2, v0))) % 6.88/1.69 % 6.88/1.69 (formula_7) % 6.88/1.69 ! [v0: int] : ! [v1: int] : ($difference(v1, $product(10, v0)) = 6 | ~ % 6.88/1.69 (fast(v0) = v1)) % 6.88/1.69 % 6.88/1.69 Those formulas are unsatisfiable: % 6.88/1.69 --------------------------------- % 6.88/1.69 % 6.88/1.69 Begin of proof % 6.88/1.69 | % 6.88/1.69 | ALPHA: (formula_4) implies: % 6.88/1.70 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v0)) | ~ % 6.88/1.70 | (u0(v0, v1) = v2) | ? [v3: int] : (u0($sum(v0, -1), v1) = v3 & % 6.88/1.70 | f0(v3) = v2)) % 6.88/1.70 | (2) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = v1 | ~ ($lesseq(v0, % 6.88/1.70 | 0) | ~ (u0(v0, v1) = v2)) % 6.88/1.70 | % 6.88/1.70 | ALPHA: (formula_5) implies: % 6.88/1.70 | (3) ! [v0: int] : ! [v1: int] : ( ~ (v0(v0) = v1) | ? [v2: int] : % 6.88/1.70 | (u0(g0, v2) = v1 & h0(v0) = v2)) % 6.88/1.70 | % 6.88/1.70 | ALPHA: (formula_6) implies: % 6.88/1.70 | (4) ! [v0: int] : ! [v1: int] : ( ~ (small(v0) = v1) | ? [v2: int] : % 6.88/1.70 | ($sum($difference($product(2, v2), v1), $product(2, v0)) = 0 & v0(v0) % 6.88/1.70 | = v2)) % 6.88/1.70 | % 6.88/1.70 | DELTA: instantiating (conjecture_1) with fresh symbols all_10_0, all_10_1, % 6.88/1.70 | all_10_2 gives: % 6.88/1.70 | (5) ~ (all_10_0 = all_10_1) & $lesseq(0, all_10_2) & fast(all_10_2) = % 6.88/1.70 | all_10_0 & small(all_10_2) = all_10_1 % 6.88/1.70 | % 6.88/1.70 | ALPHA: (5) implies: % 6.88/1.70 | (6) ~ (all_10_0 = all_10_1) % 6.88/1.70 | (7) small(all_10_2) = all_10_1 % 6.88/1.70 | (8) fast(all_10_2) = all_10_0 % 6.88/1.70 | % 6.88/1.70 | GROUND_INST: instantiating (formula_7) with all_10_2, all_10_0, simplifying % 6.88/1.70 | with (8) gives: % 6.88/1.70 | (9) $difference(all_10_0, $product(10, all_10_2)) = 6 % 6.88/1.70 | % 6.88/1.71 | REDUCE: (6), (9) imply: % 6.88/1.71 | (10) ~ ($difference(all_10_1, $product(10, all_10_2)) = 6) % 6.88/1.71 | % 6.88/1.71 | SIMP: (10) implies: % 6.88/1.71 | (11) ~ ($difference(all_10_1, $product(10, all_10_2)) = 6) % 6.88/1.71 | % 6.88/1.71 | GROUND_INST: instantiating (4) with all_10_2, all_10_1, simplifying with (7) % 6.88/1.71 | gives: % 6.88/1.71 | (12) ? [v0: int] : ($sum($difference($product(2, v0), all_10_1), % 6.88/1.71 | $product(2, all_10_2)) = 0 & v0(all_10_2) = v0) % 6.88/1.71 | % 6.88/1.71 | DELTA: instantiating (12) with fresh symbol all_25_0 gives: % 6.88/1.71 | (13) $sum($difference($product(2, all_25_0), all_10_1), $product(2, % 6.88/1.71 | all_10_2)) = 0 & v0(all_10_2) = all_25_0 % 6.88/1.71 | % 6.88/1.71 | ALPHA: (13) implies: % 6.88/1.71 | (14) $sum($difference($product(2, all_25_0), all_10_1), $product(2, % 6.88/1.71 | all_10_2)) = 0 % 6.88/1.71 | (15) v0(all_10_2) = all_25_0 % 6.88/1.71 | % 6.88/1.71 | COL_REDUCE: introducing fresh symbol sc_27_0_0 defined by: % 6.88/1.71 | (16) $sum($difference(all_25_0, all_10_1), all_10_2) = sc_27_0_0 % 6.88/1.71 | % 6.88/1.71 | COMBINE_EQS: (14), (16) imply: % 6.88/1.71 | (17) $sum(all_10_1, $product(2, sc_27_0_0)) = 0 % 6.88/1.71 | % 6.88/1.71 | COMBINE_EQS: (16), (17) imply: % 6.88/1.71 | (18) $sum($sum(all_25_0, all_10_2), sc_27_0_0) = 0 % 6.88/1.71 | % 6.88/1.71 | REDUCE: (11), (17) imply: % 6.88/1.71 | (19) ~ ($sum($product(5, all_10_2), sc_27_0_0) = -3) % 6.88/1.71 | % 6.88/1.71 | SIMP: (19) implies: % 6.88/1.71 | (20) ~ ($sum($product(5, all_10_2), sc_27_0_0) = -3) % 6.88/1.71 | % 6.88/1.71 | REDUCE: (15), (18) imply: % 6.88/1.71 | (21) v0(all_10_2) = $difference($product(-1, all_10_2), sc_27_0_0) % 6.88/1.71 | % 6.88/1.71 | GROUND_INST: instantiating (3) with all_10_2, $difference($product(-1, % 6.88/1.71 | all_10_2), sc_27_0_0), simplifying with (21) gives: % 6.88/1.71 | (22) ? [v0: int] : (u0(g0, v0) = $difference($product(-1, all_10_2), % 6.88/1.71 | sc_27_0_0) & h0(all_10_2) = v0) % 6.88/1.71 | % 6.88/1.71 | DELTA: instantiating (22) with fresh symbol all_32_0 gives: % 6.88/1.71 | (23) u0(g0, all_32_0) = $difference($product(-1, all_10_2), sc_27_0_0) & % 6.88/1.71 | h0(all_10_2) = all_32_0 % 6.88/1.71 | % 6.88/1.71 | ALPHA: (23) implies: % 6.88/1.71 | (24) h0(all_10_2) = all_32_0 % 6.88/1.71 | (25) u0(g0, all_32_0) = $difference($product(-1, all_10_2), sc_27_0_0) % 6.88/1.71 | % 6.88/1.71 | REDUCE: (25), (formula_2) imply: % 6.88/1.71 | (26) u0(2, all_32_0) = $difference($product(-1, all_10_2), sc_27_0_0) % 6.88/1.71 | % 6.88/1.71 | GROUND_INST: instantiating (formula_3) with all_10_2, all_32_0, simplifying % 6.88/1.71 | with (24) gives: % 6.88/1.71 | (27) all_32_0 = all_10_2 % 6.88/1.71 | % 6.88/1.71 | REDUCE: (26), (27) imply: % 6.88/1.71 | (28) u0(2, all_10_2) = $difference($product(-1, all_10_2), sc_27_0_0) % 6.88/1.71 | % 6.88/1.71 | GROUND_INST: instantiating (1) with 2, all_10_2, $difference($product(-1, % 6.88/1.71 | all_10_2), sc_27_0_0), simplifying with (28) gives: % 6.88/1.71 | (29) ? [v0: int] : (u0(1, all_10_2) = v0 & f0(v0) = % 6.88/1.71 | $difference($product(-1, all_10_2), sc_27_0_0)) % 6.88/1.71 | % 6.88/1.71 | DELTA: instantiating (29) with fresh symbol all_43_0 gives: % 6.88/1.72 | (30) u0(1, all_10_2) = all_43_0 & f0(all_43_0) = $difference($product(-1, % 6.88/1.72 | all_10_2), sc_27_0_0) % 6.88/1.72 | % 6.88/1.72 | ALPHA: (30) implies: % 6.88/1.72 | (31) f0(all_43_0) = $difference($product(-1, all_10_2), sc_27_0_0) % 6.88/1.72 | (32) u0(1, all_10_2) = all_43_0 % 6.88/1.72 | % 6.88/1.72 | GROUND_INST: instantiating (formula_1) with all_43_0, $difference($product(-1, % 6.88/1.72 | all_10_2), sc_27_0_0), simplifying with (31) gives: % 6.88/1.72 | (33) $sum($sum($product(2, all_43_0), all_10_2), sc_27_0_0) = -1 % 6.88/1.72 | % 6.88/1.72 | COL_REDUCE: introducing fresh symbol sc_51_0_0 defined by: % 6.88/1.72 | (34) all_43_0 = sc_51_0_0 % 6.88/1.72 | % 6.88/1.72 | COMBINE_EQS: (33), (34) imply: % 6.88/1.72 | (35) $sum($sum(all_10_2, sc_27_0_0), $product(2, sc_51_0_0)) = -1 % 6.88/1.72 | % 6.88/1.72 | REDUCE: (20), (35) imply: % 6.88/1.72 | (36) ~ ($sum($product(2, sc_27_0_0), $product(5, sc_51_0_0)) = -1) % 6.88/1.72 | % 6.88/1.72 | SIMP: (36) implies: % 6.88/1.72 | (37) ~ ($sum($product(2, sc_27_0_0), $product(5, sc_51_0_0)) = -1) % 6.88/1.72 | % 6.88/1.72 | REDUCE: (32), (34), (35) imply: % 6.88/1.72 | (38) u0(1, $sum($difference($product(-1, sc_27_0_0), $product(2, % 6.88/1.72 | sc_51_0_0)), -1)) = sc_51_0_0 % 6.88/1.72 | % 6.88/1.72 | GROUND_INST: instantiating (1) with 1, $sum($difference($product(-1, % 6.88/1.72 | sc_27_0_0), $product(2, sc_51_0_0)), -1), sc_51_0_0, % 6.88/1.72 | simplifying with (38) gives: % 6.88/1.72 | (39) ? [v0: int] : (u0(0, $sum($difference($product(-1, sc_27_0_0), % 6.88/1.72 | $product(2, sc_51_0_0)), -1)) = v0 & f0(v0) = sc_51_0_0) % 6.88/1.72 | % 6.88/1.72 | DELTA: instantiating (39) with fresh symbol all_62_0 gives: % 6.88/1.72 | (40) u0(0, $sum($difference($product(-1, sc_27_0_0), $product(2, % 6.88/1.72 | sc_51_0_0)), -1)) = all_62_0 & f0(all_62_0) = sc_51_0_0 % 6.88/1.72 | % 6.88/1.72 | ALPHA: (40) implies: % 6.88/1.72 | (41) f0(all_62_0) = sc_51_0_0 % 6.88/1.72 | (42) u0(0, $sum($difference($product(-1, sc_27_0_0), $product(2, % 6.88/1.72 | sc_51_0_0)), -1)) = all_62_0 % 6.88/1.72 | % 6.88/1.72 | GROUND_INST: instantiating (formula_1) with all_62_0, sc_51_0_0, simplifying % 6.88/1.72 | with (41) gives: % 6.88/1.72 | (43) $difference($product(2, all_62_0), sc_51_0_0) = -1 % 6.88/1.72 | % 6.88/1.72 | GROUND_INST: instantiating (2) with 0, $sum($difference($product(-1, % 6.88/1.72 | sc_27_0_0), $product(2, sc_51_0_0)), -1), all_62_0, % 6.88/1.72 | simplifying with (42) gives: % 6.88/1.72 | (44) $sum($sum(all_62_0, sc_27_0_0), $product(2, sc_51_0_0)) = -1 % 6.88/1.72 | % 6.88/1.72 | COMBINE_EQS: (43), (44) imply: % 6.88/1.72 | (45) $sum($product(2, sc_27_0_0), $product(5, sc_51_0_0)) = -1 % 6.88/1.72 | % 6.88/1.72 | SIMP: (45) implies: % 6.88/1.72 | (46) $sum($product(2, sc_27_0_0), $product(5, sc_51_0_0)) = -1 % 6.88/1.72 | % 6.88/1.72 | COL_REDUCE: introducing fresh symbol sc_68_0_0 defined by: % 6.88/1.72 | (47) $sum(sc_27_0_0, $product(2, sc_51_0_0)) = sc_68_0_0 % 6.88/1.72 | % 6.88/1.72 | COMBINE_EQS: (46), (47) imply: % 6.88/1.72 | (48) $sum(sc_51_0_0, $product(2, sc_68_0_0)) = -1 % 6.88/1.72 | % 6.88/1.72 | COMBINE_EQS: (47), (48) imply: % 6.88/1.72 | (49) $difference(sc_27_0_0, $product(5, sc_68_0_0)) = 2 % 6.88/1.72 | % 6.88/1.72 | REDUCE: (37), (48), (49) imply: % 6.88/1.72 | (50) $false % 6.88/1.72 | % 6.88/1.72 | CLOSE: (50) is inconsistent. % 6.88/1.72 | % 6.88/1.72 End of proof % 6.88/1.72 % SZS output end Proof for theBenchmark % 6.88/1.73 % 6.88/1.73 1126ms %------------------------------------------------------------------------------