%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX035+1 : TPTP v9.1.0. Released v9.1.0. % 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 : Tue Apr 1 02:15:29 AM UTC 2025 % Result : Theorem 84.77s 11.97s % Output : Proof 85.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWX035+1 : TPTP v9.1.0. Released v9.1.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n028.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Mar 31 14:28:49 EDT 2025 % 0.12/0.35 % CPUTime : % 0.59/0.61 ________ _____ % 0.59/0.61 ___ __ \_________(_)________________________________ % 0.59/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.59/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.59/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.59/0.61 % 0.59/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.59/0.61 (2023-06-19) % 0.59/0.61 % 0.59/0.61 (c) Philipp Rümmer, 2009-2023 % 0.59/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.59/0.61 Amanda Stjerna. % 0.59/0.61 Free software under BSD-3-Clause. % 0.59/0.61 % 0.59/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.59/0.61 % 0.59/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.64/0.63 Running up to 7 provers in parallel. % 0.70/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.00/1.29 Prover 1: Preprocessing ... % 4.00/1.30 Prover 4: Preprocessing ... % 4.66/1.34 Prover 6: Preprocessing ... % 4.66/1.34 Prover 5: Preprocessing ... % 4.66/1.34 Prover 0: Preprocessing ... % 4.66/1.35 Prover 2: Preprocessing ... % 4.66/1.35 Prover 3: Preprocessing ... % 10.21/2.08 Prover 1: Warning: ignoring some quantifiers % 10.48/2.11 Prover 5: Proving ... % 10.62/2.14 Prover 1: Constructing countermodel ... % 10.62/2.16 Prover 2: Proving ... % 10.62/2.20 Prover 3: Warning: ignoring some quantifiers % 11.20/2.22 Prover 3: Constructing countermodel ... % 11.20/2.22 Prover 6: Proving ... % 11.20/2.23 Prover 4: Warning: ignoring some quantifiers % 11.20/2.27 Prover 4: Constructing countermodel ... % 11.76/2.35 Prover 0: Proving ... % 73.82/10.41 Prover 2: stopped % 73.82/10.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 74.78/10.52 Prover 7: Preprocessing ... % 76.08/10.69 Prover 7: Warning: ignoring some quantifiers % 76.08/10.72 Prover 7: Constructing countermodel ... % 83.74/11.67 Prover 7: Found proof (size 20) % 83.74/11.68 Prover 7: proved (1261ms) % 83.74/11.68 Prover 5: stopped % 83.74/11.68 Prover 0: stopped % 83.74/11.68 Prover 6: stopped % 83.74/11.68 Prover 4: stopped % 83.74/11.69 Prover 1: stopped % 84.77/11.96 Prover 3: stopped % 84.77/11.97 % 84.77/11.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 84.77/11.97 % 84.77/11.97 % SZS output start Proof for theBenchmark % 84.77/11.98 Assumptions after simplification: % 84.77/11.98 --------------------------------- % 84.77/11.98 % 84.77/11.98 ((@*)/2) % 84.92/12.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (@*(v0, % 84.92/12.03 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v1) | ~ % 84.92/12.03 nat_succeeds(v0) | ~ times_succeeds(v0, v1, v2)) & ! [v0: $i] : ! [v1: % 84.92/12.03 $i] : ! [v2: $i] : ( ~ (@*(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ % 84.92/12.03 $i(v0) | ~ nat_succeeds(v1) | ~ nat_succeeds(v0) | times_succeeds(v0, v1, % 84.92/12.03 v2)) % 84.92/12.03 % 84.92/12.03 ((@+)/2) % 84.92/12.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ (@+(v0, % 84.92/12.03 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v0) | ~ % 84.92/12.03 plus_succeeds(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 84.92/12.03 (@+(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v0) % 84.92/12.03 | plus_succeeds(v0, v1, v2)) % 84.92/12.03 % 84.92/12.03 (corollary-(times:successor)) % 84.92/12.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 84.92/12.04 $i] : ( ~ (v5 = v3) & @*(v2, v1) = v3 & @*(v0, v1) = v4 & @+(v1, v4) = v5 & % 84.92/12.04 s(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 84.92/12.04 nat_succeeds(v1) & nat_succeeds(v0)) % 84.92/12.04 % 84.92/12.04 (id15) % 84.92/12.04 $i(0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 84.92/12.04 ( ~ (s(v3) = v0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 84.92/12.04 ~ plus_succeeds(v1, v4, v2) | ~ times_succeeds(v3, v1, v4) | % 84.92/12.04 times_succeeds(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 84.92/12.04 = 0 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ times_succeeds(v0, v1, v2) | ? % 84.92/12.04 [v3: $i] : ? [v4: $i] : (s(v3) = v0 & $i(v4) & $i(v3) & plus_succeeds(v1, % 84.92/12.04 v4, v2) & times_succeeds(v3, v1, v4))) & ! [v0: $i] : ! [v1: $i] : ! % 84.92/12.04 [v2: $i] : (v0 = 0 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ times_succeeds(v0, % 84.92/12.04 v1, v2) | ? [v3: $i] : ? [v4: $i] : (s(v3) = v0 & $i(v4) & $i(v3) & % 84.92/12.04 plus_succeeds(v1, v4, v2) & times_succeeds(v3, v1, v4))) & ? [v0: $i] : ( % 84.92/12.04 ~ $i(v0) | times_succeeds(0, v0, 0)) % 84.92/12.04 % 84.92/12.04 (id27) % 84.92/12.05 $i(0) & nat_succeeds(0) & ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ % 84.92/12.05 $i(v1) | ~ $i(v0) | ~ nat_succeeds(v1) | nat_succeeds(v0)) & ! [v0: $i] : % 84.92/12.05 (v0 = 0 | ~ $i(v0) | ~ nat_succeeds(v0) | ? [v1: $i] : (s(v1) = v0 & $i(v1) % 84.92/12.05 & nat_succeeds(v1))) % 84.92/12.05 % 84.92/12.05 (lemma-(times:existence)) % 84.92/12.05 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v1) | ~ % 84.92/12.05 nat_succeeds(v0) | ? [v2: $i] : ($i(v2) & times_succeeds(v0, v1, v2))) % 84.92/12.05 % 84.92/12.05 (lemma-(times:uniqueness)) % 84.92/12.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ $i(v3) | % 84.92/12.05 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ times_succeeds(v0, v1, v3) | ~ % 84.92/12.05 times_succeeds(v0, v1, v2)) % 84.92/12.05 % 84.92/12.05 Further assumptions not needed in the proof: % 84.92/12.05 -------------------------------------------- % 84.92/12.05 corollary-(plus:successor), corollary-(plus:types), corollary-(plus:zero), % 84.92/12.05 corollary-(times:zero), id1, id10, id11, id12, id13, id14, id16, id17, id18, % 84.92/12.05 id19, id2, id20, id21, id22, id23, id24, id25, id26, id28, id29, id3, id4, id5, % 84.92/12.05 id6, id7, id8, id9, induction, lemma-(nat:ground), lemma-(nat:termination), % 84.92/12.05 lemma-(plus:existence), lemma-(plus:ground:1), lemma-(plus:ground:2), % 84.92/12.05 lemma-(plus:ground:3), lemma-(plus:injective:second), lemma-(plus:successor), % 84.92/12.05 lemma-(plus:termination:1), lemma-(plus:termination:2), % 84.92/12.05 lemma-(plus:termination:3), lemma-(plus:types:1), lemma-(plus:types:2), % 84.92/12.05 lemma-(plus:types:3), lemma-(plus:uniqueness), lemma-(plus:zero), % 84.92/12.05 lemma-(times:ground:1), lemma-(times:ground:2), lemma-(times:termination), % 84.92/12.05 lemma-(times:types:1), lemma-(times:types:2), theorem-(plus:associative), % 84.92/12.05 theorem-(plus:commutative) % 84.92/12.05 % 84.92/12.05 Those formulas are unsatisfiable: % 84.92/12.05 --------------------------------- % 84.92/12.05 % 84.92/12.05 Begin of proof % 84.92/12.05 | % 84.92/12.05 | ALPHA: (id15) implies: % 85.12/12.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 85.12/12.05 | ~ (s(v3) = v0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 85.12/12.05 | $i(v0) | ~ plus_succeeds(v1, v4, v2) | ~ times_succeeds(v3, v1, v4) % 85.12/12.05 | | times_succeeds(v0, v1, v2)) % 85.12/12.05 | % 85.12/12.05 | ALPHA: (id27) implies: % 85.12/12.06 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ $i(v1) | ~ $i(v0) | % 85.12/12.06 | ~ nat_succeeds(v1) | nat_succeeds(v0)) % 85.12/12.06 | % 85.12/12.06 | ALPHA: ((@+)/2) implies: % 85.12/12.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (@+(v0, v1) = v2) | ~ % 85.12/12.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v0) | % 85.12/12.06 | plus_succeeds(v0, v1, v2)) % 85.12/12.06 | % 85.12/12.06 | ALPHA: ((@*)/2) implies: % 85.12/12.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (@*(v0, v1) = v2) | ~ % 85.12/12.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ nat_succeeds(v1) | ~ % 85.12/12.06 | nat_succeeds(v0) | times_succeeds(v0, v1, v2)) % 85.12/12.06 | % 85.12/12.06 | DELTA: instantiating (corollary-(times:successor)) with fresh symbols % 85.12/12.06 | all_86_0, all_86_1, all_86_2, all_86_3, all_86_4, all_86_5 gives: % 85.12/12.06 | (5) ~ (all_86_0 = all_86_2) & @*(all_86_3, all_86_4) = all_86_2 & % 85.12/12.06 | @*(all_86_5, all_86_4) = all_86_1 & @+(all_86_4, all_86_1) = all_86_0 & % 85.12/12.06 | s(all_86_5) = all_86_3 & $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & % 85.12/12.06 | $i(all_86_3) & $i(all_86_4) & $i(all_86_5) & nat_succeeds(all_86_4) & % 85.12/12.06 | nat_succeeds(all_86_5) % 85.12/12.06 | % 85.12/12.06 | ALPHA: (5) implies: % 85.12/12.06 | (6) ~ (all_86_0 = all_86_2) % 85.12/12.06 | (7) nat_succeeds(all_86_5) % 85.12/12.06 | (8) nat_succeeds(all_86_4) % 85.12/12.06 | (9) $i(all_86_5) % 85.12/12.06 | (10) $i(all_86_4) % 85.12/12.06 | (11) $i(all_86_3) % 85.12/12.06 | (12) $i(all_86_2) % 85.12/12.06 | (13) $i(all_86_1) % 85.12/12.06 | (14) $i(all_86_0) % 85.12/12.06 | (15) s(all_86_5) = all_86_3 % 85.12/12.06 | (16) @+(all_86_4, all_86_1) = all_86_0 % 85.12/12.06 | (17) @*(all_86_5, all_86_4) = all_86_1 % 85.12/12.06 | (18) @*(all_86_3, all_86_4) = all_86_2 % 85.12/12.06 | % 85.12/12.06 | GROUND_INST: instantiating (2) with all_86_3, all_86_5, simplifying with (7), % 85.12/12.06 | (9), (11), (15) gives: % 85.12/12.07 | (19) nat_succeeds(all_86_3) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (3) with all_86_4, all_86_1, all_86_0, simplifying % 85.12/12.07 | with (8), (10), (13), (14), (16) gives: % 85.12/12.07 | (20) plus_succeeds(all_86_4, all_86_1, all_86_0) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (4) with all_86_5, all_86_4, all_86_1, simplifying % 85.12/12.07 | with (7), (8), (9), (10), (13), (17) gives: % 85.12/12.07 | (21) times_succeeds(all_86_5, all_86_4, all_86_1) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (1) with all_86_3, all_86_4, all_86_0, all_86_5, % 85.12/12.07 | all_86_1, simplifying with (9), (10), (11), (13), (14), (15), % 85.12/12.07 | (20), (21) gives: % 85.12/12.07 | (22) times_succeeds(all_86_3, all_86_4, all_86_0) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (4) with all_86_3, all_86_4, all_86_2, simplifying % 85.12/12.07 | with (8), (10), (11), (12), (18), (19) gives: % 85.12/12.07 | (23) times_succeeds(all_86_3, all_86_4, all_86_2) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (lemma-(times:existence)) with all_86_3, all_86_4, % 85.12/12.07 | simplifying with (8), (10), (11), (19) gives: % 85.12/12.07 | (24) ? [v0: $i] : ($i(v0) & times_succeeds(all_86_3, all_86_4, v0)) % 85.12/12.07 | % 85.12/12.07 | DELTA: instantiating (24) with fresh symbol all_135_0 gives: % 85.12/12.07 | (25) $i(all_135_0) & times_succeeds(all_86_3, all_86_4, all_135_0) % 85.12/12.07 | % 85.12/12.07 | ALPHA: (25) implies: % 85.12/12.07 | (26) times_succeeds(all_86_3, all_86_4, all_135_0) % 85.12/12.07 | (27) $i(all_135_0) % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (lemma-(times:uniqueness)) with all_86_3, all_86_4, % 85.12/12.07 | all_86_0, all_135_0, simplifying with (10), (11), (14), (22), % 85.12/12.07 | (26), (27) gives: % 85.12/12.07 | (28) all_135_0 = all_86_0 % 85.12/12.07 | % 85.12/12.07 | GROUND_INST: instantiating (lemma-(times:uniqueness)) with all_86_3, all_86_4, % 85.12/12.07 | all_86_2, all_135_0, simplifying with (10), (11), (12), (23), % 85.12/12.07 | (26), (27) gives: % 85.12/12.07 | (29) all_135_0 = all_86_2 % 85.12/12.07 | % 85.12/12.07 | COMBINE_EQS: (28), (29) imply: % 85.12/12.07 | (30) all_86_0 = all_86_2 % 85.12/12.07 | % 85.12/12.07 | REDUCE: (6), (30) imply: % 85.12/12.07 | (31) $false % 85.12/12.07 | % 85.12/12.07 | CLOSE: (31) is inconsistent. % 85.12/12.07 | % 85.12/12.07 End of proof % 85.12/12.07 % SZS output end Proof for theBenchmark % 85.12/12.07 % 85.12/12.07 11460ms %------------------------------------------------------------------------------