TSTP Solution File: SEU150+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU150+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n006.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 17:42:48 EDT 2023
% Result : Theorem 11.16s 2.29s
% Output : Proof 13.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU150+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n006.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 : Wed Aug 23 19:29:38 EDT 2023
% 0.14/0.35 % 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
% 0.20/0.62 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
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.10/1.19 Prover 1: Preprocessing ...
% 3.10/1.19 Prover 4: Preprocessing ...
% 3.45/1.22 Prover 5: Preprocessing ...
% 3.45/1.22 Prover 3: Preprocessing ...
% 3.45/1.22 Prover 0: Preprocessing ...
% 3.45/1.23 Prover 6: Preprocessing ...
% 3.45/1.23 Prover 2: Preprocessing ...
% 8.61/2.01 Prover 1: Warning: ignoring some quantifiers
% 8.61/2.02 Prover 5: Proving ...
% 9.12/2.09 Prover 4: Warning: ignoring some quantifiers
% 9.12/2.09 Prover 1: Constructing countermodel ...
% 9.12/2.11 Prover 6: Proving ...
% 9.83/2.12 Prover 3: Warning: ignoring some quantifiers
% 9.83/2.15 Prover 3: Constructing countermodel ...
% 10.30/2.19 Prover 4: Constructing countermodel ...
% 10.30/2.19 Prover 2: Proving ...
% 10.30/2.25 Prover 0: Proving ...
% 11.16/2.29 Prover 6: proved (1642ms)
% 11.16/2.29
% 11.16/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.16/2.29
% 11.16/2.29 Prover 3: stopped
% 11.16/2.31 Prover 2: stopped
% 11.16/2.32 Prover 5: stopped
% 11.43/2.33 Prover 0: stopped
% 11.54/2.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.54/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.54/2.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.54/2.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.54/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.54/2.34 Prover 1: Found proof (size 11)
% 11.54/2.34 Prover 1: proved (1705ms)
% 11.54/2.34 Prover 4: stopped
% 11.54/2.35 Prover 7: Preprocessing ...
% 11.54/2.38 Prover 8: Preprocessing ...
% 11.54/2.38 Prover 11: Preprocessing ...
% 11.54/2.39 Prover 13: Preprocessing ...
% 11.54/2.40 Prover 10: Preprocessing ...
% 12.10/2.42 Prover 7: stopped
% 12.10/2.44 Prover 10: stopped
% 12.10/2.45 Prover 11: stopped
% 12.10/2.46 Prover 13: stopped
% 12.51/2.54 Prover 8: Warning: ignoring some quantifiers
% 12.95/2.56 Prover 8: Constructing countermodel ...
% 12.95/2.57 Prover 8: stopped
% 12.95/2.57
% 12.95/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.95/2.57
% 12.95/2.58 % SZS output start Proof for theBenchmark
% 13.07/2.59 Assumptions after simplification:
% 13.07/2.59 ---------------------------------
% 13.07/2.59
% 13.07/2.59 (commutativity_k2_tarski)
% 13.07/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) |
% 13.07/2.62 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 13.07/2.62
% 13.07/2.62 (t8_zfmisc_1)
% 13.07/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.07/2.62 (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~
% 13.07/2.62 $i(v1) | ~ $i(v0))
% 13.07/2.62
% 13.07/2.62 (t9_zfmisc_1)
% 13.07/2.62 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v2 = v1) &
% 13.07/2.62 singleton(v0) = v3 & unordered_pair(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1)
% 13.07/2.62 & $i(v0))
% 13.07/2.62
% 13.07/2.62 Further assumptions not needed in the proof:
% 13.07/2.63 --------------------------------------------
% 13.07/2.63 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0,
% 13.07/2.63 commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, d1_xboole_0, d1_zfmisc_1,
% 13.07/2.63 d2_tarski, d2_xboole_0, d3_tarski, d3_xboole_0, d4_xboole_0, d7_xboole_0,
% 13.07/2.63 d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski,
% 13.07/2.63 dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0,
% 13.07/2.63 fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 13.07/2.63 irreflexivity_r2_xboole_0, l1_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1,
% 13.07/2.63 l4_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 13.07/2.63 symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole,
% 13.07/2.63 t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski,
% 13.07/2.63 t2_xboole_1, t33_xboole_1, t36_xboole_1, t37_xboole_1, t39_xboole_1, t3_boole,
% 13.07/2.63 t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole,
% 13.07/2.63 t4_xboole_0, t60_xboole_1, t63_xboole_1, t69_enumset1, t6_boole, t6_zfmisc_1,
% 13.07/2.63 t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1
% 13.07/2.63
% 13.07/2.63 Those formulas are unsatisfiable:
% 13.07/2.63 ---------------------------------
% 13.07/2.63
% 13.07/2.63 Begin of proof
% 13.07/2.63 |
% 13.07/2.63 | DELTA: instantiating (t9_zfmisc_1) with fresh symbols all_75_0, all_75_1,
% 13.07/2.63 | all_75_2, all_75_3 gives:
% 13.07/2.63 | (1) ~ (all_75_1 = all_75_2) & singleton(all_75_3) = all_75_0 &
% 13.07/2.63 | unordered_pair(all_75_2, all_75_1) = all_75_0 & $i(all_75_0) &
% 13.07/2.63 | $i(all_75_1) & $i(all_75_2) & $i(all_75_3)
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (1) implies:
% 13.07/2.63 | (2) ~ (all_75_1 = all_75_2)
% 13.07/2.63 | (3) $i(all_75_3)
% 13.07/2.63 | (4) $i(all_75_2)
% 13.07/2.63 | (5) $i(all_75_1)
% 13.07/2.63 | (6) unordered_pair(all_75_2, all_75_1) = all_75_0
% 13.07/2.63 | (7) singleton(all_75_3) = all_75_0
% 13.07/2.63 |
% 13.07/2.63 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_75_2, all_75_1,
% 13.07/2.63 | all_75_0, simplifying with (4), (5), (6) gives:
% 13.07/2.63 | (8) unordered_pair(all_75_1, all_75_2) = all_75_0 & $i(all_75_0)
% 13.07/2.63 |
% 13.07/2.63 | ALPHA: (8) implies:
% 13.07/2.63 | (9) unordered_pair(all_75_1, all_75_2) = all_75_0
% 13.07/2.63 |
% 13.07/2.64 | GROUND_INST: instantiating (t8_zfmisc_1) with all_75_3, all_75_2, all_75_1,
% 13.07/2.64 | all_75_0, simplifying with (3), (4), (5), (6), (7) gives:
% 13.07/2.64 | (10) all_75_2 = all_75_3
% 13.07/2.64 |
% 13.07/2.64 | REDUCE: (2), (10) imply:
% 13.07/2.64 | (11) ~ (all_75_1 = all_75_3)
% 13.07/2.64 |
% 13.07/2.64 | REDUCE: (9), (10) imply:
% 13.07/2.64 | (12) unordered_pair(all_75_1, all_75_3) = all_75_0
% 13.07/2.64 |
% 13.07/2.64 | GROUND_INST: instantiating (t8_zfmisc_1) with all_75_3, all_75_1, all_75_3,
% 13.07/2.64 | all_75_0, simplifying with (3), (5), (7), (12) gives:
% 13.07/2.64 | (13) all_75_1 = all_75_3
% 13.07/2.64 |
% 13.07/2.64 | REDUCE: (11), (13) imply:
% 13.07/2.64 | (14) $false
% 13.07/2.64 |
% 13.07/2.64 | CLOSE: (14) is inconsistent.
% 13.07/2.64 |
% 13.07/2.64 End of proof
% 13.07/2.64 % SZS output end Proof for theBenchmark
% 13.07/2.64
% 13.07/2.64 2024ms
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