TSTP Solution File: SEU149+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU149+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 : n031.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 17:42:47 EDT 2023
% Result : Theorem 12.55s 2.50s
% Output : Proof 16.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU149+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 15:37:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.50/1.26 Prover 1: Preprocessing ...
% 3.98/1.26 Prover 4: Preprocessing ...
% 4.24/1.31 Prover 2: Preprocessing ...
% 4.24/1.31 Prover 6: Preprocessing ...
% 4.24/1.31 Prover 0: Preprocessing ...
% 4.24/1.31 Prover 3: Preprocessing ...
% 4.24/1.31 Prover 5: Preprocessing ...
% 8.66/1.94 Prover 1: Warning: ignoring some quantifiers
% 9.22/2.01 Prover 5: Proving ...
% 9.22/2.02 Prover 3: Warning: ignoring some quantifiers
% 9.22/2.05 Prover 3: Constructing countermodel ...
% 9.22/2.05 Prover 1: Constructing countermodel ...
% 9.22/2.06 Prover 6: Proving ...
% 9.22/2.07 Prover 4: Warning: ignoring some quantifiers
% 10.27/2.13 Prover 2: Proving ...
% 10.27/2.17 Prover 4: Constructing countermodel ...
% 10.27/2.19 Prover 0: Proving ...
% 11.65/2.34 Prover 3: gave up
% 11.65/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.55/2.44 Prover 7: Preprocessing ...
% 12.55/2.50 Prover 2: proved (1844ms)
% 12.55/2.50
% 12.55/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.55/2.50
% 12.55/2.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.55/2.50 Prover 0: stopped
% 12.55/2.50 Prover 5: stopped
% 13.27/2.52 Prover 6: stopped
% 13.27/2.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.27/2.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.27/2.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.27/2.56 Prover 8: Preprocessing ...
% 13.91/2.60 Prover 10: Preprocessing ...
% 13.91/2.61 Prover 7: Warning: ignoring some quantifiers
% 13.91/2.62 Prover 11: Preprocessing ...
% 13.91/2.62 Prover 13: Preprocessing ...
% 13.91/2.64 Prover 7: Constructing countermodel ...
% 14.54/2.78 Prover 13: Warning: ignoring some quantifiers
% 14.54/2.78 Prover 8: Warning: ignoring some quantifiers
% 15.23/2.80 Prover 13: Constructing countermodel ...
% 15.39/2.80 Prover 10: Warning: ignoring some quantifiers
% 15.39/2.81 Prover 8: Constructing countermodel ...
% 15.50/2.81 Prover 10: Constructing countermodel ...
% 15.50/2.85 Prover 7: Found proof (size 13)
% 15.50/2.85 Prover 7: proved (492ms)
% 15.50/2.85 Prover 13: stopped
% 15.50/2.85 Prover 10: stopped
% 15.50/2.85 Prover 4: stopped
% 15.50/2.85 Prover 8: stopped
% 15.50/2.85 Prover 1: stopped
% 15.50/2.86 Prover 11: Warning: ignoring some quantifiers
% 15.50/2.88 Prover 11: Constructing countermodel ...
% 15.50/2.90 Prover 11: stopped
% 15.50/2.90
% 15.50/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.50/2.90
% 15.50/2.90 % SZS output start Proof for theBenchmark
% 15.50/2.91 Assumptions after simplification:
% 15.50/2.91 ---------------------------------
% 15.50/2.91
% 15.50/2.91 (commutativity_k2_tarski)
% 16.13/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) |
% 16.13/2.93 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i]
% 16.13/2.93 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) |
% 16.13/2.93 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2)))
% 16.13/2.93
% 16.13/2.93 (d2_tarski)
% 16.13/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 |
% 16.13/2.94 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 16.13/2.94 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 16.13/2.94 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 16.13/2.94 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~
% 16.13/2.94 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1:
% 16.13/2.94 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~
% 16.13/2.94 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.13/2.94 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0,
% 16.13/2.94 v2))
% 16.13/2.94
% 16.13/2.94 (t69_enumset1)
% 16.13/2.94 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 16.13/2.94 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 16.13/2.94 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 16.13/2.94
% 16.13/2.94 (t8_zfmisc_1)
% 16.13/2.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 16.13/2.94 singleton(v0) = v3 & unordered_pair(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1)
% 16.13/2.94 & $i(v0))
% 16.13/2.94
% 16.13/2.94 Further assumptions not needed in the proof:
% 16.13/2.94 --------------------------------------------
% 16.13/2.94 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0,
% 16.13/2.94 commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, d1_xboole_0, d1_zfmisc_1,
% 16.13/2.94 d2_xboole_0, d3_tarski, d3_xboole_0, d4_xboole_0, d7_xboole_0, d8_xboole_0,
% 16.13/2.94 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0,
% 16.13/2.94 dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 16.13/2.94 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0,
% 16.13/2.94 l1_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, rc1_xboole_0,
% 16.13/2.94 rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, t12_xboole_1,
% 16.13/2.94 t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1,
% 16.13/2.94 t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t36_xboole_1,
% 16.13/2.94 t37_xboole_1, t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1,
% 16.13/2.94 t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1,
% 16.13/2.94 t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole,
% 16.13/2.94 t8_xboole_1
% 16.13/2.94
% 16.13/2.94 Those formulas are unsatisfiable:
% 16.13/2.94 ---------------------------------
% 16.13/2.94
% 16.13/2.94 Begin of proof
% 16.13/2.94 |
% 16.13/2.94 | ALPHA: (commutativity_k2_tarski) implies:
% 16.13/2.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 16.13/2.94 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 &
% 16.13/2.94 | $i(v2)))
% 16.13/2.94 |
% 16.13/2.94 | ALPHA: (d2_tarski) implies:
% 16.13/2.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 16.13/2.94 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2))
% 16.13/2.95 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 =
% 16.13/2.95 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 16.13/2.95 | $i(v1) | ~ $i(v0) | ~ in(v3, v2))
% 16.13/2.95 |
% 16.13/2.95 | ALPHA: (t69_enumset1) implies:
% 16.13/2.95 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 16.13/2.95 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 16.13/2.95 |
% 16.13/2.95 | DELTA: instantiating (t8_zfmisc_1) with fresh symbols all_73_0, all_73_1,
% 16.13/2.95 | all_73_2, all_73_3 gives:
% 16.13/2.95 | (5) ~ (all_73_2 = all_73_3) & singleton(all_73_3) = all_73_0 &
% 16.13/2.95 | unordered_pair(all_73_2, all_73_1) = all_73_0 & $i(all_73_0) &
% 16.13/2.95 | $i(all_73_1) & $i(all_73_2) & $i(all_73_3)
% 16.13/2.95 |
% 16.13/2.95 | ALPHA: (5) implies:
% 16.13/2.95 | (6) ~ (all_73_2 = all_73_3)
% 16.13/2.95 | (7) $i(all_73_3)
% 16.13/2.95 | (8) $i(all_73_2)
% 16.13/2.95 | (9) $i(all_73_1)
% 16.13/2.95 | (10) unordered_pair(all_73_2, all_73_1) = all_73_0
% 16.13/2.95 | (11) singleton(all_73_3) = all_73_0
% 16.13/2.95 |
% 16.13/2.95 | GROUND_INST: instantiating (1) with all_73_1, all_73_2, all_73_0, simplifying
% 16.13/2.95 | with (8), (9), (10) gives:
% 16.13/2.95 | (12) unordered_pair(all_73_1, all_73_2) = all_73_0 & $i(all_73_0)
% 16.13/2.95 |
% 16.13/2.95 | ALPHA: (12) implies:
% 16.13/2.95 | (13) $i(all_73_0)
% 16.13/2.95 |
% 16.13/2.95 | GROUND_INST: instantiating (2) with all_73_2, all_73_1, all_73_0, simplifying
% 16.13/2.95 | with (8), (9), (10), (13) gives:
% 16.13/2.95 | (14) in(all_73_2, all_73_0)
% 16.13/2.95 |
% 16.13/2.95 | GROUND_INST: instantiating (4) with all_73_3, all_73_0, simplifying with (7),
% 16.13/2.95 | (11) gives:
% 16.13/2.95 | (15) unordered_pair(all_73_3, all_73_3) = all_73_0 & $i(all_73_0)
% 16.13/2.95 |
% 16.13/2.95 | ALPHA: (15) implies:
% 16.13/2.95 | (16) unordered_pair(all_73_3, all_73_3) = all_73_0
% 16.13/2.95 |
% 16.13/2.95 | GROUND_INST: instantiating (3) with all_73_3, all_73_3, all_73_0, all_73_2,
% 16.13/2.95 | simplifying with (7), (8), (13), (14), (16) gives:
% 16.13/2.95 | (17) all_73_2 = all_73_3
% 16.13/2.95 |
% 16.13/2.95 | REDUCE: (6), (17) imply:
% 16.13/2.95 | (18) $false
% 16.13/2.95 |
% 16.13/2.95 | CLOSE: (18) is inconsistent.
% 16.13/2.95 |
% 16.13/2.95 End of proof
% 16.13/2.95 % SZS output end Proof for theBenchmark
% 16.13/2.95
% 16.13/2.95 2318ms
%------------------------------------------------------------------------------