TSTP Solution File: SEU133+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU133+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 : n026.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 17:42:41 EDT 2023

% Result   : Theorem 8.49s 2.01s
% Output   : Proof 10.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU133+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n026.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 : Wed Aug 23 19:22:46 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.71  ________       _____
% 0.20/0.71  ___  __ \_________(_)________________________________
% 0.20/0.71  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.71  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.71  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.71  
% 0.20/0.71  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.71  (2023-06-19)
% 0.20/0.71  
% 0.20/0.71  (c) Philipp Rümmer, 2009-2023
% 0.20/0.71  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.71                Amanda Stjerna.
% 0.20/0.71  Free software under BSD-3-Clause.
% 0.20/0.71  
% 0.20/0.71  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.71  
% 0.20/0.71  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.72  Running up to 7 provers in parallel.
% 0.20/0.73  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.73  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.73  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.73  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.73  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.73  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.74  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.86/1.18  Prover 1: Preprocessing ...
% 2.86/1.18  Prover 4: Preprocessing ...
% 3.13/1.22  Prover 3: Preprocessing ...
% 3.13/1.22  Prover 5: Preprocessing ...
% 3.13/1.22  Prover 2: Preprocessing ...
% 3.13/1.22  Prover 6: Preprocessing ...
% 3.13/1.22  Prover 0: Preprocessing ...
% 6.29/1.74  Prover 5: Proving ...
% 6.29/1.75  Prover 1: Warning: ignoring some quantifiers
% 6.89/1.80  Prover 1: Constructing countermodel ...
% 6.89/1.85  Prover 6: Proving ...
% 7.61/1.88  Prover 3: Warning: ignoring some quantifiers
% 7.61/1.89  Prover 4: Warning: ignoring some quantifiers
% 7.74/1.90  Prover 3: Constructing countermodel ...
% 7.74/1.91  Prover 2: Proving ...
% 7.89/1.95  Prover 4: Constructing countermodel ...
% 8.49/2.01  Prover 3: proved (1275ms)
% 8.49/2.01  
% 8.49/2.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.49/2.01  
% 8.49/2.02  Prover 6: stopped
% 8.49/2.02  Prover 5: stopped
% 8.49/2.02  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.49/2.02  Prover 2: stopped
% 8.49/2.02  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.49/2.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.49/2.03  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.49/2.04  Prover 0: Proving ...
% 8.49/2.04  Prover 0: stopped
% 8.49/2.06  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.49/2.09  Prover 11: Preprocessing ...
% 8.49/2.09  Prover 10: Preprocessing ...
% 8.49/2.10  Prover 1: Found proof (size 23)
% 8.49/2.11  Prover 1: proved (1378ms)
% 8.49/2.11  Prover 4: stopped
% 8.49/2.11  Prover 7: Preprocessing ...
% 8.49/2.12  Prover 10: stopped
% 8.49/2.12  Prover 8: Preprocessing ...
% 8.49/2.13  Prover 13: Preprocessing ...
% 8.49/2.14  Prover 7: stopped
% 8.49/2.15  Prover 11: stopped
% 8.49/2.16  Prover 13: stopped
% 9.38/2.23  Prover 8: Warning: ignoring some quantifiers
% 9.38/2.25  Prover 8: Constructing countermodel ...
% 9.38/2.26  Prover 8: stopped
% 9.38/2.26  
% 9.38/2.26  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.38/2.26  
% 9.38/2.26  % SZS output start Proof for theBenchmark
% 9.38/2.27  Assumptions after simplification:
% 9.38/2.27  ---------------------------------
% 9.38/2.27  
% 9.38/2.27    (d3_tarski)
% 10.20/2.29     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1) = v2)
% 10.20/2.29      |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 10.20/2.29          v1) = v4 & in(v3, v0) = 0 & $i(v3))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 10.20/2.29      (subset(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~ (in(v2, v0)
% 10.20/2.29          = 0) |  ~ $i(v2) | in(v2, v1) = 0))
% 10.20/2.29  
% 10.20/2.29    (d4_xboole_0)
% 10.20/2.30     ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v0 |  ~
% 10.20/2.30      (set_difference(v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 10.20/2.30        $i] :  ? [v5: any] :  ? [v6: any] :  ? [v7: any] : (in(v4, v2) = v7 &
% 10.20/2.30        in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) |  ~ (v5 = 0) |
% 10.20/2.30          v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0))))) &  ! [v0: $i] :  ! [v1:
% 10.20/2.30      $i] :  ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |  ~ $i(v2) |  ~
% 10.20/2.30      $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4: any] : ( ~ (in(v3, v0) = v4) | 
% 10.20/2.30          ~ $i(v3) |  ? [v5: any] :  ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) =
% 10.20/2.30            v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0))))) &  ! [v3: $i] : ( ~
% 10.20/2.30          (in(v3, v0) = 0) |  ~ $i(v3) |  ? [v4: any] :  ? [v5: any] : (in(v3, v2)
% 10.29/2.30            = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 10.29/2.30  
% 10.29/2.30    (t36_xboole_1)
% 10.29/2.30     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] : ( ~ (v3 = 0) &
% 10.29/2.30      set_difference(v0, v1) = v2 & subset(v2, v0) = v3 & $i(v2) & $i(v1) &
% 10.29/2.30      $i(v0))
% 10.29/2.30  
% 10.29/2.30    (function-axioms)
% 10.29/2.31     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 10.29/2.31    [v3: $i] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 10.29/2.31    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.29/2.31      (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0:
% 10.29/2.31      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 10.29/2.31    : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0:
% 10.29/2.31      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.29/2.31      (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  !
% 10.29/2.31    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 10.29/2.31      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0:
% 10.29/2.31      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 10.29/2.31    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 10.29/2.31      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 10.29/2.31      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 10.29/2.31  
% 10.29/2.31  Further assumptions not needed in the proof:
% 10.29/2.31  --------------------------------------------
% 10.29/2.31  antisymmetry_r2_hidden, commutativity_k2_xboole_0, commutativity_k3_xboole_0,
% 10.29/2.31  d10_xboole_0, d1_xboole_0, d2_xboole_0, d3_xboole_0, d7_xboole_0,
% 10.29/2.31  dt_k1_xboole_0, dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0,
% 10.29/2.31  fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0,
% 10.29/2.31  l32_xboole_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski,
% 10.29/2.31  symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole,
% 10.29/2.31  t1_xboole_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1,
% 10.29/2.31  t33_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t4_boole, t4_xboole_0,
% 10.29/2.31  t6_boole, t7_boole, t7_xboole_1, t8_boole, t8_xboole_1
% 10.29/2.31  
% 10.29/2.31  Those formulas are unsatisfiable:
% 10.29/2.31  ---------------------------------
% 10.29/2.31  
% 10.29/2.31  Begin of proof
% 10.29/2.31  | 
% 10.29/2.31  | ALPHA: (d3_tarski) implies:
% 10.29/2.31  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (subset(v0, v1)
% 10.29/2.31  |            = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] : ( ~
% 10.29/2.31  |            (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 10.29/2.31  | 
% 10.29/2.31  | ALPHA: (d4_xboole_0) implies:
% 10.29/2.31  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_difference(v0, v1) =
% 10.29/2.31  |            v2) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | ( ! [v3: $i] :  ! [v4:
% 10.29/2.31  |              any] : ( ~ (in(v3, v0) = v4) |  ~ $i(v3) |  ? [v5: any] :  ? [v6:
% 10.29/2.31  |                any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4
% 10.29/2.31  |                    = 0 &  ~ (v6 = 0))))) &  ! [v3: $i] : ( ~ (in(v3, v0) = 0)
% 10.29/2.31  |              |  ~ $i(v3) |  ? [v4: any] :  ? [v5: any] : (in(v3, v2) = v5 &
% 10.29/2.31  |                in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))))
% 10.29/2.31  | 
% 10.29/2.31  | ALPHA: (function-axioms) implies:
% 10.29/2.31  |   (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 10.29/2.31  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 10.29/2.31  | 
% 10.29/2.31  | DELTA: instantiating (t36_xboole_1) with fresh symbols all_49_0, all_49_1,
% 10.29/2.31  |        all_49_2, all_49_3 gives:
% 10.29/2.31  |   (4)   ~ (all_49_0 = 0) & set_difference(all_49_3, all_49_2) = all_49_1 &
% 10.29/2.31  |        subset(all_49_1, all_49_3) = all_49_0 & $i(all_49_1) & $i(all_49_2) &
% 10.29/2.31  |        $i(all_49_3)
% 10.29/2.31  | 
% 10.29/2.31  | ALPHA: (4) implies:
% 10.29/2.32  |   (5)   ~ (all_49_0 = 0)
% 10.29/2.32  |   (6)  $i(all_49_3)
% 10.36/2.32  |   (7)  $i(all_49_2)
% 10.36/2.32  |   (8)  $i(all_49_1)
% 10.36/2.32  |   (9)  subset(all_49_1, all_49_3) = all_49_0
% 10.36/2.32  |   (10)  set_difference(all_49_3, all_49_2) = all_49_1
% 10.36/2.32  | 
% 10.36/2.32  | GROUND_INST: instantiating (1) with all_49_1, all_49_3, all_49_0, simplifying
% 10.36/2.32  |              with (6), (8), (9) gives:
% 10.36/2.32  |   (11)  all_49_0 = 0 |  ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 10.36/2.32  |             all_49_1) = 0 & in(v0, all_49_3) = v1 & $i(v0))
% 10.36/2.32  | 
% 10.36/2.32  | GROUND_INST: instantiating (2) with all_49_3, all_49_2, all_49_1, simplifying
% 10.36/2.32  |              with (6), (7), (8), (10) gives:
% 10.36/2.32  |   (12)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0, all_49_3) = v1) |  ~ $i(v0) |
% 10.36/2.32  |            ? [v2: any] :  ? [v3: any] : (in(v0, all_49_1) = v2 & in(v0,
% 10.36/2.32  |               all_49_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 &  ~ (v3 = 0))))) &  !
% 10.36/2.32  |         [v0: $i] : ( ~ (in(v0, all_49_3) = 0) |  ~ $i(v0) |  ? [v1: any] :  ?
% 10.36/2.32  |           [v2: any] : (in(v0, all_49_1) = v2 & in(v0, all_49_2) = v1 & (v2 = 0
% 10.36/2.32  |               | v1 = 0)))
% 10.36/2.32  | 
% 10.36/2.32  | ALPHA: (12) implies:
% 10.36/2.32  |   (13)   ! [v0: $i] :  ! [v1: any] : ( ~ (in(v0, all_49_3) = v1) |  ~ $i(v0) |
% 10.36/2.32  |            ? [v2: any] :  ? [v3: any] : (in(v0, all_49_1) = v2 & in(v0,
% 10.36/2.32  |               all_49_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 &  ~ (v3 = 0)))))
% 10.36/2.32  | 
% 10.36/2.32  | BETA: splitting (11) gives:
% 10.36/2.32  | 
% 10.36/2.32  | Case 1:
% 10.36/2.32  | | 
% 10.36/2.32  | |   (14)  all_49_0 = 0
% 10.36/2.32  | | 
% 10.36/2.32  | | REDUCE: (5), (14) imply:
% 10.36/2.32  | |   (15)  $false
% 10.36/2.32  | | 
% 10.36/2.32  | | CLOSE: (15) is inconsistent.
% 10.36/2.32  | | 
% 10.36/2.32  | Case 2:
% 10.36/2.32  | | 
% 10.36/2.32  | |   (16)   ? [v0: $i] :  ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_49_1) = 0 &
% 10.36/2.32  | |           in(v0, all_49_3) = v1 & $i(v0))
% 10.36/2.32  | | 
% 10.36/2.32  | | DELTA: instantiating (16) with fresh symbols all_69_0, all_69_1 gives:
% 10.36/2.32  | |   (17)   ~ (all_69_0 = 0) & in(all_69_1, all_49_1) = 0 & in(all_69_1,
% 10.36/2.32  | |           all_49_3) = all_69_0 & $i(all_69_1)
% 10.36/2.32  | | 
% 10.36/2.32  | | ALPHA: (17) implies:
% 10.36/2.32  | |   (18)   ~ (all_69_0 = 0)
% 10.36/2.32  | |   (19)  $i(all_69_1)
% 10.36/2.32  | |   (20)  in(all_69_1, all_49_3) = all_69_0
% 10.36/2.32  | |   (21)  in(all_69_1, all_49_1) = 0
% 10.36/2.32  | | 
% 10.36/2.32  | | GROUND_INST: instantiating (13) with all_69_1, all_69_0, simplifying with
% 10.36/2.32  | |              (19), (20) gives:
% 10.36/2.32  | |   (22)   ? [v0: any] :  ? [v1: any] : (in(all_69_1, all_49_1) = v0 &
% 10.36/2.32  | |           in(all_69_1, all_49_2) = v1 & ( ~ (v0 = 0) | (all_69_0 = 0 &  ~
% 10.36/2.33  | |               (v1 = 0))))
% 10.36/2.33  | | 
% 10.36/2.33  | | DELTA: instantiating (22) with fresh symbols all_80_0, all_80_1 gives:
% 10.36/2.33  | |   (23)  in(all_69_1, all_49_1) = all_80_1 & in(all_69_1, all_49_2) =
% 10.36/2.33  | |         all_80_0 & ( ~ (all_80_1 = 0) | (all_69_0 = 0 &  ~ (all_80_0 = 0)))
% 10.36/2.33  | | 
% 10.36/2.33  | | ALPHA: (23) implies:
% 10.36/2.33  | |   (24)  in(all_69_1, all_49_1) = all_80_1
% 10.36/2.33  | |   (25)   ~ (all_80_1 = 0) | (all_69_0 = 0 &  ~ (all_80_0 = 0))
% 10.36/2.33  | | 
% 10.36/2.33  | | BETA: splitting (25) gives:
% 10.36/2.33  | | 
% 10.36/2.33  | | Case 1:
% 10.36/2.33  | | | 
% 10.36/2.33  | | |   (26)   ~ (all_80_1 = 0)
% 10.36/2.33  | | | 
% 10.36/2.33  | | | GROUND_INST: instantiating (3) with 0, all_80_1, all_49_1, all_69_1,
% 10.36/2.33  | | |              simplifying with (21), (24) gives:
% 10.36/2.33  | | |   (27)  all_80_1 = 0
% 10.36/2.33  | | | 
% 10.36/2.33  | | | REDUCE: (26), (27) imply:
% 10.36/2.33  | | |   (28)  $false
% 10.36/2.33  | | | 
% 10.36/2.33  | | | CLOSE: (28) is inconsistent.
% 10.36/2.33  | | | 
% 10.36/2.33  | | Case 2:
% 10.36/2.33  | | | 
% 10.36/2.33  | | |   (29)  all_69_0 = 0 &  ~ (all_80_0 = 0)
% 10.36/2.33  | | | 
% 10.36/2.33  | | | ALPHA: (29) implies:
% 10.36/2.33  | | |   (30)  all_69_0 = 0
% 10.36/2.33  | | | 
% 10.36/2.33  | | | REDUCE: (18), (30) imply:
% 10.36/2.33  | | |   (31)  $false
% 10.36/2.33  | | | 
% 10.36/2.33  | | | CLOSE: (31) is inconsistent.
% 10.36/2.33  | | | 
% 10.36/2.33  | | End of split
% 10.36/2.33  | | 
% 10.36/2.33  | End of split
% 10.36/2.33  | 
% 10.36/2.33  End of proof
% 10.36/2.33  % SZS output end Proof for theBenchmark
% 10.36/2.33  
% 10.36/2.33  1619ms
%------------------------------------------------------------------------------