TSTP Solution File: SYN049+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN049+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%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  : 600s
% DateTime : Thu Jul 21 04:59:22 EDT 2022

% Result   : Theorem 2.43s 1.27s
% Output   : Proof 2.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN049+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%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  : 600
% 0.14/0.34  % DateTime : Tue Jul 12 06:26:35 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.48/0.59          ____       _                          
% 0.48/0.59    ___  / __ \_____(_)___  ________  __________
% 0.48/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.48/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.48/0.59  
% 0.48/0.59  A Theorem Prover for First-Order Logic
% 0.48/0.59  (ePrincess v.1.0)
% 0.48/0.59  
% 0.48/0.59  (c) Philipp Rümmer, 2009-2015
% 0.48/0.59  (c) Peter Backeman, 2014-2015
% 0.48/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.59  Bug reports to peter@backeman.se
% 0.48/0.59  
% 0.48/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.59  
% 0.48/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.18/0.89  Prover 0: Preprocessing ...
% 1.18/0.93  Prover 0: Warning: ignoring some quantifiers
% 1.36/0.94  Prover 0: Constructing countermodel ...
% 1.48/1.03  Prover 0: gave up
% 1.48/1.03  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.48/1.04  Prover 1: Preprocessing ...
% 1.82/1.09  Prover 1: Constructing countermodel ...
% 1.82/1.09  Prover 1: gave up
% 1.82/1.09  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.82/1.10  Prover 2: Preprocessing ...
% 2.01/1.14  Prover 2: Warning: ignoring some quantifiers
% 2.01/1.14  Prover 2: Constructing countermodel ...
% 2.13/1.16  Prover 2: gave up
% 2.13/1.16  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.13/1.17  Prover 3: Preprocessing ...
% 2.13/1.18  Prover 3: Warning: ignoring some quantifiers
% 2.13/1.18  Prover 3: Constructing countermodel ...
% 2.13/1.19  Prover 3: gave up
% 2.13/1.19  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.13/1.20  Prover 4: Preprocessing ...
% 2.13/1.23  Prover 4: Warning: ignoring some quantifiers
% 2.13/1.23  Prover 4: Constructing countermodel ...
% 2.43/1.26  Prover 4: proved (72ms)
% 2.43/1.27  
% 2.43/1.27  No countermodel exists, formula is valid
% 2.43/1.27  % SZS status Theorem for theBenchmark
% 2.43/1.27  
% 2.43/1.27  Generating proof ... Warning: ignoring some quantifiers
% 2.76/1.41  found it (size 14)
% 2.76/1.41  
% 2.76/1.41  % SZS output start Proof for theBenchmark
% 2.76/1.41  Assumed formulas after preprocessing and simplification: 
% 2.76/1.41  | (0)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_p(v2) = v1) |  ~ (big_p(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_q(v2) = v1) |  ~ (big_q(v2) = v0)) &  ! [v0] :  ! [v1] : ( ~ (big_p(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (v1 = 0 &  ~ (v2 = 0) & big_p(v3) = v5 & big_q(v4) = v6 & big_q(v0) = v2 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] : ( ~ (big_q(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v1 = 0) & big_p(v2) = v4 & big_p(v0) = 0 & big_q(v3) = v5 & ( ~ (v4 = 0) | v5 = 0))) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v1 = 0) & big_p(v2) = v4 & big_p(v0) = 0 & big_q(v3) = v5 & big_q(v0) = v1 & ( ~ (v4 = 0) | v5 = 0))
% 2.87/1.44  | Applying alpha-rule on (0) yields:
% 2.87/1.44  | (1)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_q(v2) = v1) |  ~ (big_q(v2) = v0))
% 2.87/1.44  | (2)  ! [v0] :  ! [v1] : ( ~ (big_p(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (v1 = 0 &  ~ (v2 = 0) & big_p(v3) = v5 & big_q(v4) = v6 & big_q(v0) = v2 & ( ~ (v5 = 0) | v6 = 0)))
% 2.87/1.44  | (3)  ! [v0] :  ! [v1] : ( ~ (big_q(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v1 = 0) & big_p(v2) = v4 & big_p(v0) = 0 & big_q(v3) = v5 & ( ~ (v4 = 0) | v5 = 0)))
% 2.87/1.44  | (4)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v1 = 0) & big_p(v2) = v4 & big_p(v0) = 0 & big_q(v3) = v5 & big_q(v0) = v1 & ( ~ (v4 = 0) | v5 = 0))
% 2.87/1.45  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_p(v2) = v1) |  ~ (big_p(v2) = v0))
% 2.87/1.45  |
% 2.87/1.45  | Instantiating (4) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields:
% 2.87/1.45  | (6)  ~ (all_1_4_4 = 0) & big_p(all_1_3_3) = all_1_1_1 & big_p(all_1_5_5) = 0 & big_q(all_1_2_2) = all_1_0_0 & big_q(all_1_5_5) = all_1_4_4 & ( ~ (all_1_1_1 = 0) | all_1_0_0 = 0)
% 2.87/1.45  |
% 2.87/1.45  | Applying alpha-rule on (6) yields:
% 2.87/1.45  | (7) big_p(all_1_3_3) = all_1_1_1
% 2.87/1.45  | (8)  ~ (all_1_1_1 = 0) | all_1_0_0 = 0
% 2.87/1.45  | (9) big_q(all_1_2_2) = all_1_0_0
% 2.87/1.45  | (10)  ~ (all_1_4_4 = 0)
% 2.87/1.45  | (11) big_p(all_1_5_5) = 0
% 2.87/1.45  | (12) big_q(all_1_5_5) = all_1_4_4
% 2.87/1.45  |
% 2.87/1.45  | Instantiating formula (2) with all_1_1_1, all_1_3_3 and discharging atoms big_p(all_1_3_3) = all_1_1_1, yields:
% 2.87/1.45  | (13)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (all_1_1_1 = 0 &  ~ (v0 = 0) & big_p(v1) = v3 & big_q(v2) = v4 & big_q(all_1_3_3) = v0 & ( ~ (v3 = 0) | v4 = 0))
% 2.87/1.45  |
% 2.87/1.45  | Instantiating formula (3) with all_1_0_0, all_1_2_2 and discharging atoms big_q(all_1_2_2) = all_1_0_0, yields:
% 2.87/1.45  | (14)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (all_1_0_0 = 0) & big_p(v0) = v2 & big_p(all_1_2_2) = 0 & big_q(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))
% 2.87/1.45  |
% 2.87/1.45  | Instantiating (14) with all_10_0_10, all_10_1_11, all_10_2_12, all_10_3_13 yields:
% 2.87/1.45  | (15)  ~ (all_1_0_0 = 0) & big_p(all_10_3_13) = all_10_1_11 & big_p(all_1_2_2) = 0 & big_q(all_10_2_12) = all_10_0_10 & ( ~ (all_10_1_11 = 0) | all_10_0_10 = 0)
% 2.87/1.45  |
% 2.87/1.45  | Applying alpha-rule on (15) yields:
% 2.87/1.45  | (16)  ~ (all_1_0_0 = 0)
% 2.87/1.45  | (17)  ~ (all_10_1_11 = 0) | all_10_0_10 = 0
% 2.87/1.45  | (18) big_q(all_10_2_12) = all_10_0_10
% 2.87/1.45  | (19) big_p(all_10_3_13) = all_10_1_11
% 2.87/1.45  | (20) big_p(all_1_2_2) = 0
% 2.87/1.45  |
% 2.87/1.45  | Instantiating (13) with all_12_0_14, all_12_1_15, all_12_2_16, all_12_3_17, all_12_4_18 yields:
% 2.87/1.45  | (21) all_1_1_1 = 0 &  ~ (all_12_4_18 = 0) & big_p(all_12_3_17) = all_12_1_15 & big_q(all_12_2_16) = all_12_0_14 & big_q(all_1_3_3) = all_12_4_18 & ( ~ (all_12_1_15 = 0) | all_12_0_14 = 0)
% 2.87/1.45  |
% 2.87/1.45  | Applying alpha-rule on (21) yields:
% 2.87/1.45  | (22) all_1_1_1 = 0
% 2.87/1.45  | (23) big_q(all_1_3_3) = all_12_4_18
% 2.87/1.45  | (24)  ~ (all_12_1_15 = 0) | all_12_0_14 = 0
% 2.87/1.45  | (25) big_p(all_12_3_17) = all_12_1_15
% 2.87/1.45  | (26)  ~ (all_12_4_18 = 0)
% 2.98/1.45  | (27) big_q(all_12_2_16) = all_12_0_14
% 2.98/1.46  |
% 2.98/1.46  +-Applying beta-rule and splitting (8), into two cases.
% 2.98/1.46  |-Branch one:
% 2.98/1.46  | (28)  ~ (all_1_1_1 = 0)
% 2.98/1.46  |
% 2.98/1.46  	| Equations (22) can reduce 28 to:
% 2.98/1.46  	| (29) $false
% 2.98/1.46  	|
% 2.98/1.46  	|-The branch is then unsatisfiable
% 2.98/1.46  |-Branch two:
% 2.98/1.46  | (22) all_1_1_1 = 0
% 2.98/1.46  | (31) all_1_0_0 = 0
% 2.98/1.46  |
% 2.98/1.46  	| Equations (31) can reduce 16 to:
% 2.98/1.46  	| (29) $false
% 2.98/1.46  	|
% 2.98/1.46  	|-The branch is then unsatisfiable
% 2.98/1.46  % SZS output end Proof for theBenchmark
% 2.98/1.46  
% 2.98/1.46  856ms
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