TSTP Solution File: SYN074+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n029.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 04:59:43 EDT 2022

% Result   : Theorem 5.22s 2.08s
% Output   : Proof 7.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SYN074+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 19:26:02 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.54/0.56          ____       _                          
% 0.54/0.56    ___  / __ \_____(_)___  ________  __________
% 0.54/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.56  
% 0.54/0.56  A Theorem Prover for First-Order Logic
% 0.54/0.57  (ePrincess v.1.0)
% 0.54/0.57  
% 0.54/0.57  (c) Philipp Rümmer, 2009-2015
% 0.54/0.57  (c) Peter Backeman, 2014-2015
% 0.54/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57  Bug reports to peter@backeman.se
% 0.54/0.57  
% 0.54/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57  
% 0.54/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.61/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.22/0.84  Prover 0: Preprocessing ...
% 1.31/0.92  Prover 0: Warning: ignoring some quantifiers
% 1.31/0.93  Prover 0: Constructing countermodel ...
% 1.65/1.03  Prover 0: gave up
% 1.65/1.04  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.65/1.05  Prover 1: Preprocessing ...
% 1.86/1.13  Prover 1: Warning: ignoring some quantifiers
% 1.86/1.14  Prover 1: Constructing countermodel ...
% 2.12/1.16  Prover 1: gave up
% 2.12/1.16  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.12/1.18  Prover 2: Preprocessing ...
% 2.27/1.21  Prover 2: Warning: ignoring some quantifiers
% 2.27/1.21  Prover 2: Constructing countermodel ...
% 2.27/1.24  Prover 2: gave up
% 2.40/1.24  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.40/1.24  Prover 3: Preprocessing ...
% 2.44/1.26  Prover 3: Warning: ignoring some quantifiers
% 2.44/1.26  Prover 3: Constructing countermodel ...
% 2.44/1.29  Prover 3: gave up
% 2.44/1.29  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.44/1.29  Prover 4: Preprocessing ...
% 2.65/1.34  Prover 4: Warning: ignoring some quantifiers
% 2.65/1.34  Prover 4: Constructing countermodel ...
% 2.82/1.40  Prover 4: gave up
% 2.82/1.40  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.82/1.40  Prover 5: Preprocessing ...
% 2.82/1.42  Prover 5: Warning: ignoring some quantifiers
% 2.82/1.42  Prover 5: Constructing countermodel ...
% 2.82/1.44  Prover 5: gave up
% 2.82/1.44  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.07/1.45  Prover 6: Preprocessing ...
% 3.07/1.46  Prover 6: Warning: ignoring some quantifiers
% 3.07/1.47  Prover 6: Constructing countermodel ...
% 3.07/1.48  Prover 6: gave up
% 3.07/1.48  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.07/1.48  Prover 7: Preprocessing ...
% 3.19/1.49  Prover 7: Proving ...
% 5.22/2.08  Prover 7: proved (596ms)
% 5.22/2.08  
% 5.22/2.08  % SZS status Theorem for theBenchmark
% 5.22/2.08  
% 5.22/2.08  Generating proof ... found it (size 41)
% 7.16/2.85  
% 7.16/2.85  % SZS output start Proof for theBenchmark
% 7.16/2.85  Assumed formulas after preprocessing and simplification: 
% 7.16/2.85  | (0)  ! [v0] :  ? [v1] : (( ~ (v1 = v0) |  ! [v2] :  ? [v3] : (( ~ (v3 = v2) |  ~ big_f(v0, v2)) & (v3 = v2 | big_f(v0, v3)))) & (v1 = v0 |  ? [v2] : (big_f(v1, v2) &  ! [v3] : (v3 = v2 |  ~ big_f(v1, v3))))) &  ? [v0] :  ? [v1] : (big_f(v0, v1) &  ! [v2] :  ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.16/2.85  | Applying alpha-rule on (0) yields:
% 7.16/2.85  | (1)  ! [v0] :  ? [v1] : (( ~ (v1 = v0) |  ! [v2] :  ? [v3] : (( ~ (v3 = v2) |  ~ big_f(v0, v2)) & (v3 = v2 | big_f(v0, v3)))) & (v1 = v0 |  ? [v2] : (big_f(v1, v2) &  ! [v3] : (v3 = v2 |  ~ big_f(v1, v3)))))
% 7.16/2.86  | (2)  ? [v0] :  ? [v1] : (big_f(v0, v1) &  ! [v2] :  ! [v3] : ( ~ big_f(v2, v3) | (v3 = v1 & v2 = v0)))
% 7.16/2.86  |
% 7.16/2.86  | Instantiating (2) with all_0_0_0, all_0_1_1 yields:
% 7.16/2.86  | (3) big_f(all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] : ( ~ big_f(v0, v1) | (v1 = all_0_0_0 & v0 = all_0_1_1))
% 7.16/2.86  |
% 7.16/2.86  | Applying alpha-rule on (3) yields:
% 7.16/2.86  | (4) big_f(all_0_1_1, all_0_0_0)
% 7.16/2.86  | (5)  ! [v0] :  ! [v1] : ( ~ big_f(v0, v1) | (v1 = all_0_0_0 & v0 = all_0_1_1))
% 7.16/2.86  |
% 7.16/2.86  | Introducing new symbol ex_9_0_2 defined by:
% 7.16/2.86  | (6) ex_9_0_2 = all_0_1_1
% 7.16/2.86  |
% 7.16/2.86  | Instantiating formula (1) with ex_9_0_2 yields:
% 7.16/2.86  | (7)  ? [v0] : (( ~ (v0 = ex_9_0_2) |  ! [v1] :  ? [v2] : (( ~ (v2 = v1) |  ~ big_f(ex_9_0_2, v1)) & (v2 = v1 | big_f(ex_9_0_2, v2)))) & (v0 = ex_9_0_2 |  ? [v1] : (big_f(v0, v1) &  ! [v2] : (v2 = v1 |  ~ big_f(v0, v2)))))
% 7.16/2.86  |
% 7.16/2.86  | Instantiating (7) with all_10_0_3 yields:
% 7.16/2.86  | (8) ( ~ (all_10_0_3 = ex_9_0_2) |  ! [v0] :  ? [v1] : (( ~ (v1 = v0) |  ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))) & (all_10_0_3 = ex_9_0_2 |  ? [v0] : (big_f(all_10_0_3, v0) &  ! [v1] : (v1 = v0 |  ~ big_f(all_10_0_3, v1))))
% 7.16/2.86  |
% 7.16/2.86  | Applying alpha-rule on (8) yields:
% 7.16/2.86  | (9)  ~ (all_10_0_3 = ex_9_0_2) |  ! [v0] :  ? [v1] : (( ~ (v1 = v0) |  ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))
% 7.16/2.86  | (10) all_10_0_3 = ex_9_0_2 |  ? [v0] : (big_f(all_10_0_3, v0) &  ! [v1] : (v1 = v0 |  ~ big_f(all_10_0_3, v1)))
% 7.16/2.86  |
% 7.16/2.86  +-Applying beta-rule and splitting (10), into two cases.
% 7.16/2.86  |-Branch one:
% 7.16/2.86  | (11) all_10_0_3 = ex_9_0_2
% 7.16/2.86  |
% 7.16/2.86  	+-Applying beta-rule and splitting (9), into two cases.
% 7.16/2.86  	|-Branch one:
% 7.16/2.86  	| (12)  ~ (all_10_0_3 = ex_9_0_2)
% 7.16/2.86  	|
% 7.16/2.86  		| Equations (11) can reduce 12 to:
% 7.16/2.86  		| (13) $false
% 7.16/2.86  		|
% 7.16/2.86  		|-The branch is then unsatisfiable
% 7.16/2.86  	|-Branch two:
% 7.16/2.86  	| (14)  ! [v0] :  ? [v1] : (( ~ (v1 = v0) |  ~ big_f(ex_9_0_2, v0)) & (v1 = v0 | big_f(ex_9_0_2, v1)))
% 7.16/2.86  	|
% 7.16/2.86  		| Introducing new symbol ex_37_0_8 defined by:
% 7.16/2.86  		| (15) ex_37_0_8 = all_0_0_0
% 7.16/2.86  		|
% 7.16/2.86  		| Instantiating formula (14) with ex_37_0_8 yields:
% 7.16/2.86  		| (16)  ? [v0] : (( ~ (v0 = ex_37_0_8) |  ~ big_f(ex_9_0_2, ex_37_0_8)) & (v0 = ex_37_0_8 | big_f(ex_9_0_2, v0)))
% 7.16/2.86  		|
% 7.16/2.86  		| Instantiating (16) with all_38_0_9 yields:
% 7.16/2.86  		| (17) ( ~ (all_38_0_9 = ex_37_0_8) |  ~ big_f(ex_9_0_2, ex_37_0_8)) & (all_38_0_9 = ex_37_0_8 | big_f(ex_9_0_2, all_38_0_9))
% 7.16/2.86  		|
% 7.16/2.86  		| Applying alpha-rule on (17) yields:
% 7.16/2.86  		| (18)  ~ (all_38_0_9 = ex_37_0_8) |  ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86  		| (19) all_38_0_9 = ex_37_0_8 | big_f(ex_9_0_2, all_38_0_9)
% 7.16/2.86  		|
% 7.16/2.86  		+-Applying beta-rule and splitting (19), into two cases.
% 7.16/2.86  		|-Branch one:
% 7.16/2.86  		| (20) big_f(ex_9_0_2, all_38_0_9)
% 7.16/2.86  		|
% 7.16/2.86  			| Instantiating formula (5) with all_38_0_9, ex_9_0_2 and discharging atoms big_f(ex_9_0_2, all_38_0_9), yields:
% 7.16/2.86  			| (21) all_38_0_9 = all_0_0_0 & ex_9_0_2 = all_0_1_1
% 7.16/2.86  			|
% 7.16/2.86  			| Applying alpha-rule on (21) yields:
% 7.16/2.86  			| (22) all_38_0_9 = all_0_0_0
% 7.16/2.86  			| (6) ex_9_0_2 = all_0_1_1
% 7.16/2.86  			|
% 7.16/2.86  			+-Applying beta-rule and splitting (18), into two cases.
% 7.16/2.86  			|-Branch one:
% 7.16/2.86  			| (24)  ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86  			|
% 7.16/2.86  				| From (6) and (24) follows:
% 7.16/2.86  				| (25)  ~ big_f(all_0_1_1, ex_37_0_8)
% 7.16/2.86  				|
% 7.16/2.86  				| From (15) and (25) follows:
% 7.16/2.86  				| (26)  ~ big_f(all_0_1_1, all_0_0_0)
% 7.16/2.86  				|
% 7.16/2.86  				| Using (4) and (26) yields:
% 7.16/2.86  				| (27) $false
% 7.16/2.86  				|
% 7.16/2.86  				|-The branch is then unsatisfiable
% 7.16/2.86  			|-Branch two:
% 7.16/2.86  			| (28)  ~ (all_38_0_9 = ex_37_0_8)
% 7.16/2.86  			|
% 7.16/2.86  				| Equations (22) can reduce 28 to:
% 7.16/2.86  				| (29)  ~ (ex_37_0_8 = all_0_0_0)
% 7.16/2.86  				|
% 7.16/2.86  				| Simplifying 29 yields:
% 7.16/2.86  				| (30)  ~ (ex_37_0_8 = all_0_0_0)
% 7.16/2.86  				|
% 7.16/2.86  				| Equations (15) can reduce 30 to:
% 7.16/2.86  				| (13) $false
% 7.16/2.86  				|
% 7.16/2.86  				|-The branch is then unsatisfiable
% 7.16/2.86  		|-Branch two:
% 7.16/2.86  		| (32) all_38_0_9 = ex_37_0_8
% 7.16/2.86  		|
% 7.16/2.86  			+-Applying beta-rule and splitting (18), into two cases.
% 7.16/2.86  			|-Branch one:
% 7.16/2.86  			| (24)  ~ big_f(ex_9_0_2, ex_37_0_8)
% 7.16/2.86  			|
% 7.16/2.86  				| From (6)(15) and (24) follows:
% 7.16/2.86  				| (26)  ~ big_f(all_0_1_1, all_0_0_0)
% 7.16/2.87  				|
% 7.16/2.87  				| Using (4) and (26) yields:
% 7.16/2.87  				| (27) $false
% 7.16/2.87  				|
% 7.16/2.87  				|-The branch is then unsatisfiable
% 7.16/2.87  			|-Branch two:
% 7.16/2.87  			| (28)  ~ (all_38_0_9 = ex_37_0_8)
% 7.16/2.87  			|
% 7.16/2.87  				| Equations (32) can reduce 28 to:
% 7.16/2.87  				| (13) $false
% 7.16/2.87  				|
% 7.16/2.87  				|-The branch is then unsatisfiable
% 7.16/2.87  |-Branch two:
% 7.16/2.87  | (12)  ~ (all_10_0_3 = ex_9_0_2)
% 7.16/2.87  | (39)  ? [v0] : (big_f(all_10_0_3, v0) &  ! [v1] : (v1 = v0 |  ~ big_f(all_10_0_3, v1)))
% 7.16/2.87  |
% 7.16/2.87  	| Instantiating (39) with all_13_0_4 yields:
% 7.16/2.87  	| (40) big_f(all_10_0_3, all_13_0_4) &  ! [v0] : (v0 = all_13_0_4 |  ~ big_f(all_10_0_3, v0))
% 7.16/2.87  	|
% 7.16/2.87  	| Applying alpha-rule on (40) yields:
% 7.16/2.87  	| (41) big_f(all_10_0_3, all_13_0_4)
% 7.16/2.87  	| (42)  ! [v0] : (v0 = all_13_0_4 |  ~ big_f(all_10_0_3, v0))
% 7.16/2.87  	|
% 7.16/2.87  	| Instantiating formula (5) with all_13_0_4, all_10_0_3 and discharging atoms big_f(all_10_0_3, all_13_0_4), yields:
% 7.16/2.87  	| (43) all_13_0_4 = all_0_0_0 & all_10_0_3 = all_0_1_1
% 7.16/2.87  	|
% 7.16/2.87  	| Applying alpha-rule on (43) yields:
% 7.16/2.87  	| (44) all_13_0_4 = all_0_0_0
% 7.16/2.87  	| (45) all_10_0_3 = all_0_1_1
% 7.16/2.87  	|
% 7.16/2.87  	| Equations (45) can reduce 12 to:
% 7.16/2.87  	| (46)  ~ (ex_9_0_2 = all_0_1_1)
% 7.16/2.87  	|
% 7.16/2.87  	| Simplifying 46 yields:
% 7.16/2.87  	| (47)  ~ (ex_9_0_2 = all_0_1_1)
% 7.16/2.87  	|
% 7.16/2.87  	| Equations (6) can reduce 47 to:
% 7.16/2.87  	| (13) $false
% 7.16/2.87  	|
% 7.16/2.87  	|-The branch is then unsatisfiable
% 7.16/2.87  % SZS output end Proof for theBenchmark
% 7.16/2.87  
% 7.16/2.87  2293ms
%------------------------------------------------------------------------------