TSTP Solution File: SEU126+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 : Tue Jul 19 08:46:45 EDT 2022
% Result : Theorem 16.86s 4.71s
% Output : Proof 22.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n010.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 : 600
% 0.13/0.34 % DateTime : Sun Jun 19 22:51:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.63/0.62 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.70 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.98 Prover 0: Preprocessing ...
% 1.78/1.14 Prover 0: Warning: ignoring some quantifiers
% 1.78/1.16 Prover 0: Constructing countermodel ...
% 2.65/1.35 Prover 0: gave up
% 2.65/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.65/1.37 Prover 1: Preprocessing ...
% 2.92/1.45 Prover 1: Warning: ignoring some quantifiers
% 2.92/1.45 Prover 1: Constructing countermodel ...
% 3.69/1.63 Prover 1: gave up
% 3.69/1.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.69/1.64 Prover 2: Preprocessing ...
% 3.69/1.71 Prover 2: Warning: ignoring some quantifiers
% 3.69/1.71 Prover 2: Constructing countermodel ...
% 4.47/1.85 Prover 2: gave up
% 4.47/1.85 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.47/1.86 Prover 3: Preprocessing ...
% 4.47/1.88 Prover 3: Warning: ignoring some quantifiers
% 4.89/1.89 Prover 3: Constructing countermodel ...
% 4.89/1.93 Prover 3: gave up
% 4.89/1.93 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.89/1.94 Prover 4: Preprocessing ...
% 5.36/2.00 Prover 4: Warning: ignoring some quantifiers
% 5.36/2.00 Prover 4: Constructing countermodel ...
% 8.80/2.81 Prover 4: gave up
% 8.80/2.82 Prover 5: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.80/2.83 Prover 5: Preprocessing ...
% 8.80/2.86 Prover 5: Warning: ignoring some quantifiers
% 8.80/2.86 Prover 5: Constructing countermodel ...
% 9.36/2.95 Prover 5: gave up
% 9.36/2.96 Prover 6: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 9.36/2.97 Prover 6: Preprocessing ...
% 9.36/3.00 Prover 6: Warning: ignoring some quantifiers
% 9.36/3.00 Prover 6: Constructing countermodel ...
% 9.78/3.08 Prover 6: gave up
% 9.78/3.08 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 9.78/3.09 Prover 7: Preprocessing ...
% 9.78/3.10 Prover 7: Proving ...
% 16.86/4.71 Prover 7: proved (1629ms)
% 16.86/4.71
% 16.86/4.71 % SZS status Theorem for theBenchmark
% 16.86/4.71
% 16.86/4.71 Generating proof ... found it (size 30)
% 22.24/6.01
% 22.24/6.01 % SZS output start Proof for theBenchmark
% 22.24/6.01 Assumed formulas after preprocessing and simplification:
% 22.24/6.01 | (0) ? [v0] : (empty(v0) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (set_union2(v4, v3) = v2) | ~ (set_union2(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v2, v1) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ~ empty(v3) | empty(v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | set_union2(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ! [v4] : (v4 = v3 | ? [v5] : (( ~ in(v5, v4) | ( ~ in(v5, v2) & ~ in(v5, v1))) & (in(v5, v4) | in(v5, v2) | in(v5, v1))))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v1, v2) = v3) | ( ! [v4] : ( ~ in(v4, v3) | in(v4, v2) | in(v4, v1)) & ! [v4] : (in(v4, v3) | ( ~ in(v4, v2) & ~ in(v4, v1))))) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v1) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v1, v0) = v2)) & ! [v1] : ! [v2] : (v2 = v1 | ~ empty(v2) | ~ empty(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ subset(v2, v1) | ~ subset(v1, v2)) & ! [v1] : ! [v2] : ( ~ empty(v2) | ~ in(v1, v2)) & ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ! [v3] : ( ~ in(v3, v1) | in(v3, v2))) & ! [v1] : ! [v2] : ( ~ in(v2, v1) | ~ in(v1, v2)) & ! [v1] : ! [v2] : (subset(v1, v2) | ? [v3] : (in(v3, v1) & ~ in(v3, v2))) & ! [v1] : (v1 = v0 | ~ empty(v1)) & ! [v1] : subset(v1, v1) & ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & set_union2(v1, v2) = v3 & subset(v1, v2)) & ? [v1] : ~ empty(v1) & ? [v1] : empty(v1))
% 22.24/6.03 | Instantiating (0) with all_0_0_0 yields:
% 22.24/6.03 | (1) empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ! [v0] : (v0 = all_0_0_0 | ~ empty(v0)) & ! [v0] : subset(v0, v0) & ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & set_union2(v0, v1) = v2 & subset(v0, v1)) & ? [v0] : ~ empty(v0) & ? [v0] : empty(v0)
% 22.24/6.04 |
% 22.24/6.04 | Applying alpha-rule on (1) yields:
% 22.24/6.04 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 22.24/6.04 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 22.24/6.04 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 22.24/6.04 | (5) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = v1) & set_union2(v0, v1) = v2 & subset(v0, v1))
% 22.24/6.04 | (6) ! [v0] : subset(v0, v0)
% 22.24/6.04 | (7) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 22.24/6.04 | (8) ? [v0] : ~ empty(v0)
% 22.24/6.04 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 22.24/6.04 | (10) ! [v0] : (v0 = all_0_0_0 | ~ empty(v0))
% 22.24/6.04 | (11) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 22.24/6.04 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 22.24/6.04 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 22.24/6.04 | (14) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 22.24/6.04 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ! [v3] : (v3 = v2 | ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) & ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0)))))
% 22.24/6.04 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, all_0_0_0) = v1))
% 22.24/6.04 | (17) ! [v0] : ! [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 22.24/6.04 | (18) empty(all_0_0_0)
% 22.24/6.04 | (19) ? [v0] : empty(v0)
% 22.24/6.04 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 22.24/6.04 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) & ~ in(v3, v0)))))
% 22.24/6.05 |
% 22.24/6.05 | Instantiating (5) with all_5_0_2, all_5_1_3, all_5_2_4 yields:
% 22.24/6.05 | (22) ~ (all_5_0_2 = all_5_1_3) & set_union2(all_5_2_4, all_5_1_3) = all_5_0_2 & subset(all_5_2_4, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | Applying alpha-rule on (22) yields:
% 22.24/6.05 | (23) ~ (all_5_0_2 = all_5_1_3)
% 22.24/6.05 | (24) set_union2(all_5_2_4, all_5_1_3) = all_5_0_2
% 22.24/6.05 | (25) subset(all_5_2_4, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | Instantiating formula (2) with all_5_0_2, all_5_1_3, all_5_2_4 and discharging atoms set_union2(all_5_2_4, all_5_1_3) = all_5_0_2, yields:
% 22.24/6.05 | (26) set_union2(all_5_1_3, all_5_2_4) = all_5_0_2
% 22.24/6.05 |
% 22.24/6.05 | Instantiating formula (7) with all_5_1_3, all_5_2_4 and discharging atoms subset(all_5_2_4, all_5_1_3), yields:
% 22.24/6.05 | (27) ! [v0] : ( ~ in(v0, all_5_2_4) | in(v0, all_5_1_3))
% 22.24/6.05 |
% 22.24/6.05 | Instantiating formula (15) with all_5_0_2, all_5_2_4, all_5_1_3 and discharging atoms set_union2(all_5_1_3, all_5_2_4) = all_5_0_2, yields:
% 22.24/6.05 | (28) ! [v0] : (v0 = all_5_0_2 | ? [v1] : (( ~ in(v1, v0) | ( ~ in(v1, all_5_1_3) & ~ in(v1, all_5_2_4))) & (in(v1, v0) | in(v1, all_5_1_3) | in(v1, all_5_2_4))))
% 22.24/6.05 |
% 22.24/6.05 | Introducing new symbol ex_75_0_10 defined by:
% 22.24/6.05 | (29) ex_75_0_10 = all_5_1_3
% 22.24/6.05 |
% 22.24/6.05 | Instantiating formula (28) with ex_75_0_10 yields:
% 22.24/6.05 | (30) ex_75_0_10 = all_5_0_2 | ? [v0] : (( ~ in(v0, ex_75_0_10) | ( ~ in(v0, all_5_1_3) & ~ in(v0, all_5_2_4))) & (in(v0, ex_75_0_10) | in(v0, all_5_1_3) | in(v0, all_5_2_4)))
% 22.24/6.05 |
% 22.24/6.05 +-Applying beta-rule and splitting (30), into two cases.
% 22.24/6.05 |-Branch one:
% 22.24/6.05 | (31) ex_75_0_10 = all_5_0_2
% 22.24/6.05 |
% 22.24/6.05 | Combining equations (29,31) yields a new equation:
% 22.24/6.05 | (32) all_5_0_2 = all_5_1_3
% 22.24/6.05 |
% 22.24/6.05 | Equations (32) can reduce 23 to:
% 22.24/6.05 | (33) $false
% 22.24/6.05 |
% 22.24/6.05 |-The branch is then unsatisfiable
% 22.24/6.05 |-Branch two:
% 22.24/6.05 | (34) ? [v0] : (( ~ in(v0, ex_75_0_10) | ( ~ in(v0, all_5_1_3) & ~ in(v0, all_5_2_4))) & (in(v0, ex_75_0_10) | in(v0, all_5_1_3) | in(v0, all_5_2_4)))
% 22.24/6.05 |
% 22.24/6.05 | Instantiating (34) with all_78_0_11 yields:
% 22.24/6.05 | (35) ( ~ in(all_78_0_11, ex_75_0_10) | ( ~ in(all_78_0_11, all_5_1_3) & ~ in(all_78_0_11, all_5_2_4))) & (in(all_78_0_11, ex_75_0_10) | in(all_78_0_11, all_5_1_3) | in(all_78_0_11, all_5_2_4))
% 22.24/6.05 |
% 22.24/6.05 | Applying alpha-rule on (35) yields:
% 22.24/6.05 | (36) ~ in(all_78_0_11, ex_75_0_10) | ( ~ in(all_78_0_11, all_5_1_3) & ~ in(all_78_0_11, all_5_2_4))
% 22.24/6.05 | (37) in(all_78_0_11, ex_75_0_10) | in(all_78_0_11, all_5_1_3) | in(all_78_0_11, all_5_2_4)
% 22.24/6.05 |
% 22.24/6.05 +-Applying beta-rule and splitting (37), into two cases.
% 22.24/6.05 |-Branch one:
% 22.24/6.05 | (38) in(all_78_0_11, ex_75_0_10)
% 22.24/6.05 |
% 22.24/6.05 +-Applying beta-rule and splitting (36), into two cases.
% 22.24/6.05 |-Branch one:
% 22.24/6.05 | (39) ~ in(all_78_0_11, ex_75_0_10)
% 22.24/6.05 |
% 22.24/6.05 | Using (38) and (39) yields:
% 22.24/6.05 | (40) $false
% 22.24/6.05 |
% 22.24/6.05 |-The branch is then unsatisfiable
% 22.24/6.05 |-Branch two:
% 22.24/6.05 | (41) ~ in(all_78_0_11, all_5_1_3) & ~ in(all_78_0_11, all_5_2_4)
% 22.24/6.05 |
% 22.24/6.05 | Applying alpha-rule on (41) yields:
% 22.24/6.05 | (42) ~ in(all_78_0_11, all_5_1_3)
% 22.24/6.05 | (43) ~ in(all_78_0_11, all_5_2_4)
% 22.24/6.05 |
% 22.24/6.05 | From (29) and (38) follows:
% 22.24/6.05 | (44) in(all_78_0_11, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | Using (44) and (42) yields:
% 22.24/6.05 | (40) $false
% 22.24/6.05 |
% 22.24/6.05 |-The branch is then unsatisfiable
% 22.24/6.05 |-Branch two:
% 22.24/6.05 | (39) ~ in(all_78_0_11, ex_75_0_10)
% 22.24/6.05 | (47) in(all_78_0_11, all_5_1_3) | in(all_78_0_11, all_5_2_4)
% 22.24/6.05 |
% 22.24/6.05 +-Applying beta-rule and splitting (47), into two cases.
% 22.24/6.05 |-Branch one:
% 22.24/6.05 | (44) in(all_78_0_11, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | From (29) and (39) follows:
% 22.24/6.05 | (42) ~ in(all_78_0_11, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | Using (44) and (42) yields:
% 22.24/6.05 | (40) $false
% 22.24/6.05 |
% 22.24/6.05 |-The branch is then unsatisfiable
% 22.24/6.05 |-Branch two:
% 22.24/6.05 | (42) ~ in(all_78_0_11, all_5_1_3)
% 22.24/6.05 | (52) in(all_78_0_11, all_5_2_4)
% 22.24/6.05 |
% 22.24/6.05 | Instantiating formula (27) with all_78_0_11 and discharging atoms in(all_78_0_11, all_5_2_4), yields:
% 22.24/6.05 | (44) in(all_78_0_11, all_5_1_3)
% 22.24/6.05 |
% 22.24/6.05 | Using (44) and (42) yields:
% 22.24/6.05 | (40) $false
% 22.24/6.05 |
% 22.24/6.05 |-The branch is then unsatisfiable
% 22.24/6.05 % SZS output end Proof for theBenchmark
% 22.24/6.05
% 22.24/6.05 5419ms
%------------------------------------------------------------------------------