TSTP Solution File: SYN069+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n007.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 04:59:39 EDT 2022
% Result : Theorem 2.85s 1.45s
% Output : Proof 3.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN069+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 17:55:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.93 Prover 0: Preprocessing ...
% 1.60/1.00 Prover 0: Warning: ignoring some quantifiers
% 1.60/1.02 Prover 0: Constructing countermodel ...
% 1.73/1.18 Prover 0: gave up
% 1.73/1.18 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.13/1.19 Prover 1: Preprocessing ...
% 2.31/1.27 Prover 1: Constructing countermodel ...
% 2.31/1.31 Prover 1: gave up
% 2.31/1.31 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.61/1.32 Prover 2: Preprocessing ...
% 2.61/1.39 Prover 2: Warning: ignoring some quantifiers
% 2.85/1.39 Prover 2: Constructing countermodel ...
% 2.85/1.45 Prover 2: proved (138ms)
% 2.85/1.45
% 2.85/1.45 No countermodel exists, formula is valid
% 2.85/1.45 % SZS status Theorem for theBenchmark
% 2.85/1.45
% 2.85/1.45 Generating proof ... Warning: ignoring some quantifiers
% 3.78/1.70 found it (size 30)
% 3.78/1.70
% 3.78/1.70 % SZS output start Proof for theBenchmark
% 3.78/1.70 Assumed formulas after preprocessing and simplification:
% 3.78/1.70 | (0) ? [v0] : (big_f(v0) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (big_h(v4, v3) = v2) | ~ (big_h(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (big_j(v4, v3) = v2) | ~ (big_j(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (big_f(v1) = 0) | ~ (big_k(v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & big_g(v4) = 0 & big_h(v1, v4) = 0 & big_j(v1, v4) = v5)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (big_f(v1) = 0) | ~ (big_g(v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & big_g(v4) = 0 & big_h(v1, v4) = 0 & big_j(v1, v4) = v5)) & ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (big_f(v1) = 0) | ~ (big_h(v1, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & big_g(v4) = 0 & big_h(v1, v4) = 0 & big_j(v1, v4) = v5)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_l(v3) = v2) | ~ (big_l(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_f(v3) = v2) | ~ (big_f(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_k(v3) = v2) | ~ (big_k(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (big_g(v3) = v2) | ~ (big_g(v3) = v1)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_l(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & big_h(v0, v1) = v3)) & ! [v1] : ! [v2] : (v2 = 0 | ~ (big_j(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & big_g(v1) = v3) | ( ~ (v3 = 0) & big_h(v0, v1) = v3))) & ! [v1] : ( ~ (big_l(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_k(v1) = v2)) & ! [v1] : ( ~ (big_f(v1) = 0) | ? [v2] : (big_g(v2) = 0 & big_h(v1, v2) = 0)) & ! [v1] : ( ~ (big_k(v1) = 0) | ? [v2] : ( ~ (v2 = 0) & big_l(v1) = v2)) & ! [v1] : ( ~ (big_g(v1) = 0) | ? [v2] : ((v2 = 0 & big_j(v0, v1) = 0) | ( ~ (v2 = 0) & big_h(v0, v1) = v2))) & ! [v1] : ( ~ (big_h(v0, v1) = 0) | big_l(v1) = 0) & ! [v1] : ( ~ (big_h(v0, v1) = 0) | ? [v2] : ((v2 = 0 & big_j(v0, v1) = 0) | ( ~ (v2 = 0) & big_g(v1) = v2))) & ? [v1] : ? [v2] : ? [v3] : big_h(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : big_j(v2, v1) = v3 & ? [v1] : ? [v2] : big_l(v1) = v2 & ? [v1] : ? [v2] : big_f(v1) = v2 & ? [v1] : ? [v2] : big_k(v1) = v2 & ? [v1] : ? [v2] : big_g(v1) = v2)
% 3.78/1.73 | Instantiating (0) with all_0_0_0 yields:
% 3.78/1.73 | (1) big_f(all_0_0_0) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_k(v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_g(v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_h(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_l(v2) = v1) | ~ (big_l(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_k(v2) = v1) | ~ (big_k(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_l(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_h(all_0_0_0, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_0_0, v0) = v1) | ? [v2] : (( ~ (v2 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_h(all_0_0_0, v0) = v2))) & ! [v0] : ( ~ (big_l(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_k(v0) = v1)) & ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : (big_g(v1) = 0 & big_h(v0, v1) = 0)) & ! [v0] : ( ~ (big_k(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_l(v0) = v1)) & ! [v0] : ( ~ (big_g(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_0_0, v0) = 0) | ( ~ (v1 = 0) & big_h(all_0_0_0, v0) = v1))) & ! [v0] : ( ~ (big_h(all_0_0_0, v0) = 0) | big_l(v0) = 0) & ! [v0] : ( ~ (big_h(all_0_0_0, v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_0_0, v0) = 0) | ( ~ (v1 = 0) & big_g(v0) = v1))) & ? [v0] : ? [v1] : ? [v2] : big_h(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : big_j(v1, v0) = v2 & ? [v0] : ? [v1] : big_l(v0) = v1 & ? [v0] : ? [v1] : big_f(v0) = v1 & ? [v0] : ? [v1] : big_k(v0) = v1 & ? [v0] : ? [v1] : big_g(v0) = v1
% 3.78/1.74 |
% 3.78/1.74 | Applying alpha-rule on (1) yields:
% 3.78/1.74 | (2) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_h(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4))
% 3.78/1.75 | (3) ? [v0] : ? [v1] : ? [v2] : big_h(v1, v0) = v2
% 3.78/1.75 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_f(v2) = v1) | ~ (big_f(v2) = v0))
% 3.78/1.75 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_l(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & big_h(all_0_0_0, v0) = v2))
% 3.78/1.75 | (6) big_f(all_0_0_0) = 0
% 3.78/1.75 | (7) ! [v0] : ( ~ (big_k(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_l(v0) = v1))
% 3.78/1.75 | (8) ! [v0] : ( ~ (big_l(v0) = 0) | ? [v1] : ( ~ (v1 = 0) & big_k(v0) = v1))
% 3.78/1.75 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_k(v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4))
% 3.78/1.75 | (10) ? [v0] : ? [v1] : big_k(v0) = v1
% 3.78/1.75 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (big_j(all_0_0_0, v0) = v1) | ? [v2] : (( ~ (v2 = 0) & big_g(v0) = v2) | ( ~ (v2 = 0) & big_h(all_0_0_0, v0) = v2)))
% 3.78/1.75 | (12) ! [v0] : ( ~ (big_h(all_0_0_0, v0) = 0) | big_l(v0) = 0)
% 3.78/1.75 | (13) ? [v0] : ? [v1] : big_g(v0) = v1
% 3.78/1.75 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_l(v2) = v1) | ~ (big_l(v2) = v0))
% 3.78/1.75 | (15) ? [v0] : ? [v1] : ? [v2] : big_j(v1, v0) = v2
% 3.78/1.75 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_g(v2) = v1) | ~ (big_g(v2) = v0))
% 3.78/1.75 | (17) ! [v0] : ( ~ (big_f(v0) = 0) | ? [v1] : (big_g(v1) = 0 & big_h(v0, v1) = 0))
% 3.78/1.75 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_j(v3, v2) = v1) | ~ (big_j(v3, v2) = v0))
% 3.78/1.75 | (19) ? [v0] : ? [v1] : big_l(v0) = v1
% 3.78/1.75 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (big_k(v2) = v1) | ~ (big_k(v2) = v0))
% 3.78/1.75 | (21) ? [v0] : ? [v1] : big_f(v0) = v1
% 3.78/1.75 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (big_f(v0) = 0) | ~ (big_g(v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & big_g(v3) = 0 & big_h(v0, v3) = 0 & big_j(v0, v3) = v4))
% 3.78/1.75 | (23) ! [v0] : ( ~ (big_h(all_0_0_0, v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_0_0, v0) = 0) | ( ~ (v1 = 0) & big_g(v0) = v1)))
% 3.78/1.75 | (24) ! [v0] : ( ~ (big_g(v0) = 0) | ? [v1] : ((v1 = 0 & big_j(all_0_0_0, v0) = 0) | ( ~ (v1 = 0) & big_h(all_0_0_0, v0) = v1)))
% 3.78/1.76 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (big_h(v3, v2) = v1) | ~ (big_h(v3, v2) = v0))
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (17) with all_0_0_0 and discharging atoms big_f(all_0_0_0) = 0, yields:
% 3.78/1.76 | (26) ? [v0] : (big_g(v0) = 0 & big_h(all_0_0_0, v0) = 0)
% 3.78/1.76 |
% 3.78/1.76 | Instantiating (26) with all_20_0_15 yields:
% 3.78/1.76 | (27) big_g(all_20_0_15) = 0 & big_h(all_0_0_0, all_20_0_15) = 0
% 3.78/1.76 |
% 3.78/1.76 | Applying alpha-rule on (27) yields:
% 3.78/1.76 | (28) big_g(all_20_0_15) = 0
% 3.78/1.76 | (29) big_h(all_0_0_0, all_20_0_15) = 0
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (12) with all_20_0_15 and discharging atoms big_h(all_0_0_0, all_20_0_15) = 0, yields:
% 3.78/1.76 | (30) big_l(all_20_0_15) = 0
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (8) with all_20_0_15 and discharging atoms big_l(all_20_0_15) = 0, yields:
% 3.78/1.76 | (31) ? [v0] : ( ~ (v0 = 0) & big_k(all_20_0_15) = v0)
% 3.78/1.76 |
% 3.78/1.76 | Instantiating (31) with all_43_0_18 yields:
% 3.78/1.76 | (32) ~ (all_43_0_18 = 0) & big_k(all_20_0_15) = all_43_0_18
% 3.78/1.76 |
% 3.78/1.76 | Applying alpha-rule on (32) yields:
% 3.78/1.76 | (33) ~ (all_43_0_18 = 0)
% 3.78/1.76 | (34) big_k(all_20_0_15) = all_43_0_18
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (9) with all_43_0_18, all_20_0_15, all_0_0_0 and discharging atoms big_f(all_0_0_0) = 0, big_k(all_20_0_15) = all_43_0_18, yields:
% 3.78/1.76 | (35) all_43_0_18 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_g(v0) = 0 & big_h(all_0_0_0, v0) = 0 & big_j(all_0_0_0, v0) = v1)
% 3.78/1.76 |
% 3.78/1.76 +-Applying beta-rule and splitting (35), into two cases.
% 3.78/1.76 |-Branch one:
% 3.78/1.76 | (36) all_43_0_18 = 0
% 3.78/1.76 |
% 3.78/1.76 | Equations (36) can reduce 33 to:
% 3.78/1.76 | (37) $false
% 3.78/1.76 |
% 3.78/1.76 |-The branch is then unsatisfiable
% 3.78/1.76 |-Branch two:
% 3.78/1.76 | (33) ~ (all_43_0_18 = 0)
% 3.78/1.76 | (39) ? [v0] : ? [v1] : ( ~ (v1 = 0) & big_g(v0) = 0 & big_h(all_0_0_0, v0) = 0 & big_j(all_0_0_0, v0) = v1)
% 3.78/1.76 |
% 3.78/1.76 | Instantiating (39) with all_52_0_19, all_52_1_20 yields:
% 3.78/1.76 | (40) ~ (all_52_0_19 = 0) & big_g(all_52_1_20) = 0 & big_h(all_0_0_0, all_52_1_20) = 0 & big_j(all_0_0_0, all_52_1_20) = all_52_0_19
% 3.78/1.76 |
% 3.78/1.76 | Applying alpha-rule on (40) yields:
% 3.78/1.76 | (41) ~ (all_52_0_19 = 0)
% 3.78/1.76 | (42) big_g(all_52_1_20) = 0
% 3.78/1.76 | (43) big_h(all_0_0_0, all_52_1_20) = 0
% 3.78/1.76 | (44) big_j(all_0_0_0, all_52_1_20) = all_52_0_19
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (23) with all_52_1_20 and discharging atoms big_h(all_0_0_0, all_52_1_20) = 0, yields:
% 3.78/1.76 | (45) ? [v0] : ((v0 = 0 & big_j(all_0_0_0, all_52_1_20) = 0) | ( ~ (v0 = 0) & big_g(all_52_1_20) = v0))
% 3.78/1.76 |
% 3.78/1.76 | Instantiating formula (11) with all_52_0_19, all_52_1_20 and discharging atoms big_j(all_0_0_0, all_52_1_20) = all_52_0_19, yields:
% 3.78/1.76 | (46) all_52_0_19 = 0 | ? [v0] : (( ~ (v0 = 0) & big_g(all_52_1_20) = v0) | ( ~ (v0 = 0) & big_h(all_0_0_0, all_52_1_20) = v0))
% 3.78/1.76 |
% 3.78/1.76 | Instantiating (45) with all_60_0_21 yields:
% 3.78/1.76 | (47) (all_60_0_21 = 0 & big_j(all_0_0_0, all_52_1_20) = 0) | ( ~ (all_60_0_21 = 0) & big_g(all_52_1_20) = all_60_0_21)
% 3.78/1.76 |
% 3.78/1.76 +-Applying beta-rule and splitting (47), into two cases.
% 3.78/1.76 |-Branch one:
% 3.78/1.76 | (48) all_60_0_21 = 0 & big_j(all_0_0_0, all_52_1_20) = 0
% 3.78/1.76 |
% 3.78/1.76 | Applying alpha-rule on (48) yields:
% 3.78/1.76 | (49) all_60_0_21 = 0
% 3.78/1.76 | (50) big_j(all_0_0_0, all_52_1_20) = 0
% 3.78/1.76 |
% 3.78/1.76 +-Applying beta-rule and splitting (46), into two cases.
% 3.78/1.76 |-Branch one:
% 3.78/1.76 | (51) all_52_0_19 = 0
% 3.78/1.76 |
% 3.78/1.76 | Equations (51) can reduce 41 to:
% 3.78/1.76 | (37) $false
% 3.78/1.76 |
% 3.78/1.76 |-The branch is then unsatisfiable
% 3.78/1.76 |-Branch two:
% 3.78/1.76 | (41) ~ (all_52_0_19 = 0)
% 3.78/1.76 | (54) ? [v0] : (( ~ (v0 = 0) & big_g(all_52_1_20) = v0) | ( ~ (v0 = 0) & big_h(all_0_0_0, all_52_1_20) = v0))
% 3.78/1.76 |
% 3.78/1.77 | Instantiating formula (18) with all_0_0_0, all_52_1_20, 0, all_52_0_19 and discharging atoms big_j(all_0_0_0, all_52_1_20) = all_52_0_19, big_j(all_0_0_0, all_52_1_20) = 0, yields:
% 3.78/1.77 | (51) all_52_0_19 = 0
% 3.78/1.77 |
% 3.78/1.77 | Equations (51) can reduce 41 to:
% 3.78/1.77 | (37) $false
% 3.78/1.77 |
% 3.78/1.77 |-The branch is then unsatisfiable
% 3.78/1.77 |-Branch two:
% 3.78/1.77 | (57) ~ (all_60_0_21 = 0) & big_g(all_52_1_20) = all_60_0_21
% 3.78/1.77 |
% 3.78/1.77 | Applying alpha-rule on (57) yields:
% 3.78/1.77 | (58) ~ (all_60_0_21 = 0)
% 3.78/1.77 | (59) big_g(all_52_1_20) = all_60_0_21
% 3.78/1.77 |
% 3.78/1.77 | Instantiating formula (16) with all_52_1_20, all_60_0_21, 0 and discharging atoms big_g(all_52_1_20) = all_60_0_21, big_g(all_52_1_20) = 0, yields:
% 3.78/1.77 | (49) all_60_0_21 = 0
% 3.78/1.77 |
% 3.78/1.77 | Equations (49) can reduce 58 to:
% 3.78/1.77 | (37) $false
% 3.78/1.77 |
% 3.78/1.77 |-The branch is then unsatisfiable
% 3.78/1.77 % SZS output end Proof for theBenchmark
% 3.78/1.77
% 3.78/1.77 1159ms
%------------------------------------------------------------------------------