TSTP Solution File: SWW951+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWW951+1 : TPTP v8.1.0. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 00:04:51 EDT 2022
% Result : Theorem 5.21s 1.91s
% Output : Proof 7.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW951+1 : TPTP v8.1.0. Released v7.4.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 5 16:14:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/0.61 ____ _
% 0.46/0.61 ___ / __ \_____(_)___ ________ __________
% 0.46/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.61
% 0.46/0.61 A Theorem Prover for First-Order Logic
% 0.46/0.62 (ePrincess v.1.0)
% 0.46/0.62
% 0.46/0.62 (c) Philipp Rümmer, 2009-2015
% 0.46/0.62 (c) Peter Backeman, 2014-2015
% 0.46/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.62 Bug reports to peter@backeman.se
% 0.46/0.62
% 0.46/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.62
% 0.46/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.98 Prover 0: Preprocessing ...
% 2.15/1.18 Prover 0: Warning: ignoring some quantifiers
% 2.15/1.20 Prover 0: Constructing countermodel ...
% 3.37/1.49 Prover 0: gave up
% 3.37/1.50 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.37/1.53 Prover 1: Preprocessing ...
% 3.88/1.61 Prover 1: Constructing countermodel ...
% 4.36/1.68 Prover 1: gave up
% 4.36/1.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.36/1.71 Prover 2: Preprocessing ...
% 4.72/1.78 Prover 2: Warning: ignoring some quantifiers
% 4.72/1.78 Prover 2: Constructing countermodel ...
% 5.21/1.91 Prover 2: proved (225ms)
% 5.21/1.91
% 5.21/1.91 No countermodel exists, formula is valid
% 5.21/1.91 % SZS status Theorem for theBenchmark
% 5.21/1.91
% 5.21/1.91 Generating proof ... Warning: ignoring some quantifiers
% 7.30/2.40 found it (size 37)
% 7.30/2.40
% 7.30/2.40 % SZS output start Proof for theBenchmark
% 7.30/2.40 Assumed formulas after preprocessing and simplification:
% 7.30/2.40 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & ~ (name_objective = name_k) & ~ (name_objective = name_c) & ~ (name_objective = constr_ZERO) & ~ (name_objective = constr_CONST_4) & ~ (name_objective = constr_CONST_3) & ~ (name_objective = constr_CONST_2) & ~ (name_objective = constr_CONST_0x30) & ~ (name_objective = constr_CONST_1) & ~ (name_k = name_c) & ~ (name_k = constr_ZERO) & ~ (name_k = constr_CONST_4) & ~ (name_k = constr_CONST_3) & ~ (name_k = constr_CONST_2) & ~ (name_k = constr_CONST_0x30) & ~ (name_k = constr_CONST_1) & ~ (name_c = constr_ZERO) & ~ (name_c = constr_CONST_4) & ~ (name_c = constr_CONST_3) & ~ (name_c = constr_CONST_2) & ~ (name_c = constr_CONST_0x30) & ~ (name_c = constr_CONST_1) & ~ (constr_ZERO = constr_CONST_4) & ~ (constr_ZERO = constr_CONST_3) & ~ (constr_ZERO = constr_CONST_2) & ~ (constr_ZERO = constr_CONST_0x30) & ~ (constr_ZERO = constr_CONST_1) & ~ (constr_CONST_4 = constr_CONST_3) & ~ (constr_CONST_4 = constr_CONST_2) & ~ (constr_CONST_4 = constr_CONST_0x30) & ~ (constr_CONST_4 = constr_CONST_1) & ~ (constr_CONST_3 = constr_CONST_2) & ~ (constr_CONST_3 = constr_CONST_0x30) & ~ (constr_CONST_3 = constr_CONST_1) & ~ (constr_CONST_2 = constr_CONST_0x30) & ~ (constr_CONST_2 = constr_CONST_1) & ~ (constr_CONST_0x30 = constr_CONST_1) & tuple_T_out_4(name_objective) = v0 & pred_attacker(v0) = v1 & pred_attacker(tuple_false) = 0 & pred_attacker(tuple_true) = 0 & pred_attacker(name_objective) = v2 & pred_attacker(name_c) = 0 & pred_attacker(constr_ZERO) = 0 & pred_attacker(constr_CONST_4) = 0 & pred_attacker(constr_CONST_3) = 0 & pred_attacker(constr_CONST_2) = 0 & pred_attacker(constr_CONST_0x30) = 0 & pred_attacker(constr_CONST_1) = 0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (constr_xor(v6, v5) = v7) | ~ (constr_xor(v3, v4) = v6) | ? [v8] : (constr_xor(v4, v5) = v8 & constr_xor(v3, v8) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (constr_xor(v4, v5) = v6) | ~ (constr_xor(v3, v6) = v7) | ? [v8] : (constr_xor(v8, v5) = v7 & constr_xor(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pred_equal(v6, v5) = v4) | ~ (pred_equal(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pred_mess(v6, v5) = v4) | ~ (pred_mess(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (constr_xor(v6, v5) = v4) | ~ (constr_xor(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = 0 | ~ (tuple_T_in_1(v4) = v6) | ~ (tuple_T_in_3(v3) = v5) | ~ (pred_attacker(v6) = 0) | ~ (pred_attacker(v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pred_mess(v4, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & pred_attacker(v4) = v6) | ( ~ (v6 = 0) & pred_attacker(v3) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (name_new0x2Dname(v5) = v4) | ~ (name_new0x2Dname(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (tuple_T_in_1(v5) = v4) | ~ (tuple_T_in_1(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (tuple_T_in_3(v5) = v4) | ~ (tuple_T_in_3(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (tuple_T_out_2(v5) = v4) | ~ (tuple_T_out_2(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (tuple_T_out_4(v5) = v4) | ~ (tuple_T_out_4(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (constr_h(v5) = v4) | ~ (constr_h(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (pred_attacker(v5) = v4) | ~ (pred_attacker(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (constr_xor(v4, v3) = v5) | constr_xor(v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (constr_xor(v3, v4) = v5) | constr_xor(v4, v3) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (constr_xor(v3, v4) = v5) | ? [v6] : ((v6 = 0 & pred_attacker(v5) = 0) | ( ~ (v6 = 0) & pred_attacker(v4) = v6) | ( ~ (v6 = 0) & pred_attacker(v3) = v6))) & ! [v3] : ! [v4] : (v4 = v3 | ~ (constr_xor(v3, constr_ZERO) = v4)) & ! [v3] : ! [v4] : (v4 = constr_ZERO | ~ (constr_xor(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (pred_equal(v3, v3) = v4)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (pred_attacker(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & tuple_T_in_1(v3) = v5 & pred_attacker(v5) = v6)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (pred_attacker(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & tuple_T_in_3(v3) = v5 & pred_attacker(v5) = v6)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (pred_attacker(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & tuple_T_out_2(v3) = v5 & pred_attacker(v5) = v6)) & ! [v3] : ! [v4] : (v4 = 0 | ~ (pred_attacker(v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & tuple_T_out_4(v3) = v5 & pred_attacker(v5) = v6)) & ! [v3] : ! [v4] : ( ~ (name_new0x2Dname(v3) = v4) | pred_attacker(v4) = 0) & ! [v3] : ! [v4] : ( ~ (pred_mess(v4, v3) = 0) | ? [v5] : ((v5 = 0 & pred_attacker(v3) = 0) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_in_1(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & tuple_T_out_2(v6) = v7 & constr_h(v5) = v6 & pred_attacker(v7) = 0 & constr_xor(name_k, v3) = v5) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_in_1(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v4) = 0) | ( ~ (v5 = 0) & pred_attacker(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_in_1(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v3) = 0) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_in_3(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v4) = 0) | ( ~ (v5 = 0) & pred_attacker(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_in_3(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v3) = 0) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_out_2(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v4) = 0) | ( ~ (v5 = 0) & pred_attacker(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_out_2(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v3) = 0) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_out_4(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v4) = 0) | ( ~ (v5 = 0) & pred_attacker(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (tuple_T_out_4(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v3) = 0) | ( ~ (v5 = 0) & pred_attacker(v4) = v5))) & ! [v3] : ! [v4] : ( ~ (constr_h(v3) = v4) | ? [v5] : ((v5 = 0 & pred_attacker(v4) = 0) | ( ~ (v5 = 0) & pred_attacker(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (constr_xor(name_k, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & tuple_T_out_2(v5) = v6 & constr_h(v4) = v5 & pred_attacker(v6) = 0) | ( ~ (v6 = 0) & tuple_T_in_1(v3) = v5 & pred_attacker(v5) = v6))) & ! [v3] : ( ~ (pred_attacker(v3) = 0) | ? [v4] : (tuple_T_in_1(v3) = v4 & pred_attacker(v4) = 0)) & ! [v3] : ( ~ (pred_attacker(v3) = 0) | ? [v4] : (tuple_T_in_3(v3) = v4 & pred_attacker(v4) = 0)) & ! [v3] : ( ~ (pred_attacker(v3) = 0) | ? [v4] : (tuple_T_out_2(v3) = v4 & pred_attacker(v4) = 0)) & ! [v3] : ( ~ (pred_attacker(v3) = 0) | ? [v4] : (tuple_T_out_4(v3) = v4 & pred_attacker(v4) = 0)) & ! [v3] : ( ~ (pred_attacker(v3) = 0) | ? [v4] : (constr_h(v3) = v4 & pred_attacker(v4) = 0)) & ? [v3] : ? [v4] : ? [v5] : pred_equal(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : pred_mess(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : constr_xor(v4, v3) = v5 & ? [v3] : ? [v4] : name_new0x2Dname(v3) = v4 & ? [v3] : ? [v4] : tuple_T_in_1(v3) = v4 & ? [v3] : ? [v4] : tuple_T_in_3(v3) = v4 & ? [v3] : ? [v4] : tuple_T_out_2(v3) = v4 & ? [v3] : ? [v4] : tuple_T_out_4(v3) = v4 & ? [v3] : ? [v4] : constr_h(v3) = v4 & ? [v3] : ? [v4] : pred_attacker(v3) = v4)
% 7.56/2.44 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 7.56/2.44 | (1) ~ (all_0_0_0 = 0) & ~ (name_objective = name_k) & ~ (name_objective = name_c) & ~ (name_objective = constr_ZERO) & ~ (name_objective = constr_CONST_4) & ~ (name_objective = constr_CONST_3) & ~ (name_objective = constr_CONST_2) & ~ (name_objective = constr_CONST_0x30) & ~ (name_objective = constr_CONST_1) & ~ (name_k = name_c) & ~ (name_k = constr_ZERO) & ~ (name_k = constr_CONST_4) & ~ (name_k = constr_CONST_3) & ~ (name_k = constr_CONST_2) & ~ (name_k = constr_CONST_0x30) & ~ (name_k = constr_CONST_1) & ~ (name_c = constr_ZERO) & ~ (name_c = constr_CONST_4) & ~ (name_c = constr_CONST_3) & ~ (name_c = constr_CONST_2) & ~ (name_c = constr_CONST_0x30) & ~ (name_c = constr_CONST_1) & ~ (constr_ZERO = constr_CONST_4) & ~ (constr_ZERO = constr_CONST_3) & ~ (constr_ZERO = constr_CONST_2) & ~ (constr_ZERO = constr_CONST_0x30) & ~ (constr_ZERO = constr_CONST_1) & ~ (constr_CONST_4 = constr_CONST_3) & ~ (constr_CONST_4 = constr_CONST_2) & ~ (constr_CONST_4 = constr_CONST_0x30) & ~ (constr_CONST_4 = constr_CONST_1) & ~ (constr_CONST_3 = constr_CONST_2) & ~ (constr_CONST_3 = constr_CONST_0x30) & ~ (constr_CONST_3 = constr_CONST_1) & ~ (constr_CONST_2 = constr_CONST_0x30) & ~ (constr_CONST_2 = constr_CONST_1) & ~ (constr_CONST_0x30 = constr_CONST_1) & tuple_T_out_4(name_objective) = all_0_2_2 & pred_attacker(all_0_2_2) = all_0_1_1 & pred_attacker(tuple_false) = 0 & pred_attacker(tuple_true) = 0 & pred_attacker(name_objective) = all_0_0_0 & pred_attacker(name_c) = 0 & pred_attacker(constr_ZERO) = 0 & pred_attacker(constr_CONST_4) = 0 & pred_attacker(constr_CONST_3) = 0 & pred_attacker(constr_CONST_2) = 0 & pred_attacker(constr_CONST_0x30) = 0 & pred_attacker(constr_CONST_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (constr_xor(v3, v2) = v4) | ~ (constr_xor(v0, v1) = v3) | ? [v5] : (constr_xor(v1, v2) = v5 & constr_xor(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (constr_xor(v1, v2) = v3) | ~ (constr_xor(v0, v3) = v4) | ? [v5] : (constr_xor(v5, v2) = v4 & constr_xor(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pred_equal(v3, v2) = v1) | ~ (pred_equal(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pred_mess(v3, v2) = v1) | ~ (pred_mess(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (constr_xor(v3, v2) = v1) | ~ (constr_xor(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (all_0_1_1 = 0 | ~ (tuple_T_in_1(v1) = v3) | ~ (tuple_T_in_3(v0) = v2) | ~ (pred_attacker(v3) = 0) | ~ (pred_attacker(v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pred_mess(v1, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & pred_attacker(v1) = v3) | ( ~ (v3 = 0) & pred_attacker(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (name_new0x2Dname(v2) = v1) | ~ (name_new0x2Dname(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_in_1(v2) = v1) | ~ (tuple_T_in_1(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_in_3(v2) = v1) | ~ (tuple_T_in_3(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_out_2(v2) = v1) | ~ (tuple_T_out_2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_out_4(v2) = v1) | ~ (tuple_T_out_4(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (constr_h(v2) = v1) | ~ (constr_h(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred_attacker(v2) = v1) | ~ (pred_attacker(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v1, v0) = v2) | constr_xor(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v0, v1) = v2) | constr_xor(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v0, v1) = v2) | ? [v3] : ((v3 = 0 & pred_attacker(v2) = 0) | ( ~ (v3 = 0) & pred_attacker(v1) = v3) | ( ~ (v3 = 0) & pred_attacker(v0) = v3))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (constr_xor(v0, constr_ZERO) = v1)) & ! [v0] : ! [v1] : (v1 = constr_ZERO | ~ (constr_xor(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_equal(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_in_1(v0) = v2 & pred_attacker(v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_in_3(v0) = v2 & pred_attacker(v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_out_2(v0) = v2 & pred_attacker(v2) = v3)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_out_4(v0) = v2 & pred_attacker(v2) = v3)) & ! [v0] : ! [v1] : ( ~ (name_new0x2Dname(v0) = v1) | pred_attacker(v1) = 0) & ! [v0] : ! [v1] : ( ~ (pred_mess(v1, v0) = 0) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & tuple_T_out_2(v3) = v4 & constr_h(v2) = v3 & pred_attacker(v4) = 0 & constr_xor(name_k, v0) = v2) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_in_3(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_in_3(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_out_2(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_out_2(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_out_4(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (tuple_T_out_4(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (constr_h(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (constr_xor(name_k, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & tuple_T_out_2(v2) = v3 & constr_h(v1) = v2 & pred_attacker(v3) = 0) | ( ~ (v3 = 0) & tuple_T_in_1(v0) = v2 & pred_attacker(v2) = v3))) & ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_in_1(v0) = v1 & pred_attacker(v1) = 0)) & ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_in_3(v0) = v1 & pred_attacker(v1) = 0)) & ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_out_2(v0) = v1 & pred_attacker(v1) = 0)) & ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_out_4(v0) = v1 & pred_attacker(v1) = 0)) & ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (constr_h(v0) = v1 & pred_attacker(v1) = 0)) & ? [v0] : ? [v1] : ? [v2] : pred_equal(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : pred_mess(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : constr_xor(v1, v0) = v2 & ? [v0] : ? [v1] : name_new0x2Dname(v0) = v1 & ? [v0] : ? [v1] : tuple_T_in_1(v0) = v1 & ? [v0] : ? [v1] : tuple_T_in_3(v0) = v1 & ? [v0] : ? [v1] : tuple_T_out_2(v0) = v1 & ? [v0] : ? [v1] : tuple_T_out_4(v0) = v1 & ? [v0] : ? [v1] : constr_h(v0) = v1 & ? [v0] : ? [v1] : pred_attacker(v0) = v1
% 7.56/2.46 |
% 7.56/2.46 | Applying alpha-rule on (1) yields:
% 7.56/2.46 | (2) ~ (name_k = constr_CONST_4)
% 7.56/2.46 | (3) ! [v0] : ! [v1] : ( ~ (tuple_T_in_3(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2)))
% 7.56/2.46 | (4) ? [v0] : ? [v1] : tuple_T_in_3(v0) = v1
% 7.56/2.46 | (5) ~ (name_objective = constr_CONST_4)
% 7.56/2.46 | (6) pred_attacker(constr_CONST_2) = 0
% 7.56/2.46 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pred_mess(v1, v0) = v2) | ? [v3] : (( ~ (v3 = 0) & pred_attacker(v1) = v3) | ( ~ (v3 = 0) & pred_attacker(v0) = v3)))
% 7.56/2.46 | (8) pred_attacker(constr_CONST_0x30) = 0
% 7.56/2.46 | (9) ? [v0] : ? [v1] : tuple_T_out_4(v0) = v1
% 7.56/2.46 | (10) ~ (name_k = constr_CONST_1)
% 7.56/2.46 | (11) ? [v0] : ? [v1] : tuple_T_out_2(v0) = v1
% 7.56/2.46 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (constr_xor(v3, v2) = v4) | ~ (constr_xor(v0, v1) = v3) | ? [v5] : (constr_xor(v1, v2) = v5 & constr_xor(v0, v5) = v4))
% 7.56/2.46 | (13) ~ (constr_ZERO = constr_CONST_1)
% 7.56/2.46 | (14) ~ (constr_CONST_2 = constr_CONST_0x30)
% 7.86/2.46 | (15) ? [v0] : ? [v1] : ? [v2] : pred_equal(v1, v0) = v2
% 7.86/2.46 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (constr_h(v2) = v1) | ~ (constr_h(v2) = v0))
% 7.86/2.46 | (17) ! [v0] : ! [v1] : ( ~ (name_new0x2Dname(v0) = v1) | pred_attacker(v1) = 0)
% 7.86/2.46 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pred_mess(v3, v2) = v1) | ~ (pred_mess(v3, v2) = v0))
% 7.86/2.46 | (19) ? [v0] : ? [v1] : constr_h(v0) = v1
% 7.86/2.46 | (20) ~ (constr_CONST_3 = constr_CONST_2)
% 7.86/2.46 | (21) ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_equal(v0, v0) = v1))
% 7.86/2.46 | (22) ~ (name_objective = name_k)
% 7.86/2.46 | (23) ~ (name_objective = name_c)
% 7.86/2.46 | (24) ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (constr_h(v0) = v1 & pred_attacker(v1) = 0))
% 7.86/2.46 | (25) ~ (constr_ZERO = constr_CONST_2)
% 7.86/2.46 | (26) pred_attacker(tuple_false) = 0
% 7.86/2.46 | (27) ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_out_2(v0) = v1 & pred_attacker(v1) = 0))
% 7.86/2.46 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_out_4(v0) = v2 & pred_attacker(v2) = v3))
% 7.86/2.46 | (29) ! [v0] : ! [v1] : (v1 = constr_ZERO | ~ (constr_xor(v0, v0) = v1))
% 7.86/2.46 | (30) pred_attacker(constr_CONST_1) = 0
% 7.86/2.46 | (31) pred_attacker(name_c) = 0
% 7.86/2.46 | (32) ! [v0] : ! [v1] : ( ~ (tuple_T_out_2(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.46 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_in_3(v2) = v1) | ~ (tuple_T_in_3(v2) = v0))
% 7.86/2.46 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_in_1(v2) = v1) | ~ (tuple_T_in_1(v2) = v0))
% 7.86/2.46 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_in_3(v0) = v2 & pred_attacker(v2) = v3))
% 7.86/2.46 | (36) ~ (name_objective = constr_CONST_1)
% 7.86/2.46 | (37) ~ (name_k = constr_CONST_3)
% 7.86/2.46 | (38) ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_in_3(v0) = v1 & pred_attacker(v1) = 0))
% 7.86/2.46 | (39) ~ (constr_CONST_4 = constr_CONST_2)
% 7.86/2.46 | (40) pred_attacker(constr_CONST_3) = 0
% 7.86/2.46 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (constr_xor(v3, v2) = v1) | ~ (constr_xor(v3, v2) = v0))
% 7.86/2.46 | (42) ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_out_4(v0) = v1 & pred_attacker(v1) = 0))
% 7.86/2.47 | (43) ~ (name_c = constr_ZERO)
% 7.86/2.47 | (44) ! [v0] : ( ~ (pred_attacker(v0) = 0) | ? [v1] : (tuple_T_in_1(v0) = v1 & pred_attacker(v1) = 0))
% 7.86/2.47 | (45) ~ (all_0_0_0 = 0)
% 7.86/2.47 | (46) ! [v0] : ! [v1] : ( ~ (tuple_T_out_4(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.47 | (47) ! [v0] : ! [v1] : ( ~ (tuple_T_in_3(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.47 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pred_equal(v3, v2) = v1) | ~ (pred_equal(v3, v2) = v0))
% 7.86/2.47 | (49) pred_attacker(constr_CONST_4) = 0
% 7.86/2.47 | (50) pred_attacker(constr_ZERO) = 0
% 7.86/2.47 | (51) pred_attacker(tuple_true) = 0
% 7.86/2.47 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_out_4(v2) = v1) | ~ (tuple_T_out_4(v2) = v0))
% 7.86/2.47 | (53) ~ (constr_ZERO = constr_CONST_3)
% 7.86/2.47 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (constr_xor(v1, v2) = v3) | ~ (constr_xor(v0, v3) = v4) | ? [v5] : (constr_xor(v5, v2) = v4 & constr_xor(v0, v1) = v5))
% 7.86/2.47 | (55) ~ (name_objective = constr_CONST_2)
% 7.86/2.47 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tuple_T_out_2(v2) = v1) | ~ (tuple_T_out_2(v2) = v0))
% 7.86/2.47 | (57) ~ (name_objective = constr_ZERO)
% 7.86/2.47 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ (constr_xor(v0, constr_ZERO) = v1))
% 7.86/2.47 | (59) ~ (name_k = constr_CONST_0x30)
% 7.86/2.47 | (60) tuple_T_out_4(name_objective) = all_0_2_2
% 7.86/2.47 | (61) ! [v0] : ! [v1] : ( ~ (constr_h(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2)))
% 7.86/2.47 | (62) ~ (name_c = constr_CONST_3)
% 7.86/2.47 | (63) ~ (name_objective = constr_CONST_3)
% 7.86/2.47 | (64) ~ (name_c = constr_CONST_4)
% 7.86/2.47 | (65) ~ (constr_CONST_4 = constr_CONST_1)
% 7.86/2.47 | (66) ~ (name_k = constr_CONST_2)
% 7.86/2.47 | (67) ~ (constr_CONST_3 = constr_CONST_1)
% 7.86/2.47 | (68) ! [v0] : ! [v1] : ( ~ (pred_mess(v1, v0) = 0) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.47 | (69) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pred_attacker(v2) = v1) | ~ (pred_attacker(v2) = v0))
% 7.86/2.47 | (70) pred_attacker(name_objective) = all_0_0_0
% 7.86/2.47 | (71) ! [v0] : ! [v1] : ( ~ (tuple_T_out_2(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2)))
% 7.86/2.47 | (72) ? [v0] : ? [v1] : tuple_T_in_1(v0) = v1
% 7.86/2.47 | (73) ! [v0] : ! [v1] : ( ~ (constr_xor(name_k, v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & tuple_T_out_2(v2) = v3 & constr_h(v1) = v2 & pred_attacker(v3) = 0) | ( ~ (v3 = 0) & tuple_T_in_1(v0) = v2 & pred_attacker(v2) = v3)))
% 7.86/2.47 | (74) ? [v0] : ? [v1] : pred_attacker(v0) = v1
% 7.86/2.47 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (all_0_1_1 = 0 | ~ (tuple_T_in_1(v1) = v3) | ~ (tuple_T_in_3(v0) = v2) | ~ (pred_attacker(v3) = 0) | ~ (pred_attacker(v2) = 0))
% 7.86/2.47 | (76) ? [v0] : ? [v1] : name_new0x2Dname(v0) = v1
% 7.86/2.47 | (77) ~ (constr_CONST_0x30 = constr_CONST_1)
% 7.86/2.47 | (78) ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & tuple_T_out_2(v3) = v4 & constr_h(v2) = v3 & pred_attacker(v4) = 0 & constr_xor(name_k, v0) = v2) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.47 | (79) pred_attacker(all_0_2_2) = all_0_1_1
% 7.86/2.47 | (80) ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_out_2(v0) = v2 & pred_attacker(v2) = v3))
% 7.86/2.47 | (81) ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v0) = 0) | ( ~ (v2 = 0) & pred_attacker(v1) = v2)))
% 7.86/2.47 | (82) ~ (constr_CONST_2 = constr_CONST_1)
% 7.86/2.47 | (83) ! [v0] : ! [v1] : ( ~ (tuple_T_out_4(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2)))
% 7.86/2.48 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v0, v1) = v2) | ? [v3] : ((v3 = 0 & pred_attacker(v2) = 0) | ( ~ (v3 = 0) & pred_attacker(v1) = v3) | ( ~ (v3 = 0) & pred_attacker(v0) = v3)))
% 7.86/2.48 | (85) ~ (name_objective = constr_CONST_0x30)
% 7.86/2.48 | (86) ~ (name_k = constr_ZERO)
% 7.86/2.48 | (87) ~ (constr_CONST_4 = constr_CONST_0x30)
% 7.86/2.48 | (88) ~ (constr_CONST_3 = constr_CONST_0x30)
% 7.86/2.48 | (89) ! [v0] : ! [v1] : (v1 = 0 | ~ (pred_attacker(v0) = v1) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & tuple_T_in_1(v0) = v2 & pred_attacker(v2) = v3))
% 7.86/2.48 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v0, v1) = v2) | constr_xor(v1, v0) = v2)
% 7.86/2.48 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (constr_xor(v1, v0) = v2) | constr_xor(v0, v1) = v2)
% 7.86/2.48 | (92) ! [v0] : ! [v1] : ( ~ (tuple_T_in_1(v0) = v1) | ? [v2] : ((v2 = 0 & pred_attacker(v1) = 0) | ( ~ (v2 = 0) & pred_attacker(v0) = v2)))
% 7.86/2.48 | (93) ~ (name_c = constr_CONST_1)
% 7.86/2.48 | (94) ? [v0] : ? [v1] : ? [v2] : constr_xor(v1, v0) = v2
% 7.86/2.48 | (95) ~ (constr_ZERO = constr_CONST_0x30)
% 7.86/2.48 | (96) ~ (name_c = constr_CONST_0x30)
% 7.86/2.48 | (97) ~ (constr_CONST_4 = constr_CONST_3)
% 7.86/2.48 | (98) ? [v0] : ? [v1] : ? [v2] : pred_mess(v1, v0) = v2
% 7.86/2.48 | (99) ~ (constr_ZERO = constr_CONST_4)
% 7.86/2.48 | (100) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (name_new0x2Dname(v2) = v1) | ~ (name_new0x2Dname(v2) = v0))
% 7.86/2.48 | (101) ~ (name_k = name_c)
% 7.86/2.48 | (102) ~ (name_c = constr_CONST_2)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (46) with all_0_2_2, name_objective and discharging atoms tuple_T_out_4(name_objective) = all_0_2_2, yields:
% 7.86/2.48 | (103) ? [v0] : ((v0 = 0 & pred_attacker(name_objective) = 0) | ( ~ (v0 = 0) & pred_attacker(all_0_2_2) = v0))
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (89) with all_0_0_0, name_objective and discharging atoms pred_attacker(name_objective) = all_0_0_0, yields:
% 7.86/2.48 | (104) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_in_1(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (35) with all_0_0_0, name_objective and discharging atoms pred_attacker(name_objective) = all_0_0_0, yields:
% 7.86/2.48 | (105) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_in_3(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (80) with all_0_0_0, name_objective and discharging atoms pred_attacker(name_objective) = all_0_0_0, yields:
% 7.86/2.48 | (106) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_out_2(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (28) with all_0_0_0, name_objective and discharging atoms pred_attacker(name_objective) = all_0_0_0, yields:
% 7.86/2.48 | (107) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_out_4(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (44) with constr_CONST_1 and discharging atoms pred_attacker(constr_CONST_1) = 0, yields:
% 7.86/2.48 | (108) ? [v0] : (tuple_T_in_1(constr_CONST_1) = v0 & pred_attacker(v0) = 0)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (38) with constr_CONST_1 and discharging atoms pred_attacker(constr_CONST_1) = 0, yields:
% 7.86/2.48 | (109) ? [v0] : (tuple_T_in_3(constr_CONST_1) = v0 & pred_attacker(v0) = 0)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (109) with all_30_0_27 yields:
% 7.86/2.48 | (110) tuple_T_in_3(constr_CONST_1) = all_30_0_27 & pred_attacker(all_30_0_27) = 0
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (110) yields:
% 7.86/2.48 | (111) tuple_T_in_3(constr_CONST_1) = all_30_0_27
% 7.86/2.48 | (112) pred_attacker(all_30_0_27) = 0
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (108) with all_32_0_28 yields:
% 7.86/2.48 | (113) tuple_T_in_1(constr_CONST_1) = all_32_0_28 & pred_attacker(all_32_0_28) = 0
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (113) yields:
% 7.86/2.48 | (114) tuple_T_in_1(constr_CONST_1) = all_32_0_28
% 7.86/2.48 | (115) pred_attacker(all_32_0_28) = 0
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (103) with all_100_0_62 yields:
% 7.86/2.48 | (116) (all_100_0_62 = 0 & pred_attacker(name_objective) = 0) | ( ~ (all_100_0_62 = 0) & pred_attacker(all_0_2_2) = all_100_0_62)
% 7.86/2.48 |
% 7.86/2.48 +-Applying beta-rule and splitting (116), into two cases.
% 7.86/2.48 |-Branch one:
% 7.86/2.48 | (117) all_100_0_62 = 0 & pred_attacker(name_objective) = 0
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (117) yields:
% 7.86/2.48 | (118) all_100_0_62 = 0
% 7.86/2.48 | (119) pred_attacker(name_objective) = 0
% 7.86/2.48 |
% 7.86/2.49 +-Applying beta-rule and splitting (107), into two cases.
% 7.86/2.49 |-Branch one:
% 7.86/2.49 | (120) all_0_0_0 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (120) can reduce 45 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 |-Branch two:
% 7.86/2.49 | (45) ~ (all_0_0_0 = 0)
% 7.86/2.49 | (123) ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_out_4(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.49 |
% 7.86/2.49 +-Applying beta-rule and splitting (104), into two cases.
% 7.86/2.49 |-Branch one:
% 7.86/2.49 | (120) all_0_0_0 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (120) can reduce 45 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 |-Branch two:
% 7.86/2.49 | (45) ~ (all_0_0_0 = 0)
% 7.86/2.49 | (127) ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_in_1(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.49 |
% 7.86/2.49 +-Applying beta-rule and splitting (106), into two cases.
% 7.86/2.49 |-Branch one:
% 7.86/2.49 | (120) all_0_0_0 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (120) can reduce 45 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 |-Branch two:
% 7.86/2.49 | (45) ~ (all_0_0_0 = 0)
% 7.86/2.49 | (131) ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_out_2(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.49 |
% 7.86/2.49 +-Applying beta-rule and splitting (105), into two cases.
% 7.86/2.49 |-Branch one:
% 7.86/2.49 | (120) all_0_0_0 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (120) can reduce 45 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 |-Branch two:
% 7.86/2.49 | (45) ~ (all_0_0_0 = 0)
% 7.86/2.49 | (135) ? [v0] : ? [v1] : ( ~ (v1 = 0) & tuple_T_in_3(name_objective) = v0 & pred_attacker(v0) = v1)
% 7.86/2.49 |
% 7.86/2.49 | Instantiating formula (69) with name_objective, 0, all_0_0_0 and discharging atoms pred_attacker(name_objective) = all_0_0_0, pred_attacker(name_objective) = 0, yields:
% 7.86/2.49 | (120) all_0_0_0 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (120) can reduce 45 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 |-Branch two:
% 7.86/2.49 | (138) ~ (all_100_0_62 = 0) & pred_attacker(all_0_2_2) = all_100_0_62
% 7.86/2.49 |
% 7.86/2.49 | Applying alpha-rule on (138) yields:
% 7.86/2.49 | (139) ~ (all_100_0_62 = 0)
% 7.86/2.49 | (140) pred_attacker(all_0_2_2) = all_100_0_62
% 7.86/2.49 |
% 7.86/2.49 | Instantiating formula (75) with all_32_0_28, all_30_0_27, constr_CONST_1, constr_CONST_1 and discharging atoms tuple_T_in_1(constr_CONST_1) = all_32_0_28, tuple_T_in_3(constr_CONST_1) = all_30_0_27, pred_attacker(all_32_0_28) = 0, pred_attacker(all_30_0_27) = 0, yields:
% 7.86/2.49 | (141) all_0_1_1 = 0
% 7.86/2.49 |
% 7.86/2.49 | Instantiating formula (69) with all_0_2_2, all_100_0_62, all_0_1_1 and discharging atoms pred_attacker(all_0_2_2) = all_100_0_62, pred_attacker(all_0_2_2) = all_0_1_1, yields:
% 7.86/2.49 | (142) all_100_0_62 = all_0_1_1
% 7.86/2.49 |
% 7.86/2.49 | Combining equations (141,142) yields a new equation:
% 7.86/2.49 | (118) all_100_0_62 = 0
% 7.86/2.49 |
% 7.86/2.49 | Equations (118) can reduce 139 to:
% 7.86/2.49 | (121) $false
% 7.86/2.49 |
% 7.86/2.49 |-The branch is then unsatisfiable
% 7.86/2.49 % SZS output end Proof for theBenchmark
% 7.86/2.49
% 7.86/2.49 1866ms
%------------------------------------------------------------------------------