TSTP Solution File: NUM844+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 : Mon Jul 18 08:49:05 EDT 2022
% Result : Theorem 3.05s 1.44s
% Output : Proof 4.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n021.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 : Tue Jul 5 04:45:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.49/0.58 ____ _
% 0.49/0.58 ___ / __ \_____(_)___ ________ __________
% 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.58
% 0.49/0.58 A Theorem Prover for First-Order Logic
% 0.49/0.58 (ePrincess v.1.0)
% 0.49/0.58
% 0.49/0.58 (c) Philipp Rümmer, 2009-2015
% 0.49/0.58 (c) Peter Backeman, 2014-2015
% 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.58 Bug reports to peter@backeman.se
% 0.49/0.58
% 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.58
% 0.49/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.94 Prover 0: Preprocessing ...
% 2.39/1.24 Prover 0: Constructing countermodel ...
% 3.05/1.44 Prover 0: proved (806ms)
% 3.05/1.44
% 3.05/1.44 No countermodel exists, formula is valid
% 3.05/1.44 % SZS status Theorem for theBenchmark
% 3.05/1.44
% 3.05/1.44 Generating proof ... found it (size 8)
% 4.76/1.86
% 4.76/1.86 % SZS output start Proof for theBenchmark
% 4.76/1.86 Assumed formulas after preprocessing and simplification:
% 4.76/1.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v3) & vplus(v6, v1) = v2 & vplus(v2, vd413) = v7 & vplus(v1, v2) = v3 & vplus(v0, v7) = v8 & vplus(v0, v4) = v3 & vplus(v0, vd413) = v1 & vplus(vd413, v2) = v4 & vsucc(v6) = v2 & vsucc(vd413) = v5 & vsucc(vd411) = v2 & vmul(v2, v5) = v3 & vmul(v2, v1) = v2 & vmul(v2, vd413) = v1 & vmul(vd411, v1) = v6 & vmul(vd411, vd413) = v0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vplus(v12, v11) = v13) | ~ (vplus(v9, v10) = v12) | ? [v14] : (vplus(v10, v11) = v14 & vplus(v9, v14) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (vplus(v10, v11) = v12) | ~ (vplus(v9, v12) = v13) | ? [v14] : (vplus(v14, v11) = v13 & vplus(v9, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (vplus(v12, v11) = v10) | ~ (vplus(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (vmul(v12, v11) = v10) | ~ (vmul(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vplus(v11, v10) = v12) | ~ (vsucc(v9) = v11) | ? [v13] : (vplus(v9, v10) = v13 & vsucc(v13) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vplus(v11, v9) = v12) | ~ (vmul(v9, v10) = v11) | ? [v13] : (vsucc(v10) = v13 & vmul(v9, v13) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vplus(v9, v11) = v12) | ~ (vsucc(v10) = v11) | ? [v13] : (vplus(v9, v10) = v13 & vsucc(v13) = v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (vsucc(v10) = v11) | ~ (vmul(v9, v11) = v12) | ? [v13] : (vplus(v13, v9) = v12 & vmul(v9, v10) = v13)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (vskolem2(v11) = v10) | ~ (vskolem2(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (vsucc(v11) = v10) | ~ (vsucc(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (vsucc(v10) = v11) | ~ (vsucc(v9) = v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v10, v9) = v11) | vplus(v9, v10) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v10, v1) = v11) | ~ greater(v9, v10) | geq(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v10, v1) = v11) | ~ less(v9, v11) | leq(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v9, v10) = v11) | vplus(v10, v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v9, v10) = v11) | ? [v12] : ? [v13] : (vplus(v12, v10) = v13 & vsucc(v11) = v13 & vsucc(v9) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (vplus(v9, v10) = v11) | ? [v12] : ? [v13] : (vplus(v9, v12) = v13 & vsucc(v11) = v13 & vsucc(v10) = v12)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (vmul(v9, v1) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (vmul(v1, v9) = v10)) & ! [v9] : ! [v10] : (v9 = v1 | ~ (vskolem2(v9) = v10) | vsucc(v10) = v9) & ! [v9] : ! [v10] : ( ~ (vplus(v9, v1) = v10) | vsucc(v9) = v10) & ! [v9] : ! [v10] : ( ~ (vplus(v1, v9) = v10) | vsucc(v9) = v10) & ! [v9] : ! [v10] : ( ~ (vsucc(v9) = v10) | vplus(v9, v1) = v10) & ! [v9] : ! [v10] : ( ~ (vsucc(v9) = v10) | vplus(v1, v9) = v10) & ! [v9] : ~ (vsucc(v9) = v9))
% 4.86/1.90 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 4.86/1.90 | (1) ~ (all_0_0_0 = all_0_5_5) & vplus(all_0_2_2, v1) = all_0_6_6 & vplus(all_0_6_6, vd413) = all_0_1_1 & vplus(all_0_7_7, all_0_6_6) = all_0_5_5 & vplus(all_0_8_8, all_0_1_1) = all_0_0_0 & vplus(all_0_8_8, all_0_4_4) = all_0_5_5 & vplus(all_0_8_8, vd413) = all_0_7_7 & vplus(vd413, all_0_6_6) = all_0_4_4 & vsucc(all_0_2_2) = all_0_6_6 & vsucc(vd413) = all_0_3_3 & vsucc(vd411) = all_0_6_6 & vmul(all_0_6_6, all_0_3_3) = all_0_5_5 & vmul(all_0_6_6, v1) = all_0_6_6 & vmul(all_0_6_6, vd413) = all_0_7_7 & vmul(vd411, v1) = all_0_2_2 & vmul(vd411, vd413) = all_0_8_8 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v3) = v4) | ? [v5] : (vplus(v5, v2) = v4 & vplus(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v1) = v3) | ~ (vsucc(v0) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v0) = v3) | ~ (vmul(v0, v1) = v2) | ? [v4] : (vsucc(v1) = v4 & vmul(v0, v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v0, v2) = v3) | ~ (vsucc(v1) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v0) = v2) | vplus(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ greater(v0, v1) | geq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ less(v0, v2) | leq(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v3, v1) = v4 & vsucc(v2) = v4 & vsucc(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v0, v3) = v4 & vsucc(v2) = v4 & vsucc(v1) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1)) & ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0) & ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1) & ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v0, v1) = v1) & ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v1, v0) = v1) & ! [v0] : ~ (vsucc(v0) = v0)
% 4.86/1.90 |
% 4.86/1.91 | Applying alpha-rule on (1) yields:
% 4.86/1.91 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 4.86/1.91 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v0) = v3) | ~ (vmul(v0, v1) = v2) | ? [v4] : (vsucc(v1) = v4 & vmul(v0, v4) = v3))
% 4.86/1.91 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ greater(v0, v1) | geq(v0, v2))
% 4.86/1.91 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v0, v3) = v4 & vsucc(v2) = v4 & vsucc(v1) = v3))
% 4.86/1.91 | (6) vplus(all_0_2_2, v1) = all_0_6_6
% 4.86/1.91 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 4.86/1.91 | (8) ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v0, v1) = v1)
% 4.86/1.91 | (9) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 4.86/1.91 | (10) vsucc(vd411) = all_0_6_6
% 4.86/1.91 | (11) vmul(all_0_6_6, vd413) = all_0_7_7
% 4.86/1.91 | (12) vmul(vd411, vd413) = all_0_8_8
% 4.86/1.91 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0))
% 4.86/1.91 | (14) ! [v0] : ~ (vsucc(v0) = v0)
% 4.86/1.91 | (15) ~ (all_0_0_0 = all_0_5_5)
% 4.86/1.91 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1))
% 4.86/1.91 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 4.86/1.91 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v0) = v2) | vplus(v0, v1) = v2)
% 4.86/1.91 | (19) vplus(all_0_8_8, all_0_1_1) = all_0_0_0
% 4.86/1.91 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4))
% 4.86/1.91 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 4.86/1.91 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v1) = v2) | ~ (vsucc(v0) = v2))
% 4.86/1.91 | (23) vplus(vd413, all_0_6_6) = all_0_4_4
% 4.86/1.91 | (24) vmul(vd411, v1) = all_0_2_2
% 4.86/1.91 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 4.86/1.91 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v3, v1) = v4 & vsucc(v2) = v4 & vsucc(v0) = v3))
% 4.86/1.91 | (27) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 4.86/1.91 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ less(v0, v2) | leq(v0, v1))
% 4.86/1.91 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v0, v2) = v3) | ~ (vsucc(v1) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3))
% 4.86/1.91 | (30) vplus(all_0_8_8, vd413) = all_0_7_7
% 4.86/1.91 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1))
% 4.86/1.91 | (32) vsucc(all_0_2_2) = all_0_6_6
% 4.86/1.91 | (33) vmul(all_0_6_6, all_0_3_3) = all_0_5_5
% 4.86/1.91 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v1) = v3) | ~ (vsucc(v0) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3))
% 4.86/1.91 | (35) vplus(all_0_7_7, all_0_6_6) = all_0_5_5
% 4.86/1.91 | (36) ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v1, v0) = v1)
% 4.86/1.91 | (37) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 4.86/1.91 | (38) vsucc(vd413) = all_0_3_3
% 4.86/1.91 | (39) vplus(all_0_6_6, vd413) = all_0_1_1
% 4.86/1.91 | (40) vmul(all_0_6_6, v1) = all_0_6_6
% 4.86/1.91 | (41) vplus(all_0_8_8, all_0_4_4) = all_0_5_5
% 4.86/1.91 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v3) = v4) | ? [v5] : (vplus(v5, v2) = v4 & vplus(v0, v1) = v5))
% 4.86/1.92 |
% 4.86/1.92 | Instantiating formula (18) with all_0_1_1, all_0_6_6, vd413 and discharging atoms vplus(all_0_6_6, vd413) = all_0_1_1, yields:
% 4.86/1.92 | (43) vplus(vd413, all_0_6_6) = all_0_1_1
% 4.86/1.92 |
% 4.86/1.92 | Instantiating formula (21) with vd413, all_0_6_6, all_0_1_1, all_0_4_4 and discharging atoms vplus(vd413, all_0_6_6) = all_0_1_1, vplus(vd413, all_0_6_6) = all_0_4_4, yields:
% 4.86/1.92 | (44) all_0_1_1 = all_0_4_4
% 4.86/1.92 |
% 4.86/1.92 | From (44) and (19) follows:
% 4.86/1.92 | (45) vplus(all_0_8_8, all_0_4_4) = all_0_0_0
% 4.86/1.92 |
% 4.86/1.92 | Instantiating formula (21) with all_0_8_8, all_0_4_4, all_0_0_0, all_0_5_5 and discharging atoms vplus(all_0_8_8, all_0_4_4) = all_0_0_0, vplus(all_0_8_8, all_0_4_4) = all_0_5_5, yields:
% 4.86/1.92 | (46) all_0_0_0 = all_0_5_5
% 4.86/1.92 |
% 4.86/1.92 | Equations (46) can reduce 15 to:
% 4.86/1.92 | (47) $false
% 4.86/1.92 |
% 4.86/1.92 |-The branch is then unsatisfiable
% 4.86/1.92 % SZS output end Proof for theBenchmark
% 4.86/1.92
% 4.86/1.92 1326ms
%------------------------------------------------------------------------------