TSTP Solution File: NUM847+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 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 : Mon Jul 18 08:49:07 EDT 2022
% Result : Theorem 2.71s 1.35s
% Output : Proof 4.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM847+2 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n007.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 : Fri Jul 8 01:07:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.59 (ePrincess v.1.0)
% 0.51/0.59
% 0.51/0.59 (c) Philipp Rümmer, 2009-2015
% 0.51/0.59 (c) Peter Backeman, 2014-2015
% 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.59 Bug reports to peter@backeman.se
% 0.51/0.59
% 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.59
% 0.51/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.56/0.94 Prover 0: Preprocessing ...
% 2.17/1.19 Prover 0: Constructing countermodel ...
% 2.71/1.35 Prover 0: proved (705ms)
% 2.71/1.35
% 2.71/1.35 No countermodel exists, formula is valid
% 2.71/1.35 % SZS status Theorem for theBenchmark
% 2.71/1.35
% 2.71/1.35 Generating proof ... found it (size 10)
% 4.60/1.75
% 4.60/1.75 % SZS output start Proof for theBenchmark
% 4.60/1.75 Assumed formulas after preprocessing and simplification:
% 4.60/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v13 = v2) & vplus(v4, vd436) = v12 & vplus(v3, v12) = v13 & vplus(v3, v9) = v8 & vplus(v3, v4) = v1 & vplus(v3, vd436) = v8 & vplus(v1, vd436) = v2 & vplus(vd437, v6) = v7 & vplus(vd437, v1) = v11 & vplus(vd437, vd439) = v0 & vsucc(v0) = v5 & vsucc(vd439) = v6 & vsucc(vd437) = v10 & vmul(vd436, v11) = v8 & vmul(vd436, v10) = v8 & vmul(vd436, v7) = v2 & vmul(vd436, v5) = v2 & vmul(vd436, v0) = v1 & vmul(vd436, v1) = v9 & vmul(vd436, vd439) = v4 & vmul(vd436, vd437) = v3 & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (vplus(v17, v16) = v18) | ~ (vplus(v14, v15) = v17) | ? [v19] : (vplus(v15, v16) = v19 & vplus(v14, v19) = v18)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (vplus(v15, v16) = v17) | ~ (vplus(v14, v17) = v18) | ? [v19] : (vplus(v19, v16) = v18 & vplus(v14, v15) = v19)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (vplus(v17, v16) = v15) | ~ (vplus(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (vmul(v17, v16) = v15) | ~ (vmul(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vplus(v16, v15) = v17) | ~ (vsucc(v14) = v16) | ? [v18] : (vplus(v14, v15) = v18 & vsucc(v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vplus(v16, v14) = v17) | ~ (vmul(v14, v15) = v16) | ? [v18] : (vsucc(v15) = v18 & vmul(v14, v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vplus(v14, v16) = v17) | ~ (vsucc(v15) = v16) | ? [v18] : (vplus(v14, v15) = v18 & vsucc(v18) = v17)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (vsucc(v15) = v16) | ~ (vmul(v14, v16) = v17) | ? [v18] : (vplus(v18, v14) = v17 & vmul(v14, v15) = v18)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (vskolem2(v16) = v15) | ~ (vskolem2(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (vsucc(v16) = v15) | ~ (vsucc(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v15, v14) = v16) | vplus(v14, v15) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v15, v1) = v16) | ~ greater(v14, v15) | geq(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v15, v1) = v16) | ~ less(v14, v16) | leq(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v14, v15) = v16) | vplus(v15, v14) = v16) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v14, v15) = v16) | ? [v17] : ? [v18] : (vplus(v17, v15) = v18 & vsucc(v16) = v18 & vsucc(v14) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (vplus(v14, v15) = v16) | ? [v17] : ? [v18] : (vplus(v14, v17) = v18 & vsucc(v16) = v18 & vsucc(v15) = v17)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (vmul(v14, v1) = v15)) & ! [v14] : ! [v15] : (v15 = v14 | ~ (vmul(v1, v14) = v15)) & ! [v14] : ! [v15] : (v14 = v1 | ~ (vskolem2(v14) = v15) | vsucc(v15) = v14) & ! [v14] : ! [v15] : ( ~ (vplus(v14, v1) = v15) | vsucc(v14) = v15) & ! [v14] : ! [v15] : ( ~ (vplus(v1, v14) = v15) | vsucc(v14) = v15) & ! [v14] : ! [v15] : ( ~ (vsucc(v14) = v15) | vplus(v14, v1) = v15) & ! [v14] : ! [v15] : ( ~ (vsucc(v14) = v15) | vplus(v1, v14) = v15) & ! [v14] : ~ (vsucc(v14) = v14))
% 4.67/1.80 | 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, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 yields:
% 4.67/1.80 | (1) ~ (all_0_0_0 = all_0_11_11) & vplus(all_0_9_9, vd436) = all_0_1_1 & vplus(all_0_10_10, all_0_1_1) = all_0_0_0 & vplus(all_0_10_10, all_0_4_4) = all_0_5_5 & vplus(all_0_10_10, all_0_9_9) = all_0_12_12 & vplus(all_0_10_10, vd436) = all_0_5_5 & vplus(all_0_12_12, vd436) = all_0_11_11 & vplus(vd437, all_0_7_7) = all_0_6_6 & vplus(vd437, v1) = all_0_2_2 & vplus(vd437, vd439) = all_0_13_13 & vsucc(all_0_13_13) = all_0_8_8 & vsucc(vd439) = all_0_7_7 & vsucc(vd437) = all_0_3_3 & vmul(vd436, all_0_2_2) = all_0_5_5 & vmul(vd436, all_0_3_3) = all_0_5_5 & vmul(vd436, all_0_6_6) = all_0_11_11 & vmul(vd436, all_0_8_8) = all_0_11_11 & vmul(vd436, all_0_13_13) = all_0_12_12 & vmul(vd436, v1) = all_0_4_4 & vmul(vd436, vd439) = all_0_9_9 & vmul(vd436, vd437) = all_0_10_10 & ! [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] : ( ~ (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)
% 4.79/1.82 |
% 4.79/1.82 | Applying alpha-rule on (1) yields:
% 4.79/1.82 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v0, v3) = v4 & vsucc(v2) = v4 & vsucc(v1) = v3))
% 4.79/1.82 | (3) vplus(vd437, all_0_7_7) = all_0_6_6
% 4.79/1.82 | (4) ~ (all_0_0_0 = all_0_11_11)
% 4.79/1.82 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v1, v2) = v3) | ~ (vplus(v0, v3) = v4) | ? [v5] : (vplus(v5, v2) = v4 & vplus(v0, v1) = v5))
% 4.79/1.82 | (6) vsucc(all_0_13_13) = all_0_8_8
% 4.79/1.82 | (7) vsucc(vd437) = all_0_3_3
% 4.79/1.82 | (8) vmul(vd436, all_0_8_8) = all_0_11_11
% 4.79/1.82 | (9) vmul(vd436, all_0_13_13) = all_0_12_12
% 4.79/1.82 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | vplus(v1, v0) = v2)
% 4.79/1.82 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v0) = v2) | vplus(v0, v1) = v2)
% 4.79/1.82 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 4.79/1.82 | (13) ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v0, v1) = v1)
% 4.79/1.82 | (14) ! [v0] : ! [v1] : ( ~ (vplus(v0, v1) = v1) | vsucc(v0) = v1)
% 4.79/1.82 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vsucc(v1) = v2) | ~ (vmul(v0, v2) = v3) | ? [v4] : (vplus(v4, v0) = v3 & vmul(v0, v1) = v4))
% 4.79/1.82 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ less(v0, v2) | leq(v0, v1))
% 4.79/1.82 | (17) vplus(vd437, v1) = all_0_2_2
% 4.79/1.83 | (18) vmul(vd436, vd439) = all_0_9_9
% 4.79/1.83 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v1, v0) = v1))
% 4.79/1.83 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v0, v2) = v3) | ~ (vsucc(v1) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3))
% 4.79/1.83 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ (vmul(v0, v1) = v1))
% 4.79/1.83 | (22) vplus(vd437, vd439) = all_0_13_13
% 4.79/1.83 | (23) ! [v0] : ~ (vsucc(v0) = v0)
% 4.79/1.83 | (24) ! [v0] : ! [v1] : ( ~ (vsucc(v0) = v1) | vplus(v1, v0) = v1)
% 4.79/1.83 | (25) ! [v0] : ! [v1] : ( ~ (vplus(v1, v0) = v1) | vsucc(v0) = v1)
% 4.79/1.83 | (26) vmul(vd436, vd437) = all_0_10_10
% 4.79/1.83 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v1, v1) = v2) | ~ greater(v0, v1) | geq(v0, v2))
% 4.79/1.83 | (28) ! [v0] : ! [v1] : (v0 = v1 | ~ (vskolem2(v0) = v1) | vsucc(v1) = v0)
% 4.79/1.83 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~ (vskolem2(v2) = v0))
% 4.79/1.83 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v0) = v3) | ~ (vmul(v0, v1) = v2) | ? [v4] : (vsucc(v1) = v4 & vmul(v0, v4) = v3))
% 4.79/1.83 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 4.79/1.83 | (32) vplus(all_0_9_9, vd436) = all_0_1_1
% 4.79/1.83 | (33) vplus(all_0_10_10, all_0_4_4) = all_0_5_5
% 4.79/1.83 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 4.79/1.83 | (35) vplus(all_0_10_10, all_0_9_9) = all_0_12_12
% 4.79/1.83 | (36) vmul(vd436, all_0_6_6) = all_0_11_11
% 4.79/1.83 | (37) vplus(all_0_10_10, vd436) = all_0_5_5
% 4.79/1.83 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (vplus(v2, v1) = v3) | ~ (vsucc(v0) = v2) | ? [v4] : (vplus(v0, v1) = v4 & vsucc(v4) = v3))
% 4.79/1.83 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (vplus(v3, v2) = v4) | ~ (vplus(v0, v1) = v3) | ? [v5] : (vplus(v1, v2) = v5 & vplus(v0, v5) = v4))
% 4.79/1.83 | (40) vmul(vd436, all_0_3_3) = all_0_5_5
% 4.79/1.83 | (41) vmul(vd436, v1) = all_0_4_4
% 4.79/1.83 | (42) vmul(vd436, all_0_2_2) = all_0_5_5
% 4.79/1.83 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (vplus(v0, v1) = v2) | ? [v3] : ? [v4] : (vplus(v3, v1) = v4 & vsucc(v2) = v4 & vsucc(v0) = v3))
% 4.79/1.83 | (44) vsucc(vd439) = all_0_7_7
% 4.79/1.83 | (45) vplus(all_0_12_12, vd436) = all_0_11_11
% 4.79/1.83 | (46) vplus(all_0_10_10, all_0_1_1) = all_0_0_0
% 4.79/1.83 |
% 4.79/1.83 | Instantiating formula (5) with all_0_0_0, all_0_1_1, vd436, all_0_9_9, all_0_10_10 and discharging atoms vplus(all_0_9_9, vd436) = all_0_1_1, vplus(all_0_10_10, all_0_1_1) = all_0_0_0, yields:
% 4.79/1.83 | (47) ? [v0] : (vplus(v0, vd436) = all_0_0_0 & vplus(all_0_10_10, all_0_9_9) = v0)
% 4.79/1.84 |
% 4.79/1.84 | Instantiating (47) with all_29_0_29 yields:
% 4.79/1.84 | (48) vplus(all_29_0_29, vd436) = all_0_0_0 & vplus(all_0_10_10, all_0_9_9) = all_29_0_29
% 4.79/1.84 |
% 4.79/1.84 | Applying alpha-rule on (48) yields:
% 4.79/1.84 | (49) vplus(all_29_0_29, vd436) = all_0_0_0
% 4.79/1.84 | (50) vplus(all_0_10_10, all_0_9_9) = all_29_0_29
% 4.79/1.84 |
% 4.79/1.84 | Instantiating formula (34) with all_0_10_10, all_0_9_9, all_29_0_29, all_0_12_12 and discharging atoms vplus(all_0_10_10, all_0_9_9) = all_29_0_29, vplus(all_0_10_10, all_0_9_9) = all_0_12_12, yields:
% 4.79/1.84 | (51) all_29_0_29 = all_0_12_12
% 4.79/1.84 |
% 4.79/1.84 | From (51) and (49) follows:
% 4.79/1.84 | (52) vplus(all_0_12_12, vd436) = all_0_0_0
% 4.79/1.84 |
% 4.79/1.84 | Instantiating formula (34) with all_0_12_12, vd436, all_0_0_0, all_0_11_11 and discharging atoms vplus(all_0_12_12, vd436) = all_0_0_0, vplus(all_0_12_12, vd436) = all_0_11_11, yields:
% 4.79/1.84 | (53) all_0_0_0 = all_0_11_11
% 4.79/1.84 |
% 4.79/1.84 | Equations (53) can reduce 4 to:
% 4.79/1.84 | (54) $false
% 4.79/1.84 |
% 4.79/1.84 |-The branch is then unsatisfiable
% 4.79/1.84 % SZS output end Proof for theBenchmark
% 4.79/1.84
% 4.79/1.84 1236ms
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