TSTP Solution File: NUM851+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM851+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 : 300s
% DateTime : Thu Aug 31 11:50:25 EDT 2023
% Result : Theorem 8.36s 2.01s
% Output : Proof 11.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM851+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n027.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Aug 25 09:46:03 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.17/0.63 ________ _____
% 0.17/0.63 ___ __ \_________(_)________________________________
% 0.17/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.63
% 0.17/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.63 (2023-06-19)
% 0.17/0.63
% 0.17/0.63 (c) Philipp Rümmer, 2009-2023
% 0.17/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.63 Amanda Stjerna.
% 0.17/0.63 Free software under BSD-3-Clause.
% 0.17/0.63
% 0.17/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.63
% 0.17/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.65 Running up to 7 provers in parallel.
% 0.17/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.17/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 2.65/1.14 Prover 1: Preprocessing ...
% 2.65/1.14 Prover 4: Preprocessing ...
% 2.85/1.19 Prover 3: Preprocessing ...
% 2.85/1.19 Prover 6: Preprocessing ...
% 2.85/1.19 Prover 2: Preprocessing ...
% 2.85/1.19 Prover 0: Preprocessing ...
% 2.85/1.19 Prover 5: Preprocessing ...
% 6.21/1.68 Prover 1: Warning: ignoring some quantifiers
% 6.89/1.73 Prover 4: Warning: ignoring some quantifiers
% 6.89/1.74 Prover 3: Warning: ignoring some quantifiers
% 6.89/1.77 Prover 4: Constructing countermodel ...
% 6.89/1.78 Prover 1: Constructing countermodel ...
% 6.89/1.78 Prover 0: Proving ...
% 6.89/1.78 Prover 6: Proving ...
% 6.89/1.79 Prover 3: Constructing countermodel ...
% 7.36/1.83 Prover 5: Proving ...
% 8.36/1.94 Prover 2: Proving ...
% 8.36/2.00 Prover 3: proved (1331ms)
% 8.36/2.00
% 8.36/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.36/2.01
% 8.36/2.02 Prover 5: stopped
% 8.36/2.02 Prover 0: stopped
% 8.36/2.02 Prover 2: stopped
% 8.36/2.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.36/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.36/2.02 Prover 6: stopped
% 8.36/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.36/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.00/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.00/2.08 Prover 11: Preprocessing ...
% 9.42/2.11 Prover 7: Preprocessing ...
% 9.42/2.11 Prover 10: Preprocessing ...
% 9.42/2.13 Prover 13: Preprocessing ...
% 9.42/2.13 Prover 8: Preprocessing ...
% 9.42/2.21 Prover 1: Found proof (size 33)
% 9.42/2.21 Prover 1: proved (1550ms)
% 9.42/2.21 Prover 4: stopped
% 9.42/2.22 Prover 13: stopped
% 9.42/2.26 Prover 10: Warning: ignoring some quantifiers
% 9.42/2.27 Prover 10: Constructing countermodel ...
% 9.42/2.28 Prover 10: stopped
% 9.42/2.28 Prover 7: Warning: ignoring some quantifiers
% 9.42/2.30 Prover 11: Warning: ignoring some quantifiers
% 9.42/2.30 Prover 7: Constructing countermodel ...
% 9.42/2.32 Prover 7: stopped
% 10.96/2.33 Prover 11: Constructing countermodel ...
% 10.96/2.33 Prover 8: Warning: ignoring some quantifiers
% 11.09/2.34 Prover 11: stopped
% 11.09/2.34 Prover 8: Constructing countermodel ...
% 11.09/2.36 Prover 8: stopped
% 11.09/2.36
% 11.09/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.09/2.36
% 11.09/2.37 % SZS output start Proof for theBenchmark
% 11.29/2.38 Assumptions after simplification:
% 11.29/2.38 ---------------------------------
% 11.29/2.38
% 11.29/2.38 (ass(cond(270, 0), 0))
% 11.29/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (vmul(v0, v1) = v2) | ~ $i(v1)
% 11.29/2.42 | ~ $i(v0) | (vmul(v1, v0) = v2 & $i(v2)))
% 11.29/2.42
% 11.29/2.42 (ass(cond(281, 0), 0))
% 11.29/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.29/2.43 $i] : ( ~ (vplus(v3, v4) = v5) | ~ (vmul(v0, v2) = v4) | ~ (vmul(v0, v1) =
% 11.29/2.43 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (vplus(v1, v2) =
% 11.29/2.43 v6 & vmul(v0, v6) = v5 & $i(v6) & $i(v5)))
% 11.29/2.43
% 11.29/2.43 (holds(conseq_conjunct1(conseq(302)), 474, 0))
% 11.29/2.43 vplus(vd471, vd473) = vd470 & $i(vd470) & $i(vd473) & $i(vd471)
% 11.29/2.43
% 11.29/2.43 (holds(conseq_conjunct2(conseq(302)), 475, 0))
% 11.29/2.43 $i(vd470) & $i(vd469) & $i(vd473) & $i(vd471) & ? [v0: $i] : ? [v1: $i] :
% 11.29/2.43 (vplus(vd471, vd473) = v1 & vmul(v1, vd469) = v0 & vmul(vd470, vd469) = v0 &
% 11.29/2.43 $i(v1) & $i(v0))
% 11.29/2.43
% 11.29/2.43 (holds(conseq_conjunct2(conseq(302)), 475, 1))
% 11.58/2.44 $i(vd469) & $i(vd473) & $i(vd471) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 11.58/2.44 ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v1) & vplus(v2, v3) = v4 & vplus(vd471,
% 11.58/2.44 vd473) = v0 & vmul(v0, vd469) = v1 & vmul(vd473, vd469) = v3 & vmul(vd471,
% 11.58/2.44 vd469) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.58/2.44
% 11.58/2.44 (function-axioms)
% 11.58/2.45 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.58/2.45 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 11.58/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.58/2.45 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 11.58/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.58/2.45 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 11.58/2.45 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.58/2.45 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 11.58/2.45 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2)
% 11.58/2.45 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 11.58/2.45 : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0)) &
% 11.58/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) |
% 11.58/2.45 ~ (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.58/2.45 | ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 11.58/2.45
% 11.58/2.45 Further assumptions not needed in the proof:
% 11.58/2.45 --------------------------------------------
% 11.58/2.45 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(241,
% 11.58/2.45 0), 0), ass(cond(253, 0), 0), ass(cond(261, 0), 0), ass(cond(290, 0), 0),
% 11.58/2.45 ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0),
% 11.58/2.45 0), ass(cond(61, 0), 0), ass(cond(73, 0), 0), ass(cond(81, 0), 0),
% 11.58/2.45 ass(cond(goal(88), 0), 0), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 2),
% 11.58/2.45 ass(cond(goal(88), 0), 3), def(cond(conseq(axiom(3)), 11), 1), holds(antec(302),
% 11.58/2.45 472, 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 11.58/2.45 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 11.58/2.45 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))
% 11.58/2.45
% 11.58/2.45 Those formulas are unsatisfiable:
% 11.58/2.45 ---------------------------------
% 11.58/2.45
% 11.58/2.45 Begin of proof
% 11.58/2.46 |
% 11.58/2.46 | ALPHA: (holds(conseq_conjunct2(conseq(302)), 475, 0)) implies:
% 11.68/2.46 | (1) ? [v0: $i] : ? [v1: $i] : (vplus(vd471, vd473) = v1 & vmul(v1, vd469)
% 11.68/2.46 | = v0 & vmul(vd470, vd469) = v0 & $i(v1) & $i(v0))
% 11.68/2.46 |
% 11.68/2.46 | ALPHA: (holds(conseq_conjunct1(conseq(302)), 474, 0)) implies:
% 11.68/2.46 | (2) vplus(vd471, vd473) = vd470
% 11.68/2.46 |
% 11.68/2.46 | ALPHA: (holds(conseq_conjunct2(conseq(302)), 475, 1)) implies:
% 11.68/2.46 | (3) $i(vd471)
% 11.68/2.46 | (4) $i(vd473)
% 11.68/2.46 | (5) $i(vd469)
% 11.68/2.47 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 11.68/2.47 | ~ (v4 = v1) & vplus(v2, v3) = v4 & vplus(vd471, vd473) = v0 &
% 11.68/2.47 | vmul(v0, vd469) = v1 & vmul(vd473, vd469) = v3 & vmul(vd471, vd469) =
% 11.68/2.47 | v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.68/2.47 |
% 11.68/2.47 | ALPHA: (function-axioms) implies:
% 11.68/2.47 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.68/2.47 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 11.68/2.47 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.68/2.47 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 11.68/2.47 |
% 11.68/2.47 | DELTA: instantiating (1) with fresh symbols all_28_0, all_28_1 gives:
% 11.68/2.47 | (9) vplus(vd471, vd473) = all_28_0 & vmul(all_28_0, vd469) = all_28_1 &
% 11.68/2.47 | vmul(vd470, vd469) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 11.68/2.47 |
% 11.68/2.47 | ALPHA: (9) implies:
% 11.68/2.47 | (10) $i(all_28_0)
% 11.68/2.47 | (11) vmul(all_28_0, vd469) = all_28_1
% 11.68/2.47 | (12) vplus(vd471, vd473) = all_28_0
% 11.68/2.47 |
% 11.68/2.47 | DELTA: instantiating (6) with fresh symbols all_33_0, all_33_1, all_33_2,
% 11.68/2.47 | all_33_3, all_33_4 gives:
% 11.68/2.48 | (13) ~ (all_33_0 = all_33_3) & vplus(all_33_2, all_33_1) = all_33_0 &
% 11.68/2.48 | vplus(vd471, vd473) = all_33_4 & vmul(all_33_4, vd469) = all_33_3 &
% 11.68/2.48 | vmul(vd473, vd469) = all_33_1 & vmul(vd471, vd469) = all_33_2 &
% 11.68/2.48 | $i(all_33_0) & $i(all_33_1) & $i(all_33_2) & $i(all_33_3) &
% 11.68/2.48 | $i(all_33_4)
% 11.68/2.48 |
% 11.68/2.48 | ALPHA: (13) implies:
% 11.68/2.48 | (14) ~ (all_33_0 = all_33_3)
% 11.68/2.48 | (15) vmul(vd471, vd469) = all_33_2
% 11.68/2.48 | (16) vmul(vd473, vd469) = all_33_1
% 11.68/2.48 | (17) vmul(all_33_4, vd469) = all_33_3
% 11.68/2.48 | (18) vplus(vd471, vd473) = all_33_4
% 11.68/2.48 | (19) vplus(all_33_2, all_33_1) = all_33_0
% 11.68/2.48 |
% 11.68/2.48 | GROUND_INST: instantiating (8) with all_28_0, all_33_4, vd473, vd471,
% 11.68/2.48 | simplifying with (12), (18) gives:
% 11.68/2.48 | (20) all_33_4 = all_28_0
% 11.68/2.48 |
% 11.68/2.48 | GROUND_INST: instantiating (8) with vd470, all_33_4, vd473, vd471, simplifying
% 11.68/2.48 | with (2), (18) gives:
% 11.68/2.48 | (21) all_33_4 = vd470
% 11.68/2.48 |
% 11.68/2.48 | COMBINE_EQS: (20), (21) imply:
% 11.68/2.48 | (22) all_28_0 = vd470
% 11.68/2.48 |
% 11.68/2.48 | SIMP: (22) implies:
% 11.68/2.48 | (23) all_28_0 = vd470
% 11.68/2.48 |
% 11.68/2.48 | REDUCE: (17), (21) imply:
% 11.68/2.48 | (24) vmul(vd470, vd469) = all_33_3
% 11.68/2.48 |
% 11.68/2.48 | REDUCE: (11), (23) imply:
% 11.68/2.48 | (25) vmul(vd470, vd469) = all_28_1
% 11.68/2.48 |
% 11.68/2.48 | REDUCE: (10), (23) imply:
% 11.68/2.48 | (26) $i(vd470)
% 11.68/2.48 |
% 11.68/2.49 | GROUND_INST: instantiating (7) with all_28_1, all_33_3, vd469, vd470,
% 11.68/2.49 | simplifying with (24), (25) gives:
% 11.68/2.49 | (27) all_33_3 = all_28_1
% 11.68/2.49 |
% 11.68/2.49 | REDUCE: (14), (27) imply:
% 11.68/2.49 | (28) ~ (all_33_0 = all_28_1)
% 11.68/2.49 |
% 11.68/2.49 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd471, vd469, all_33_2,
% 11.68/2.49 | simplifying with (3), (5), (15) gives:
% 11.68/2.49 | (29) vmul(vd469, vd471) = all_33_2 & $i(all_33_2)
% 11.68/2.49 |
% 11.68/2.49 | ALPHA: (29) implies:
% 11.68/2.49 | (30) vmul(vd469, vd471) = all_33_2
% 11.68/2.49 |
% 11.68/2.49 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd473, vd469, all_33_1,
% 11.68/2.49 | simplifying with (4), (5), (16) gives:
% 11.68/2.49 | (31) vmul(vd469, vd473) = all_33_1 & $i(all_33_1)
% 11.68/2.49 |
% 11.68/2.49 | ALPHA: (31) implies:
% 11.68/2.49 | (32) vmul(vd469, vd473) = all_33_1
% 11.68/2.49 |
% 11.68/2.49 | GROUND_INST: instantiating (ass(cond(270, 0), 0)) with vd470, vd469, all_28_1,
% 11.68/2.49 | simplifying with (5), (25), (26) gives:
% 11.68/2.49 | (33) vmul(vd469, vd470) = all_28_1 & $i(all_28_1)
% 11.68/2.49 |
% 11.68/2.49 | ALPHA: (33) implies:
% 11.68/2.49 | (34) vmul(vd469, vd470) = all_28_1
% 11.68/2.49 |
% 11.68/2.49 | GROUND_INST: instantiating (ass(cond(281, 0), 0)) with vd469, vd471, vd473,
% 11.68/2.49 | all_33_2, all_33_1, all_33_0, simplifying with (3), (4), (5),
% 11.68/2.49 | (19), (30), (32) gives:
% 11.68/2.49 | (35) ? [v0: $i] : (vplus(vd471, vd473) = v0 & vmul(vd469, v0) = all_33_0 &
% 11.68/2.50 | $i(v0) & $i(all_33_0))
% 11.68/2.50 |
% 11.68/2.50 | DELTA: instantiating (35) with fresh symbol all_57_0 gives:
% 11.68/2.50 | (36) vplus(vd471, vd473) = all_57_0 & vmul(vd469, all_57_0) = all_33_0 &
% 11.68/2.50 | $i(all_57_0) & $i(all_33_0)
% 11.68/2.50 |
% 11.68/2.50 | ALPHA: (36) implies:
% 11.68/2.50 | (37) vmul(vd469, all_57_0) = all_33_0
% 11.68/2.50 | (38) vplus(vd471, vd473) = all_57_0
% 11.68/2.50 |
% 11.68/2.50 | GROUND_INST: instantiating (8) with vd470, all_57_0, vd473, vd471, simplifying
% 11.68/2.50 | with (2), (38) gives:
% 11.68/2.50 | (39) all_57_0 = vd470
% 11.68/2.50 |
% 11.68/2.50 | REDUCE: (37), (39) imply:
% 11.68/2.50 | (40) vmul(vd469, vd470) = all_33_0
% 11.68/2.50 |
% 11.68/2.50 | GROUND_INST: instantiating (7) with all_28_1, all_33_0, vd470, vd469,
% 11.68/2.50 | simplifying with (34), (40) gives:
% 11.68/2.50 | (41) all_33_0 = all_28_1
% 11.68/2.50 |
% 11.68/2.50 | REDUCE: (28), (41) imply:
% 11.68/2.50 | (42) $false
% 11.68/2.50 |
% 11.68/2.50 | CLOSE: (42) is inconsistent.
% 11.68/2.50 |
% 11.68/2.50 End of proof
% 11.68/2.50 % SZS output end Proof for theBenchmark
% 11.68/2.50
% 11.68/2.50 1869ms
%------------------------------------------------------------------------------