TSTP Solution File: NUM846+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM846+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 : n010.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 11:50:22 EDT 2023
% Result : Theorem 5.25s 1.54s
% Output : Proof 7.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM846+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n010.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 : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:16:20 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.12 Prover 1: Preprocessing ...
% 2.55/1.12 Prover 4: Preprocessing ...
% 2.98/1.16 Prover 0: Preprocessing ...
% 2.98/1.16 Prover 6: Preprocessing ...
% 2.98/1.16 Prover 5: Preprocessing ...
% 2.98/1.16 Prover 3: Preprocessing ...
% 2.98/1.16 Prover 2: Preprocessing ...
% 4.31/1.43 Prover 3: Warning: ignoring some quantifiers
% 4.31/1.45 Prover 1: Warning: ignoring some quantifiers
% 4.31/1.47 Prover 3: Constructing countermodel ...
% 4.31/1.48 Prover 1: Constructing countermodel ...
% 4.31/1.48 Prover 6: Proving ...
% 5.25/1.49 Prover 5: Proving ...
% 5.25/1.51 Prover 4: Constructing countermodel ...
% 5.25/1.52 Prover 0: Proving ...
% 5.25/1.54 Prover 3: proved (879ms)
% 5.25/1.54
% 5.25/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.25/1.54
% 5.25/1.54 Prover 0: stopped
% 5.25/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.25/1.54 Prover 6: stopped
% 5.25/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.25/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.82/1.56 Prover 5: stopped
% 5.82/1.56 Prover 2: Proving ...
% 5.82/1.56 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.82/1.56 Prover 2: stopped
% 5.82/1.56 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.82/1.58 Prover 10: Preprocessing ...
% 5.82/1.59 Prover 8: Preprocessing ...
% 5.82/1.59 Prover 11: Preprocessing ...
% 6.21/1.60 Prover 13: Preprocessing ...
% 6.21/1.61 Prover 7: Preprocessing ...
% 6.58/1.69 Prover 8: Warning: ignoring some quantifiers
% 6.58/1.71 Prover 8: Constructing countermodel ...
% 6.58/1.71 Prover 7: Warning: ignoring some quantifiers
% 6.58/1.72 Prover 10: Warning: ignoring some quantifiers
% 6.58/1.72 Prover 10: Constructing countermodel ...
% 6.58/1.73 Prover 11: Constructing countermodel ...
% 6.58/1.73 Prover 7: Constructing countermodel ...
% 6.58/1.73 Prover 13: Warning: ignoring some quantifiers
% 6.58/1.74 Prover 13: Constructing countermodel ...
% 7.34/1.78 Prover 1: Found proof (size 47)
% 7.34/1.78 Prover 1: proved (1131ms)
% 7.34/1.78 Prover 11: stopped
% 7.34/1.78 Prover 7: stopped
% 7.34/1.78 Prover 8: stopped
% 7.34/1.79 Prover 10: stopped
% 7.34/1.79 Prover 13: stopped
% 7.34/1.79 Prover 4: Found proof (size 47)
% 7.34/1.79 Prover 4: proved (1133ms)
% 7.34/1.79
% 7.34/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/1.79
% 7.66/1.80 % SZS output start Proof for theBenchmark
% 7.66/1.80 Assumptions after simplification:
% 7.66/1.80 ---------------------------------
% 7.66/1.80
% 7.66/1.80 (holds(284, 438, 1))
% 7.66/1.83 $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 7.66/1.83 (vsucc(vd437) = v0 & vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 &
% 7.66/1.83 vplus(v2, vd436) = v1 & $i(v2) & $i(v1) & $i(v0))
% 7.66/1.83
% 7.66/1.83 (holds(285, 440, 0))
% 7.66/1.83 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 7.66/1.83 ? [v3: $i] : (vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436,
% 7.66/1.83 vd437) = v2 & vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) &
% 7.66/1.83 $i(v2) & $i(v1) & $i(v0))
% 7.66/1.83
% 7.66/1.83 (holds(286, 441, 0))
% 7.66/1.84 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 7.66/1.84 ? [v3: $i] : ? [v4: $i] : (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436,
% 7.66/1.84 v4) = v2 & vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437,
% 7.66/1.84 vd439) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.66/1.84
% 7.66/1.84 (holds(286, 441, 1))
% 7.66/1.84 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 7.66/1.84 ? [v3: $i] : (vsucc(v0) = v1 & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 &
% 7.66/1.84 vplus(v3, vd436) = v2 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1)
% 7.66/1.84 & $i(v0))
% 7.66/1.84
% 7.66/1.84 (holds(286, 441, 2))
% 7.66/1.84 $i(vd439) & $i(vd437) & $i(vd436) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 7.66/1.84 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v2) &
% 7.66/1.84 vmul(vd436, v0) = v1 & vmul(vd436, vd439) = v4 & vmul(vd436, vd437) = v3 &
% 7.66/1.84 vplus(v5, vd436) = v6 & vplus(v3, v4) = v5 & vplus(v1, vd436) = v2 &
% 7.66/1.84 vplus(vd437, vd439) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 7.66/1.84 $i(v1) & $i(v0))
% 7.66/1.84
% 7.66/1.84 (function-axioms)
% 7.92/1.85 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.92/1.85 [v3: $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 7.92/1.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.92/1.85 : (v1 = v0 | ~ (greater(v3, v2) = v1) | ~ (greater(v3, v2) = v0)) & ! [v0:
% 7.92/1.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.92/1.85 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0:
% 7.92/1.85 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 7.92/1.85 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 7.92/1.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vmul(v3, v2) = v1) | ~
% 7.92/1.85 (vmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 7.92/1.85 : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: $i]
% 7.92/1.85 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (vskolem2(v2) = v1) | ~
% 7.92/1.85 (vskolem2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 7.92/1.85 ~ (vsucc(v2) = v1) | ~ (vsucc(v2) = v0))
% 7.92/1.85
% 7.92/1.85 Further assumptions not needed in the proof:
% 7.92/1.85 --------------------------------------------
% 7.92/1.85 ass(cond(12, 0), 0), ass(cond(20, 0), 0), ass(cond(228, 0), 0), ass(cond(234,
% 7.92/1.85 0), 0), ass(cond(241, 0), 0), ass(cond(253, 0), 0), ass(cond(270, 0), 0),
% 7.92/1.85 ass(cond(33, 0), 0), ass(cond(43, 0), 0), ass(cond(52, 0), 0), ass(cond(6, 0),
% 7.92/1.85 0), ass(cond(61, 0), 0), holds(284, 438, 0), holds(284, 438, 2),
% 7.92/1.85 qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0),
% 7.92/1.85 holds(definiens(29), 44, 0))), qu(cond(conseq(axiom(3)), 32),
% 7.92/1.85 and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))
% 7.92/1.85
% 7.92/1.85 Those formulas are unsatisfiable:
% 7.92/1.85 ---------------------------------
% 7.92/1.85
% 7.92/1.85 Begin of proof
% 7.92/1.85 |
% 7.92/1.85 | ALPHA: (holds(286, 441, 1)) implies:
% 7.92/1.85 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vsucc(v0) = v1
% 7.92/1.85 | & vmul(vd436, v1) = v2 & vmul(vd436, v0) = v3 & vplus(v3, vd436) = v2
% 7.92/1.85 | & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.92/1.85 |
% 7.92/1.85 | ALPHA: (holds(286, 441, 0)) implies:
% 7.92/1.85 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 7.92/1.85 | (vsucc(v3) = v4 & vsucc(vd439) = v0 & vmul(vd436, v4) = v2 &
% 7.92/1.85 | vmul(vd436, v1) = v2 & vplus(vd437, v0) = v1 & vplus(vd437, vd439) =
% 7.92/1.85 | v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 7.92/1.85 |
% 7.92/1.85 | ALPHA: (holds(285, 440, 0)) implies:
% 7.92/1.85 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (vmul(vd436,
% 7.92/1.85 | v0) = v1 & vmul(vd436, vd439) = v3 & vmul(vd436, vd437) = v2 &
% 7.92/1.85 | vplus(v2, v3) = v1 & vplus(vd437, vd439) = v0 & $i(v3) & $i(v2) &
% 7.92/1.85 | $i(v1) & $i(v0))
% 7.92/1.85 |
% 7.92/1.85 | ALPHA: (holds(284, 438, 1)) implies:
% 7.92/1.86 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (vsucc(vd437) = v0 &
% 7.92/1.86 | vmul(vd436, v0) = v1 & vmul(vd436, vd437) = v2 & vplus(v2, vd436) =
% 7.92/1.86 | v1 & $i(v2) & $i(v1) & $i(v0))
% 7.92/1.86 |
% 7.92/1.86 | ALPHA: (holds(286, 441, 2)) implies:
% 7.92/1.86 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 7.92/1.86 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v2) & vmul(vd436, v0) = v1 &
% 7.92/1.86 | vmul(vd436, vd439) = v4 & vmul(vd436, vd437) = v3 & vplus(v5, vd436)
% 7.92/1.86 | = v6 & vplus(v3, v4) = v5 & vplus(v1, vd436) = v2 & vplus(vd437,
% 7.92/1.86 | vd439) = v0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 7.92/1.86 | $i(v0))
% 7.92/1.86 |
% 7.92/1.86 | ALPHA: (function-axioms) implies:
% 7.92/1.86 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.92/1.86 | (vplus(v3, v2) = v1) | ~ (vplus(v3, v2) = v0))
% 7.92/1.86 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.92/1.86 | (vmul(v3, v2) = v1) | ~ (vmul(v3, v2) = v0))
% 7.92/1.86 |
% 7.92/1.86 | DELTA: instantiating (4) with fresh symbols all_24_0, all_24_1, all_24_2
% 7.92/1.86 | gives:
% 7.92/1.86 | (8) vsucc(vd437) = all_24_2 & vmul(vd436, all_24_2) = all_24_1 &
% 7.92/1.86 | vmul(vd436, vd437) = all_24_0 & vplus(all_24_0, vd436) = all_24_1 &
% 7.92/1.86 | $i(all_24_0) & $i(all_24_1) & $i(all_24_2)
% 7.92/1.86 |
% 7.92/1.86 | ALPHA: (8) implies:
% 7.92/1.86 | (9) vmul(vd436, vd437) = all_24_0
% 7.92/1.86 |
% 7.92/1.86 | DELTA: instantiating (1) with fresh symbols all_28_0, all_28_1, all_28_2,
% 7.92/1.86 | all_28_3 gives:
% 7.92/1.86 | (10) vsucc(all_28_3) = all_28_2 & vmul(vd436, all_28_2) = all_28_1 &
% 7.92/1.86 | vmul(vd436, all_28_3) = all_28_0 & vplus(all_28_0, vd436) = all_28_1 &
% 7.92/1.86 | vplus(vd437, vd439) = all_28_3 & $i(all_28_0) & $i(all_28_1) &
% 7.92/1.86 | $i(all_28_2) & $i(all_28_3)
% 7.92/1.86 |
% 7.92/1.86 | ALPHA: (10) implies:
% 7.92/1.86 | (11) vplus(vd437, vd439) = all_28_3
% 7.92/1.86 | (12) vplus(all_28_0, vd436) = all_28_1
% 7.92/1.86 | (13) vmul(vd436, all_28_3) = all_28_0
% 7.92/1.86 |
% 7.92/1.86 | DELTA: instantiating (3) with fresh symbols all_30_0, all_30_1, all_30_2,
% 7.92/1.86 | all_30_3 gives:
% 7.92/1.86 | (14) vmul(vd436, all_30_3) = all_30_2 & vmul(vd436, vd439) = all_30_0 &
% 7.92/1.86 | vmul(vd436, vd437) = all_30_1 & vplus(all_30_1, all_30_0) = all_30_2 &
% 7.92/1.86 | vplus(vd437, vd439) = all_30_3 & $i(all_30_0) & $i(all_30_1) &
% 7.92/1.86 | $i(all_30_2) & $i(all_30_3)
% 7.92/1.86 |
% 7.92/1.87 | ALPHA: (14) implies:
% 7.92/1.87 | (15) vplus(vd437, vd439) = all_30_3
% 7.92/1.87 | (16) vplus(all_30_1, all_30_0) = all_30_2
% 7.92/1.87 | (17) vmul(vd436, vd437) = all_30_1
% 7.92/1.87 | (18) vmul(vd436, vd439) = all_30_0
% 7.92/1.87 | (19) vmul(vd436, all_30_3) = all_30_2
% 7.92/1.87 |
% 7.92/1.87 | DELTA: instantiating (2) with fresh symbols all_32_0, all_32_1, all_32_2,
% 7.92/1.87 | all_32_3, all_32_4 gives:
% 7.92/1.87 | (20) vsucc(all_32_1) = all_32_0 & vsucc(vd439) = all_32_4 & vmul(vd436,
% 7.92/1.87 | all_32_0) = all_32_2 & vmul(vd436, all_32_3) = all_32_2 &
% 7.92/1.87 | vplus(vd437, all_32_4) = all_32_3 & vplus(vd437, vd439) = all_32_1 &
% 7.92/1.87 | $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) &
% 7.92/1.87 | $i(all_32_4)
% 7.92/1.87 |
% 7.92/1.87 | ALPHA: (20) implies:
% 7.92/1.87 | (21) vplus(vd437, vd439) = all_32_1
% 7.92/1.87 |
% 7.92/1.87 | DELTA: instantiating (5) with fresh symbols all_34_0, all_34_1, all_34_2,
% 7.92/1.87 | all_34_3, all_34_4, all_34_5, all_34_6 gives:
% 7.92/1.87 | (22) ~ (all_34_0 = all_34_4) & vmul(vd436, all_34_6) = all_34_5 &
% 7.92/1.87 | vmul(vd436, vd439) = all_34_2 & vmul(vd436, vd437) = all_34_3 &
% 7.92/1.87 | vplus(all_34_1, vd436) = all_34_0 & vplus(all_34_3, all_34_2) =
% 7.92/1.87 | all_34_1 & vplus(all_34_5, vd436) = all_34_4 & vplus(vd437, vd439) =
% 7.92/1.87 | all_34_6 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) &
% 7.92/1.87 | $i(all_34_4) & $i(all_34_5) & $i(all_34_6)
% 7.92/1.87 |
% 7.92/1.87 | ALPHA: (22) implies:
% 7.92/1.87 | (23) ~ (all_34_0 = all_34_4)
% 7.92/1.87 | (24) vplus(vd437, vd439) = all_34_6
% 7.92/1.87 | (25) vplus(all_34_5, vd436) = all_34_4
% 7.92/1.87 | (26) vplus(all_34_3, all_34_2) = all_34_1
% 7.92/1.87 | (27) vplus(all_34_1, vd436) = all_34_0
% 7.92/1.87 | (28) vmul(vd436, vd437) = all_34_3
% 7.92/1.87 | (29) vmul(vd436, vd439) = all_34_2
% 7.92/1.87 | (30) vmul(vd436, all_34_6) = all_34_5
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (6) with all_28_3, all_32_1, vd439, vd437,
% 7.92/1.87 | simplifying with (11), (21) gives:
% 7.92/1.87 | (31) all_32_1 = all_28_3
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (6) with all_32_1, all_34_6, vd439, vd437,
% 7.92/1.87 | simplifying with (21), (24) gives:
% 7.92/1.87 | (32) all_34_6 = all_32_1
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (6) with all_30_3, all_34_6, vd439, vd437,
% 7.92/1.87 | simplifying with (15), (24) gives:
% 7.92/1.87 | (33) all_34_6 = all_30_3
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (7) with all_30_1, all_34_3, vd437, vd436,
% 7.92/1.87 | simplifying with (17), (28) gives:
% 7.92/1.87 | (34) all_34_3 = all_30_1
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (7) with all_24_0, all_34_3, vd437, vd436,
% 7.92/1.87 | simplifying with (9), (28) gives:
% 7.92/1.87 | (35) all_34_3 = all_24_0
% 7.92/1.87 |
% 7.92/1.87 | GROUND_INST: instantiating (7) with all_30_0, all_34_2, vd439, vd436,
% 7.92/1.87 | simplifying with (18), (29) gives:
% 7.92/1.87 | (36) all_34_2 = all_30_0
% 7.92/1.87 |
% 7.92/1.87 | COMBINE_EQS: (34), (35) imply:
% 7.92/1.87 | (37) all_30_1 = all_24_0
% 7.92/1.87 |
% 7.92/1.87 | COMBINE_EQS: (32), (33) imply:
% 7.92/1.87 | (38) all_32_1 = all_30_3
% 7.92/1.87 |
% 7.92/1.87 | SIMP: (38) implies:
% 7.92/1.87 | (39) all_32_1 = all_30_3
% 7.92/1.87 |
% 7.92/1.87 | COMBINE_EQS: (31), (39) imply:
% 7.92/1.87 | (40) all_30_3 = all_28_3
% 7.92/1.87 |
% 7.92/1.87 | SIMP: (40) implies:
% 7.92/1.87 | (41) all_30_3 = all_28_3
% 7.92/1.87 |
% 7.92/1.87 | COMBINE_EQS: (33), (41) imply:
% 7.92/1.87 | (42) all_34_6 = all_28_3
% 7.92/1.87 |
% 7.92/1.87 | REDUCE: (30), (42) imply:
% 7.92/1.88 | (43) vmul(vd436, all_28_3) = all_34_5
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (19), (41) imply:
% 7.92/1.88 | (44) vmul(vd436, all_28_3) = all_30_2
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (26), (35), (36) imply:
% 7.92/1.88 | (45) vplus(all_24_0, all_30_0) = all_34_1
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (16), (37) imply:
% 7.92/1.88 | (46) vplus(all_24_0, all_30_0) = all_30_2
% 7.92/1.88 |
% 7.92/1.88 | GROUND_INST: instantiating (6) with all_30_2, all_34_1, all_30_0, all_24_0,
% 7.92/1.88 | simplifying with (45), (46) gives:
% 7.92/1.88 | (47) all_34_1 = all_30_2
% 7.92/1.88 |
% 7.92/1.88 | GROUND_INST: instantiating (7) with all_28_0, all_34_5, all_28_3, vd436,
% 7.92/1.88 | simplifying with (13), (43) gives:
% 7.92/1.88 | (48) all_34_5 = all_28_0
% 7.92/1.88 |
% 7.92/1.88 | GROUND_INST: instantiating (7) with all_30_2, all_34_5, all_28_3, vd436,
% 7.92/1.88 | simplifying with (43), (44) gives:
% 7.92/1.88 | (49) all_34_5 = all_30_2
% 7.92/1.88 |
% 7.92/1.88 | COMBINE_EQS: (48), (49) imply:
% 7.92/1.88 | (50) all_30_2 = all_28_0
% 7.92/1.88 |
% 7.92/1.88 | COMBINE_EQS: (47), (50) imply:
% 7.92/1.88 | (51) all_34_1 = all_28_0
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (27), (51) imply:
% 7.92/1.88 | (52) vplus(all_28_0, vd436) = all_34_0
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (25), (48) imply:
% 7.92/1.88 | (53) vplus(all_28_0, vd436) = all_34_4
% 7.92/1.88 |
% 7.92/1.88 | GROUND_INST: instantiating (6) with all_28_1, all_34_0, vd436, all_28_0,
% 7.92/1.88 | simplifying with (12), (52) gives:
% 7.92/1.88 | (54) all_34_0 = all_28_1
% 7.92/1.88 |
% 7.92/1.88 | GROUND_INST: instantiating (6) with all_34_4, all_34_0, vd436, all_28_0,
% 7.92/1.88 | simplifying with (52), (53) gives:
% 7.92/1.88 | (55) all_34_0 = all_34_4
% 7.92/1.88 |
% 7.92/1.88 | COMBINE_EQS: (54), (55) imply:
% 7.92/1.88 | (56) all_34_4 = all_28_1
% 7.92/1.88 |
% 7.92/1.88 | REDUCE: (23), (54), (56) imply:
% 7.92/1.88 | (57) $false
% 7.92/1.88 |
% 7.92/1.88 | CLOSE: (57) is inconsistent.
% 7.92/1.88 |
% 7.92/1.88 End of proof
% 7.92/1.88 % SZS output end Proof for theBenchmark
% 7.92/1.88
% 7.92/1.88 1247ms
%------------------------------------------------------------------------------